A Course in Electrical Engineering Direct Current.pdf

TEXTS ELECTRICALENGINEERING A ENaiNEERING ELECTRICAL VOLUME DIRECT IN COURSE I CURRENTS ELECTRICAL ENGINEERING TEXTS A of series of which Professor electrical Clifford. E. Harry Harvard of is by a committee engineers Gordon Electrical University, Kay Mc- Engineering. Chairman ana Editor. Consulting Laws outlined textbooks well-known of " ELECTRICAL Lawrence MEASUREMENTS " PRINCIPLES OF RENT ALTERNATING-CUR- MACHINERY Lawrence " PRINCIPLES Langadorf OF ALTERNATING RENTS CUR- " PRINCIPLES OF DIRECT-CURRENT MACHINES Dawes " COURSE ELECTRICAL IN Vol. Vol. I. II. " " Direct ING ENGINEER- Currents Alternating Currents ELECTRICAL ENGINEERING TEXTS COURSE A ELECTRICAI IN ENGmEEROG VOLUME DIRECT I CURRENTS BY ASSISTANT PB0FB880B school; OF EMGIMESBINO, BLKCTBICAL iNSTrrxmB American mxmbeb, 370 YORK: LONDON : HARVABD BNQIKBlSBINa BuscTBicAii Imfbession COMPANY, BOOK McGRAW-HILL of Edition First Fifth THB XTC. BNOINEBBB, NEW S. B. L. DAWES, CHESTER SEVENTH 6 4 8 BOU VERIE 1920 AVENUE ST., E. C. 4 Inc- TV. HARVARD UNtvVRSlTY EHUlNEERlNQ 6cH00L "ilVl^li IIMMV C"LL""l Copyright, 1920, by McGraw-Hill TUB MAPXiK Book PRBSS the Company, Inc. TOKK Z*A Digitized by f CjOOgle ^ . this type analysis. except In students liberal use same time for more part a have of been this work which as of is short the time needs illustrative late assimi- consulting rule a industrial carried are sive. their after request. a made. sufficientlycomprehen- student usually to and a text one time foremen's much does out mathematical have not ready with of contact his available for class-room of the foregoing types carefully kept in mind figures and general detailed any by only ing tak- are of their give them ning plan- not field.who part involving not during the preparing a books text and students subject in not Engineering. magnetism more Electrical general field of Electrical the these scope McGraw-Hill demand a manner implies. libraries the taking Ordinarily. Electrical but reference instructors work. These and for carefully considered. to the at as obtainable Men to difiiculty in obtaining of information also engineering does course only in the evening. which in met are Electrical Engineering advanced Electrical the of in begin with and the at of the two discussion These practice.PREFACE For time some Engineering past the editors have Texts in covering text experienced simple a Engineering Accordingly. require access useful Engineering often men fragmentary of written were general character and specialize in the electrical courses on volumes two Engineering volumes two to and sive comprehen- a series. title the As been had volumes to direct a the less or alternating and etc. intended are already are of types many transmission two vance ad- gradually of the machinery. the books of conceptions of the problems and has as a been result. current elementary most and current-flow thorough should Electrical Such training. be straightforward brevity the of number in courses find discussions of their references.. students as books stepping a the to stone which Texts devices. Gambridqe. in the matter Also C. Because this work is not intended for advanced students in Electrical Engineering. tends only to developthe memorizing as such treatment of certain formulae which are soon forgotten.little is limited to simple calculus is used and the mathematics or no equations.attempt has been made to show the ultimate bearing upon generalengineering practice. f Mass.even In any course though it be intended for non-electrical engineers. in Electrical Engineering. CUfiford of The Harvard EngineeringSchool. The student takes interest in the theory when he sees that it can be appUed more to the solvingof practical problems. January 1920. . E.vi PREFACE frequentdiscussions of the methods of making measurements and laboratorytests are included. L.the author feels that the student gains littlefrom a hurried and superficial of treatment the subject.especially abstract portions. Harvard University.for his suggestionsand for the care and pains which he has taken many of editingthe manuscripts. The author is indebted to several of the manufacturing tographs companies who have cooperatedin the matter of supplyingphoto Procuts and material for the text. Accordingly the attempt has been made in this text to develop and explain each phenomenon from a few fundamental and well-understood statements ment laws rather than to give mere of facts. and particularly fessor H. D. in the treatment of the more Throughout the text. Such treatwill develop the student's reasoningpowers and give him involved trainingthat will be useful in the solution of the more engineeringproblems that may arise later in his career. 7 Intensity.CONTENTS Paqh Preface v CHAPTER Magnetism I Magnets and and 1.Electromagnetic Flux Density Compass Needle Magnetic Figures Magnetic Induction Law of the Magnetic Field 18. Lines 12. Magnets 2. 15. Magnetic 5 10. Relation 25. Laminated 20.. Pole 11.of Breaking 2 a Bar Magnet. Effect. Magnetic Field of Two 26. 17. Artificial Magnetism Materials Magnets Magnets Field 5. Magnetic Field of 27. 3 7. The Commercial 29. 13. Magnetic 6. Magnetic 3. Magnet Forms 7 8 10 11 12 of Magnets 13 14 Magnets 14 Screens 21. Field 5 Force Strength 5 of Force 6 . 16. The Solenoid 28.. Earth's 15 Magnetism CHAPTER II 17 Electromagnetism Field 23. Other 19. Theory Consequent Poles 9. Weber's 3 8. Magnetic 24. Magnetizing 15 22. The Horseshoe of Surrounding Field Magnetic a a to Conductor 17 Current 18 Parallel Smgle Turn Conductors 19 20 21 Solenoid 22 24 Solenoid vii . 14. Natural 4. Electrical Energy 60 and Energy Units 65. Volume Resistivity or 34 Resistivity 35 38. 55 in a Parallel Circuit Circuit Series-parallel 56 58 62.viii CONTENTS Pagx 30. Unit of Resistance 32 35. Table 44 * . Resistances 41. The Parallel Circuit 60. 51. The Series Circuit 59. The 60. LiftingMagnet 26 Magnetic Separator Magnetic Circuits 32.) can Working Table. Resistance 32 and Direction of Current Resistance 36. Specific 37. 46. 48.AmeriWire Gage (B.Standard Annealed Copper Wire. The 27 of Dynamos CHAPTER 27 III Resistance 31 33. English Units Annealed Bare Concentric Lay Cables of Standard Copper. CHAPTER 53. The Circular-mil-foot 43. " S. Ohm's Electricity 49 51 of Voltage and Current 52 53 Law 58. 54 . W. Units English . American Wire (A. Division of Current 61. . 36 Conductivity 40. Heat 62 . Conductance 39. 47.). Difference of Potential 56. Per Cent. 1 " 36 in Series and in Parallel 37 38 39 of Resistivities 40 Temperature Coefficient of Resistance Alloys Temperature Coefficients of Resistance Temperature Coefficients of Copper at Different 41 43 43 Initial Temperatures 43 49. Electrical Resistance 31 34. Gage G. Nature 45 46 52. The 31. The Circular Mil 42. Electrical Power 58 63. Law and the Electric Circuit of the Flow of Measurement 57. Solid. The 48 48 55. 46 IV ElectromagneticUnits 54. Thermal 61 64. Conductors Ohm's 44 ' . Polarization 88 86A. Rating of Batteries 106 from Service 107 108 110 . Primary Cells 86 84. Assumed 80. Dry Cells Storage Batteries 91. 100. Potential Drop Drop Potential in Feeder in Feeder SupplyingOne Supplying Two Concentrated Concentrated at Different Points 68. Vehicle Batteries 101. Electrolyte Gravity Specific Installingand Removing 105 98. Daniell Cell 86B. 92. Further 74. 76 77 Laws 79 Direction of Current of Application Secondary and 75 Cells 81 Kirchhoff's Laws CHAPTER Primary 73 82 VI Batteries 84 81. Batteries 71 73. 73 75. Gravity Cell 87. Weston 90.ix CONTENTS Paqb 66. StationaryBatteries 103 95. Tanks 103 96. Internal Resistance 87 85. 101 . Power in 67 CHAPTER Forces Electromotive Battery Loads 65 Feeder a 63 . Grouping of 77. Principleof Electric Batteries 84 82. 64 of Feeders Loss Load V Kirchhoff's " Battery Electromotive Force and 71. Estimation 69. Faure or 91 91 Cell 92 94 96 Cell Pasted 97 Plate. The 94. Kirchhoff's Laws 78. 67. Standard Lead 93. Edison-Lalande 88. 99. ReceivingEnergy Battery Cells in Series Equal Batteries in Parallel Series-parallel Grouping of Cells 76. Definitions 85 83. Laws Resistance 68 68 70 72. Applicationsof Kirchhoff's 79. Le Clanch^ 89 90 Cell Cell 89. Separators 104 97. Battery Resistance and Current 70. Hot-wire 118. Adjustment of the Watthour The . Voltage Measurements with the Potentiometer of Current Measurement with Potentiometer The 128. 136. 134. The 147 The 148 124. 161 Meter CHAPTER Magnetic . 158 of 165 VIII Magnetic Circuit Ampere-turns Reluctance of the Magnetic Circuit Permeabilityof Iron and Steel Law of the Magnetic Circuit Determination 157 169 The 138. 126. The Voltmeter Method 139 120. The Wheatstone The Slide Wire Bridge Bridge 141 121. Charging and 108. Efficiencyof 110. Charging Ill 103. 153 Potentiometer " Northrup Low Resistance 127. Electroplating 117 118 Storage Batteries Instruments 118 120 and Principleof Direct-current 112. Temperature 114 and Weights of Lead Cells. 135 Instruments 136 Method 137 144 122. Multipliersor 117. The D'Arsonval Galvanometer 114. 113. Measurement 130.CONTENTS X Paob 102. The 123. 135. The Wattmeter 131. Applications 109. of Trial and Method 140. . Capacities 106. 107. 115 Discharging CHAPTER Electrical 114 Measurements 122 Instruments 122 Galvanometer 123 Shunts 126 128 134 Extension Coils 116. Murray Loop Varley Loop Insulation Testing 125. Voltmeters VII Electrical 111. . The Watthour of Power 133. Voltmeter-ammeter 119. 160 132. The Nickel-iron-alkaline Battery 105. 137.155 162 Meter Circuit 139. Ammeters 115. The Leeds 129. 150 Potentiometer. Battery Installations 114 104. Error Ampere-turns Use of the Magnetization Curves 169 170 171 173 174 175 176 178 . Hysteresis Loss HysteresiB 182 144.. Fleming'sRight 218 166.. Linkages 145. Magnetic Pull 197 181 183 Electromotive Force Force 184 of Self-induction CHAPTER 186 193 IX CAPACITANCE EliECTROSTATICS: 198 150. Energy of the Magnetic Field Inductance Mutual 149. 206 209 Generator Hand 205 208 of CHAPTER 204 Voltage Generated of " Several Coil Sides per Slot Through an MultiplexWindings EqualizingConnections Wave Winding 173. Generated 163. Lap Winding 169. Frame a 233 in Lap Windings Winding Types of Windings Wave Cores and Shoes 229 230 of Brushes Through 177. 157. Lap Winding 168. 156. 166. Number 174. Electrostatic lines 200 153. 219 222 223 175. 155. Calculation 159. 224 Armature and a 236 238 243 244 246 249 250 .3d CONTENTS Paob 141.. Capacitance Inductive Capacity or Dielectric Constant Specific EquivalentCapacitanceof Condensers in Parallel Equivalent Capacitanceof Condensers in Series 202 154.. Uses of the Two 176. Paths 170. Magnetic Calculations in Dynamos 170 142. Induced 146. Paths . 171. Electrostatic Induction 199 152. 191 148. Field Cores Coil. Electrostatic Charges 198 151. Direction 215 Force Electromotive of Induced Electromotive 167. 143. Electromotive 147... 215 Rule by the Revolution Gramme-ring Winding Drum Winding 164. Measurement 160. Energy Stored 158. Cable in Condensers The Capacitance Capacitance of a Total Location Testing" of 211 Disconnection 213 X 215 161. 172. Force.. Definition 162. Field Resistance Curve 187. Determination 186. XI Characteristics Electromotive Force in Saturation 183. Total Characteristic 201.xii CONTsENTS Page 178. 309 210. Characteristic Armature . The 184. 280 281 285 ^Characteristics " 288 292 Regulation 293 Generator 202. The 205. 265 Up 266 267 Multi-polarMachines in 272 Reaction Armature 274 ! Electromotive Shunt 198. Compound Effect of Speed. The 180. The Unipolaror Homopolar 207. Counter 215. Torque Conductor Carrying Current Rule 310 . Critical Field Resistance 190. The a Electromotive Shunt Reaction Motor and Motor 313 316 Force Brush Position in a Motor 319 321 . Field Coils 254 181. Generator Fails to Build 191. Types of Generators 188. The TirrillRegulator 295 299 . Determination 204. 203. Effect of Variable 206. The Generator Generator 200. 311 312 213. Compensating 194. The 196. of Series Turns. Definition 309 209. The 276 of Self-induction Force 199. 197. 305 Generator 305 306 CHAPTER The 261 Line XII Motor 309 208. Series Generator 300 301 Speed Upon Characteristics. The 255 Brushes CHAPTER Generator 182. The Armature 251 Commutator 253 179. Armature Reaction 192. Principle Force Developed with 211. Armature 216. . Commutation 195. Sparking at the Commutator Commutating Poles (orInterpoles). Armature Reaction 193. . Torque Developed by 214. The 262 263 Generator Shunt 264 189. Hysteresis 257 Armature an 257 Curve 258 260 of the Saturation 185. Fleming'sLeft-hand 212. xiii CONTENTS Page 217. 390 394 252. Stray-power Curves 233. 235. Feeders Electric Railway Distribution 255. Circuit Breakers 234. 225. Three-wire 244. 385 391 Set and 382 Control 396 . Magnetic Blow-outs 221. Resistance 222. 383 Loads Systems of Feeding Series-Parallel System Edison 3-wire System Voltage Unbalancing Two-generator Method Storage Battery 243. Power 239. Electrolysis Station Batteries Resistance 390 Mains.'397 399 401 . Distributed Voltage 248. The 324 Series Motor The 219. 236. Speed Control Railway Motor Control Dynamic Braking Motor Testing" Prony Measurement of Speed 223. 224.348 Brake 353 XIII CHAPTER 355 Losses. 245. Measurement 232. Efficiencies of Motors 231. Operation Losses 228. Efficiency 355 359 and Generators 230. 384 385 " Advantages 395 253. 381 240. Opposition Test" Kapp's Method Ratings and Heating Parallel Running of Shunt Generators Parallel Running of Compound Generators 237. Balancer 250. 226. Dynamo 229. 338 Units 339 345 347 . Eppicibncy. 254. 249. 247. of 361 Stray Power 363 DISTRIBUTION AND 365 368 372 374 377 CHAPTER rBANSMISSION 360 OF XIV PoWER Distribution Systems 380 380 238. 329 Starters 338 220. Central 388 Generator 251. 246. Distribution 383 242. Motor 328 Motor Compound 218. Voltage and Weight of Conductor Size of Conductors 241. Solid PER Layer APPENDIX Current-Carrying Questions Problems Questions Problems Questions Problems Questions Problems Questions Problems Questions PROBLEBfS Questions Problems Questions Problems Questions Problems Questions Problems Questions Problems Questions Problems Questions Problems Questions Problems Index A Units APPENDIX Specific 401 on on on on on on on on on on on ON on on on on on on on on on on on on on on on on Capacity Chapter Chapter Chapter Chapter Chapter Chapter I Chapter Chapter Chapter CHAPTER Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter Chapter 409 D of Wires and Cables . III 413 . End 258. In. VII 427 430 434 438 442 VIII 447 VIII 449 IX 455 IX 456 X 458 X XI XI XII XII XIII 460 461 465 467 470 474 XIII 476 XIV 477 XIV 480 485 .. 414 416 III 417 IV 420 Chapter Chapter in C IV 421 V 425 V VI VI VII. 410 . FloatingBattery 403 269. 412 II II Amperes Winding 411 I .xiv CONTENTS Page Electromotive 256. Series Distribution 405 CeU Cells Force Control 402 APPENDIX Relations op 407 B Gbayities 408 APPENDIX Table OP TtiBNs Sq. Counter 267. piece of hardened to have which acquired it will steel be rubbed a retain very able appreci- indefinitely. of given first noted were of property not " If a lodestone. iron. pointing north leading stone. . ancients. known ore magic these to Asia attracting bits discovered of such Magnesia. phenomena practicaluse of Lodestone name composed are The century. at magnets magnetite. notably south. only metal (and are attracted all such magnetism. hence the fact that The gave such have to name the magnets was had the stones having the with of an chemical 4. Natural for used to a as of their some (or steel)is far superior to all Iron " substances far inferior to apparatus. Materials.COURSE A IN ENaiNEERING ELECTRICAL VOLUME I DIRECT CURRENTS CHAPTER AND MAGNETISM 1. an of their imderlying principlesis essential to a clear conception of operation of of the 2. and magnetic poles of magnets. Magnetic " Certain found were magnetic alloys)possess those material. Artificial Liquid is also oxygen iron property or of until the a in in stone as tenth and or navigation Natural metallurgy of stones. Magnets. if suspended freely. Magnetic metals other and practicallythe nickel and which by the Minor.was tweKth of iron. stones. the 3. Magnets. and Magnets I magnetism MAGNETS involved are in operation the Therefore ing understandpracticallyall electrical apparatus. it will be found amount magnetic properties. it the is Cobalt purposes. composition FesO*. the magnets 6. if the lines of induction of such a field be determined experimentally. The two poles are distinguishedby which the positionwhich they seek if suspended freely.and the other the south-seeking practiceit is assumed that the lines of induction leave the magnet it at the south pole. 1. to field about It is found a bar magnet. If a piece of soft steel or soft as Such a iron be similarly treated. Within the at the north pole and re-enter as if it existed in . In short. through which these lines pass is called the magneticfield.or south pole. Further.an electric will be shown current later. soft iron use magnetism respond closelyto changes It is found magnetizing force. magnets commonly derive their initialexcitation from. These regionsare called other region as shown some the poles of the magnet. magnetos.it is found that from one to emanate region of the magnet and enter they seem in Fig.DIRECT CURRENTS steel magnet is called an Artificial artificial magnet. are high degree even in aged artificially. itseK that of its magnetism with time. that magnetism manifests of magnetism or lines of called lines lines.it retains but a very small portionof the magnetism initially imparted to it. " Magnetic Field. in electricalinstruments. make it desirable to use hardened steel when a These properties permanent is desired and magnet it is essential that the or loses some of permanency or steel when even hardened Where a 1. The region in space induction. The one pole or north pole for points north is called the north-seeking pole. Magnetic " of steel ages is desired.or as Fig. . It as is evident that if the magnet be cut alongthe line XX Fig. later. north and a new a new which. 3 (b). and their north 3.is offered by Weber's Theory which has been expanded by Ewing. etc.neutralized each other.and no external effect is produced.hysteresis.3 (a). This is shown in Fig.4 CURRENTS DIRECT occurring in the magnetizationof iron. " Weber's polesare molecular theory of magnets. Upon the applicationof a magnetizingforce. The molecules of a magnet are assimied to be an indefinitely great nimiber in Fig.3 (c).however.Each of the small particles of the bar magnet. each having its own possesses the properties and its own north south pole. .so that the various north and south poles as way. Under ordinary of very small magnets as shown conditions these small magnets are arranged in a haphazard shown at (a).before the fracture took place.occurring in iron subjectedto a magnetizingforce. south pole will result. all pointingin the tion generaldirecthe magnetizing force. This theory is further substantiated by grindinga permanent magnet into very small particles. Further. the small magnets tend to so arrange themselves that their axes are parallel (") f If N TT-Sl IZs\rE Z3] s if N sWaW N SN stf s" m D 8 a\y ss 'rM 4" s P^ SiV H 8 OF! 8if_a if"S H C) FiQ. all neutralize one another. This will be considered same .. the theory offers a rational explanation of saturation. or a south pole. is in a way illustrative of the field resultingfrom consequent poles. 4. Fig. 10. " m' one this it may be that like polesrepelone another another.11. 4. " Consequent poles.) and unlike polesattract one another. Pole Strength. two bar magnets are used and exists between the adjacent north poles. magnets arranged so that two north or two south poles This is illustrated in exist in the same portion of the magnet. attraction (or repulsion) between versely two given poles is found to be in- (5) Attraction 6. acting in opposition. AND 5 MAGNETS Consequent poles are occasionally found in bar magnets where different portionshave been rubbed by a north pole. Consequent in due fact to the that the bar consists of two reality poles are Consequent 8. a small air-gap When a freelysuspended north pole is Magnetic Force.have been placed upon the bar. if a south pole is brought in the presence of a north pole. poles." The force of FiQ. " with the distance between them. stated From ^h^f (cm.) (a) Repulsion attracted toward the north pole. " Fig. The magnetic field shown in Fig. however. of such strengththat if placedat a Repulsion and magnetic between the square of the distance between of the poles are that the dimensions as ^ tion attrac- poles. or when excitingcoils. brought in the vicinity of another m north pole. whereas.provided compared A unit magnetic pole is one distance of one centimeter in the small . In or more this case. South poles are also found to repel 9.MAGNETISM Poles. it is repulsed. page 11.it is immediately (cm. and be determined the force . The force urging this pole will be greatestwhere the lines of induction are the most dense. the force will be proportionalto the number of lines per unit area taken perpendicular to the lines in the fieldin which the pole finds itself.^^ --103^-^2^^^^^' _ (10. Two north poles. moreover. Ans. apart. a magnetic upon force does exist within the magnet.54 10. 75.one having a strength of 600 units and the other a strengthof 150 units. existingbetween poles in air may follows: as / where m' and dynes ^TT- = (1) the respectivepolestrengths(interms of a unit pole) of two magnetic poles. Pole strengthis measured by the number of unit poleswhich. be attraction or repulsion as according as the poles are unlike or like. pass completelythrough the solid metal of the magnet.741 gram. similar From these statements it can be seen to lines of induction. This on the subjectlines of induction The fallacyof so and lines of force are criminately used indis- doing is immediately apparent The lines of induction consideringa solid bar magnet. Lines of Force. 2. to represent the forces at the can various pointsin the magnetic field.000 _ _^ .6 CURRENTS DIRECT tvillrepelit with a freespace from a similar poleof equalstrength force of one dyne.16)" _ 728 ^ = 0. ifplaced side by side. ^- 2. but this force can only by making a cavity in the magnet. To be sure.placed a distance r cm. whereas the lines of force terminate at the poles. 5. This force may shown in Fig. Poles repeleach other. " ^Thus far the observed.and in what direction does " it act? 4 in. In much of the literature 1. pole will be urged along the lines of induction.and. be drawn. What is the force in grams actingbetween these poles. magnetic field has been studied only with respect to the Unes of magnetism or induction. be formulated The force /. If a singlenorth pole be placed in such a field two effects will be 11. m are Example. = 4 X 500X150 .16 = cm. would be equivalentto the polein question.are placed a distance of 4 inches apart. that lines offorce. In free space. flux density and field intensity are the same. Intensity.however. One line offorceperpendicularto centimeter represents unit field and passing through a square intensity. Unit field to the number is defined the fisld as strengthwhich will act upon a unit intensity pole with a forceof one dyne. f n 1 . the lines of force and the lines of induction bar. . . ^Flux density is the number 13. ^^^ ^ perpendicularto the induction. be The confused. It has been stated that the force acting a magnetic pole placed in a magnetic field is proportional upon of lines of induction at that point. Density. 6. of lines of ^^ait n-po1c sput "^"- cm. of a unit force emanating N-pole. It is evident that if a pole of m units be placed in a field of intensityH. Field " f pole placed in such A that it will have no mX = H dynes be of such small field must a (2) magnitude disturbingeffect upon appreciable the magnetic field. but the expression '* lines per square centimeter" inch" square used in '* and are lines more practical work per often when ^"- 6-" Lines from . By definition the force exerted by a unit pole upon another unit pole at centimeter distance in air is always one dyne. the force acting on this pole is 12. The field intensity on a sphericalsurface of one centimeter radius must then be unity and can be representedby one line per square centimeter over the entire sphericalsurface as shown in Fig. material the two are entirely different.MAGNETISM 7 MAGNETS AND dicated acting under these conditions is quite distinct from that inby the number of lines of induction passingthrough the In air. Flux induction " per unit taken area. coincide. but within magnetic numerically.) is often called the gauss. should two The density (one line not '^ ^"^Mm of Radius ^ unit of flux per sq. speaking of flux density. . Field intensityis usuallyrepresentedby the symbol H. . =444dynes. cm. permanently magnetized and accurately balanced upon a sharp pivot.4 = 10 X 400 mm' f^l^^ Compass Needle.020 lines. cm. Area of surface of sphere 4irr* 4ir9 113 sq. " = Flux density Force upon As = -jj^ pole of 10 units 44. the force may (seePar. Example." 319 grams. the needle is enclosed in an air-tight for mechanical case are protection. A pole having a strength of 400 units is placed at the center What is the flux density at the surof a sphere having a radius of 3 cm.. given some distinguishing used for lecture purposes. 6 represents a portion of a spherical surface of one centimeter radius and shows roughly the passage of one Une of force through each square centimeter of surface. what force (grams) will a pole. ".120 lines per = = ^ ^ or sq. 10). pole faces.6 lines of force.4 gausses. Example. = a 14.120 gausses. Mariners' compasses mounted carefullyupon gimbals. Upon steel ships.each unit pole must Since a CURRENTS there are = Fig. face will be what units of the sphere and exerted on a poleof 10 force placed at the surface of the sphere? 400 X 4ir Total lines emanating from pole 5. A total flux of 200. square. steel needle = 44. 444 = also be determined check.000 dynes = . The north pole of the needle is usually colored blue or With the exception of a few mark. Ans. X 10 3X3 " The dynes. in the unit north pole. Being in air tl^s value of flux density also equals the field intensity. The north-seeking end or north pole pointsnorth.000 lines passes in air between two parallel The With field is uniformly distributed. lines of force. A pole having a strengthof m units will radiate irm 12. be acted if placed in this field? upon " 200 ' Flux density 000 3. the law of inverse squares . = Ans. compass consists of a ened hard- bar. 3.8 DIRECT the surface of 47r square centimeters upon have radiatingfrom it 4x unit sphere. / = H X m 100 = 312.000 ^^:j " " 3. so that they always hang level.120 X 312.each 8 cm. The = = = by . H.heavy iron balls placednear the compass or small . This also explains each line originating the appearance of the 47r term so often encountered in magnetic formulas.and the south-seekingend points south.having a strength of 100 units. end of the needle pointingin the direction of the lines of force or naagnetic lines. " This as Elxploringthe field about a in bar magnet with a compass. By placing a and to show if the . Fig. " the north pole of Compass the magnet needle and shown bar magnet. Likewise.the compass the north direction of the magnetic field in which it finds itself. mine is very useful in practical work for it enables one to deterand generators the polarityof the various polesof motors excitingcoils are correctlyconnected.MAGNETISM are necessary to AND 9 MAGNETS compensate for the magnetic effect of the ship itself. the Fig. the polarity of a magnet of the compass is By means The south poleof the compass readily determined. 7. This is illustrated in Fig. north pole of the compass points to the south poleof the magnet. 8. needle always tends to set itselfin the Fiuiiher. points to Fia. 8. needle follows immediately from the This action of the compass law that like polesrepeland unlike poles attract each other.7. Fig. On the other hand.10 DIRECT points in the region of a magnet. In Fig. It will be noted in Fig.unlike poles adjacent. in very . If a card be placed over a magnet and the card. 9 shows the magnetic field due to two bar magnets placed side by side and having unlike polesadjacent.and close detail the character the resultant of the figureshows magnetic field. Magnetic Figures. acting to pull the unlike poles together. point. " Magnetic of the lines of force at that figure. at each point. 8. In mapping out a field in small compass and drawing same CURRENTS at the various this way it must be remembered that the earth's field may exert considerable influence on the compass needle in addition to the eflfectof the field being studied.the field around the magnet maybe mapped out as shown in Fig. 10 the lines of ing to repelone force from the two like polesappear another. Fig. having the two north polesadjacent. Fig. " Fig. 11 shows of repulsionbetween a state fieldobtained by placingthe bar magnets end to end.the arrow arrow an pointingin the direction as the needle. indicatthe the poles. bar magnets when like poles 10 shows the fielddue to these same are adjacent. 9. at each point set themselves in the direction The filings 15. a magnetic figureis obiron filings be sprinkledover tained. 9 that the lines of force like elastic bands stretched from one seem pole to the other. . attraction vicinity between the two results. This offers further explanation of the attraction of iron to polesof magnets.12 DIRECT magnet is broughtnear the CURRENTS u*on a induced. From of magnets to attract soft iron is readilyunderstood. 12 (a). It is sometimes polebe noticed that if comparativelyweak a north brought into the of a strong north pole. " Poles produced Fig. Proper method bar magnets. "keeper" When a of soft iron should horseshoe be magnet placed across is not the in use a poles. In this it is easy to reverse the polarityof a compass needle by holding way end too close to a strong magnetic pole of the same one polarity. " of " from the fact repulsionof magnetic poles. when two bar magnets are put away in shown as box. by magnetic (6). 12 (b). the ability north This is illustratedin Fig. They will retain their magnetism better under these conditions. Law always that the mcmmum am^mnt tends to so conform itself of flux is attained. 12 (a). of the Magnetic Field. traction and similar reason.and these pole magnet two poles being of unlike polarityare then attracted toward each other.but comes that the strong north poleinduces a south pole which overpowers the existingweak north pole and results in attraction. For in a a Fig. This is no violation of the laws governing the at- Soft Iron Soft Iron FiQ. keeping 12 " induction. The iron is drawn toward the magnet utiUze it as a part of their return so that the magnetic lines may " . poleis similarly the foregoing. An opposite of to that the is induced in the iron. The magneticfield 17. rather than the repulsionwhich might be expected. the adjacent ends should be of oppositepolarity. 118.a north and a shown south pole are obtained. 13 (a) shows compact. The maximum flux is against the poles. Chap. 14. a soft- Fig. All the magnetic flux is contained in the ring and littleexternal " effect is noted. However. horseshoe magnet of Fig. Fiu'ther. pole is equally effective. as isused in Weston page 130 direct-current Digitized by (^OOgle . ring magnet.for two reasons. " Horse-shoe magnet attracting iron armature. Other Forms The simple bar magnet frequently is not suitable for practical For the same amount work. 18.if brought near this gap. A piece of soft iron. This type is not very useful. of material. VII. path through the air is materiallyshortened. Fig. if the ring be cut as in Fig. is very useful. 13. a comparatively strong field exists. The two poles being near 14. shown in Fig. 14. other forms are more powerful and more closed a Fig. The the polesof the magnet.if the function each shows of the magnet is to exert a pullupon an armature. will be strongly attracted and will tend to be drawn the gap and thus shorten the length of the flux path. 13 (").MAGNETISM AND path. The across horseshoe magnet. since iron conducts This these lines much is illustrated in the armature is drawn toward 13 MAGNETS better than the air. " Ring magnets. and the return (b) (a) Fig. a horseshoe magnet such instruments. each other. exists when the armature of Magnets.so that the number of magnetic lines is materiallyincreased. such " This shell 17. Magnet Screens. It is found that thin steel magnets are stronger in proportion to their weight than thick ones. 16. Fig. is more than one made of a singlepiece of metal. " is no insulator for magnetic known appreciable change in the flux or in the pull is noticed if glass. Laminated form of " horse-shoe magnet for telephone generally used and ignitionmagnetos. " Compound or laminated bar Fio. generators. instrument stray fields due an This is done shown iron sTiell as by in Fig. Compound magnet magnet. screen. 16 shows the 19. carryingcurrents. laminations. There 20. flux. placed in the magnetic field. of material a magnet made For a given amount up of several in Figs. " from Magnetic with to to be MreeneS. or other paper. conductors surrounding the 17. used horse-shoe in magnetos. copper.as shown 15 and powerful 16.14 DIRECT CURRENTS Magnets. However. No Soft iron pole pieces Fig. of a magnet wood. it isoften electrical measuring shield galvanometers and material be desirable instruments to from the earth's field and InBtrament Fig. 16. by-passes practicallythe entire flux and thus . etc. " magnet Magnetizing with an shoe horseelectromagnet. Fig. 19. Magnetizing.it is well to rub one end with the north pole of the inducing magnet and the other end with the be done simultaneously south pole. This may by the "divided touch" in Fig. The The earth behaves as a huge Magnetism. 22. effective than more one shell of the total same thickness. are Three or four shells. 19 shows this method of magnetizing a horseshoe An armature or "keeper" magnet. Divided " be between by placing them Fig. the screeningof the most 21. sides of the bar. Such.MAGNETISM 15 MAGNETS AND the sensitive portionsof the instrument. bar magnet. A magnet may be magnetized by merely The resultingpolarity at rubbing it with another magnet. damage to the electric circuit. It is admethod visable shown " to rub both Stronger magnets may 18. with air spaces between. The heavy rush of current is usually sufficient to leave the steel in a strongly magnetized condition. the polesof which are not far from the geographical Earth's " . Fig. 18. should the poles of the horseshoe magnet be placed across before the tion removing it from electromagnet. prevents itfrom affecting The smaller the becomes. are used only in connection with sensitive galvanometers. Upon closingthe switch. around A few turns the magnet and be wound resistance wire may connected in series with a fuse to the of low current supply mains. found be to the more effectivethe screening openingsin the shell. a powerful electromagnet. however. in contact any point is oppositeto that of the last pole which came with this point. touch obtained poles the method of magnetizing. Therefore.an enormous but the fuse blows immediately and prevents passes temporarily. Magnetizain a also be produced by inserting the magnet may suitable excitingcoil and allowing a heavy current to flow in of a the very coil. The field of the earth's field at New not horizontal) York intensity(total.the compass pointsto the true north in only a few placeson the earth's surface.but assumes a position making some angle with the horizontal. ing the declination at various parts of the earth.about 1000 miles from the geographicalnorth pole. it is about 9" west. The dip undergoes changes similar to those in the variation.61 C.S. freelysuspended and balanced needle does not take up a when under the influence to the earth's surface. The undergoes due possibly very small dailyvariation and an annual variation. The south magnetic pole been located but experiment pointsto the existence of has never two south poles. to the influence of the sun and the moon.although this value changes slightly A from time to time. The deviation from the true north and magnetic maps are provided showis called the declination. called the variation At New York tion gradual varia- change. corrected be needle must correspondingly. . A careful record is a ments. This angle is called the dip York it is about 70* North.G.16 DIRECT CURRENTS poles.and navigation. kept of this secular variation and scientificmeasuresuch as are used in astronomy. The north magnetic pole (correspondingto the south pole of a magnet) is situated in Boothia Felix. is about 0. At New of the needle. The declination undergoes a from year to year. Due to the non-coincidence of the geographical and magnetic poles and to the presence of magnetic materials in the earth. surveying. units. positionparallel of the earth's magnetism alone. but " in 1819 for Oersted electric an existed field about Magnetic " indicating the thus a 20. It is further set itself at cylindrical relation. that the 21. Surrounding right angles conductor.II CHAPTER ELECTR0MA6NETISM 23. If a be brought carrying observed the Fig. field. points in when held that the (if there 2 a beneath the magnetic are no direction conductor. the Lines " a needle single deflects. needle the surrounding " a always tends When Klines of force " cylindrical that into of presence conductor. needle conductor it to it is held Fig. compass conductor to only existed not Conductor. a relation some it remained but magnetism. current a of 22. of force conductor the surrounding current " outwards. inwards. been and Magnetic Field suspected that this relation Fio. conductor. flux other opposite exists to that Further in conductors 17 circles in the which it assumes investigation about the vicinity) as shows conductor shown in . the above that show to neighborhood magnetic a long electricity definite a straight had It between was current. 20.21 and 22.) are compasses arranged as shown in Fig. 20. in Fig. is dependent upon The relation of the two is shown in Fig. the direction in which circles have their centers at the planes are their perpendicularto in the conductor be reversed.for the direction of the field to reverse above the conductor be must oppositeto beneath that the ductor. the These 22. 23.18 CURRENTS DIRECT Figs. The fact that the magnetic to the conductor field exists in circles perpendicidar explainsthe from a point above needle when moved reversal of the compass the conductor to a point beneath it. arrow.by the rection in their needles which point. dot at the and a cross are two be remembered. 21 and conductor of the center and If the conductor. current needle is deflected will be the compass seen also. Iron filings sprinkledon the cardboard form circles. dithey will indicate. is is A flowing circle flowingout of . is brought vertically current a This is illustrated in down of through horizontal sheet a cardboard. 23. of 24.showing that the direction of this magnetic field the direction of the current. paper. that the magnetic lines circles having the axis of the are wire as a center. 23 is illustrative of this concentric The experiment shown A conductor carrying relation of the flux to the conductor. Fig. inside (0) indicates that the current represents center There the feathered (O) indicates represents the that end the approachingtipof an of an current arrow. lation re- " of the current in a conductor magnetic simple rules by and the direction of the field surrounding the conductor." Magnetic A definite tion the direc- exists between Investigation of the magnetic field surrounding a conductor. this relation may which 1 A circle into the having having and a the paper. (A current concentric of about 100 obtain to If four or is amperes distinct more sary neces- figures. Relation Field to Current. con- ^ Figs. . The but these circles are not concentric magnetic lines are circles. " field similar to that Fig. transformer coils have been pulled out of plaiceand transformers wrecked by the forces produced by the enormous currents arising under shortcircuit conditions. south a north pole which shown in This magnetic poleand possess a all the A compass propertiesof similar poles of a short bar magnet. Bus-bars been wrenched from have their clamps. 26 are shown two parallelconductors carry current in opposite directions. when the -conductors the flux passes rate. the direction shown. as longercircidar. area with through which the conductor. and flowing in the same This effect is especially pronounced in modern largecapacity the power systems. he repelled from each other. FiQ. the foregoing. number of either with crowded between conductors the another one or the conductors farther apart.-Magnetic a field produced by field has single turn.25. 27 is obtained. From be formulated. All electriccircuits tend to take such a positionas vdll make their currents parallel direction. (^oogle . of the conductors reduces the length of path ahcd through which the lines must pass. gle Magnetic Field of a SinIf a wire carryinga Turn. 27. the conditions which exist when In Fig. the needle placed in this field assumes north pole pointingin the direction of the magnetic lines. current be bent into a loop a 26. The fielddue to each conductor separately is stillcircular in form but the resultant magnetic lines are no is shown in Fig.the followingrules may Conductors carryingcurrent in the same direction tend to be drawn conductors carryingcurrent in oppositedirections tend to together. that so magnetic circuit in this case also tends to so conform itself that the magnetic flux is a maximum. and The lines are therefore tend to push the Again. sepa- is increased..20 DIRECT CURRENTS The pullingtogether magnetic lines is a maximum. or by simple method. " field produced Magnetic by helix a or solenoid. 29. where when lookingdown lookingdown current exciting upon a will be clockwise arrows the direction of current upon a direction in the coil will be counter-clockwise by the "iV. The wound electric conductor An " in the form carrying current is called a solenoid. the current For pole and to direction of exciting current. when the Fig. 27. 28." of the W solenoid be flows in the helix may the corkscrew rule of Par.21 ELECTROMAGNETISM Solendid. is shown ' the the ciu-rent of magnetic Relation " flux within may as pole shown pole the direction shown by the "S. The solenoid winding consist of several layersas shown in Fig. 29." south as north . in Fig. The solenoid flows through the conductor is shown be considered as consistingof a largenumber of the turns may of helix and a Fig. in the "aS''show example. A simple solenoid and the magnetic field produced within it when current in Fig. rule. 27 placed together. Another by the hand at the ends of the in the coil. shown The to relation of the direction of the the direction in which determined Fig. 30. 24. 28. 30. for operating in automatic motor contactors starters (Par. The flux due to the solenoid produces magnetic poles in Fig. II). for operating valves. The Commercial CURRENTS Solenoid. 237). positionof equilibriumis reached when the center of the plunger reaches the center of the solenoid (Fig. Fig. " Simple solenoid and plunger. to be drawn as ** " within the solenoid. for arc lamp feeds (Chap. The iron-clad feature pulland produces a very increases decided the increase of range of uniform pullas the plunger . other XIII.22 DIRECT 28. Fig.and for niunerous In practically allinstances a soft iron (orsteel) plungpurposes. 31. to obtain the tractive pullrequiredof The operationof a solenoid and plungerisindicated the solenoid.219). the plunger will be of such sign the plunger. Iron-clad "solenoid and plunger with stop. Vol. 30.30). for operating voltageregulatingdevices (Par.(seePar.207). 31 iron-clad*' solenoid commonly used for tractive shows an A '* work. 11) and in er or such is necessary armature a direction Fig. The pole nearer on that it will be urged along the Unes of force. " The solenoid is used in practicefor trippingcircuit breakers (Par. brake be applied immediately. a 10 8 12 Z". is interrupteddue to Plunger electrothe power when operating a crane broken wire or other accident. 33. It will be noted made that the iron-clad feature and have but littleeffect except near the stop the end of the stroke. 32. Section 5. 31 but without a (c) shows the effect of the stop. Underbill. When the power or liftingmotor magnet Fig. 33. curve "stop'' on the pull. 30. curve (") this solenoid is shows the pull when iron-clad as in Fig. plunger electromagnet. When from the " * " Standard Handbook.23 ELECTROMAGNETISM approaches the end solenoid the of the becomes a 6 Distance " Pull the characteristics of the now when occurs shows 32 the stop "a" is used. results of solenoid tests by C. in that the plunger is near the end of the maximum the stop. When stroke. must One method of accomplishing this is shown ii^Fig.This changes 4 Fig." . pull Fig. of important practical application in the braking of the solenoid occurs An elevators and is removed cranes. the a brake. R.' Curve (a) is the pull upon the plunger of a simple solenoid like that of Fig.Inches of solenoid solenoid on plunger. 24 DIRECT CURRENTS interrupted.34) become excited. The sounder for any " The use of an armature m with solenoids is well illustrated by the relay or the used in telegraphy.buzzers. To reason. are (^oogle . connection etc. thus releasingthe brake. pressingthese against the brake drum the power Z". the power. A plunger electromagnetis most suitable the pull must for this piu-pose because the stroke is short and be positive. making contact FF and thus completely closingthe magnetic with the cores D close any circuit. the plunger P is pulledup.and also by electric bells. each being placed on one of the legs of a horseshoe When the coilsC (Fig. As a rule.the plunger P of the solenoid A drops. 34. is Solenoid. for under these conditions the magnetic lines stillexist after the excitation is removed. A is not allowed to close the magnetic circuit comthe armatiu-e pletely. [lard solenoids llubbtr- Fia. Horseshoe 29. increase the efifectivenessof such devices two . or U-shaped magnet. The contacts secondary circuit that the be operating. When is appliedto the lifting motor. The spring T draws the armature relay may back againsta stop S when the excitation is removed. preventingrapid release of the The stop S' prevents the armature armatiu-e.thus effectingthe braking action.due partlyto gravityand partlyto the action of the springs S. used. A is attracted because of the tendency of the the iron armature magnetic lines to make their path of minimum length. The springsS immediately force the levers L againstthe brake bands B. " Telegraph relay. " Cutler-Hammer Gross-section 36-inch Coil Shield of of a magnet. liftingmagnet. handling heavy castings.ELECTROMAONETISM 25 L"*di." Fig. . mil EbelT Terminal On* Oritj- Luff for S-Folnt 8i"pmiai"m Ooil HaiTDAt Case R"niDv"ble Top PUto of Coil Spool High Permeability Spool for Coil Coil of Strap Copper "^ Non-magnetie aianganese Steel *nd iDiBer Pole ShoM Outer Fig. 36. 35. be picked up and laid down again without being disarranged. but very the billets cannot be picked up when red hot as they lose their at this temperature. Liftingmagnets effect a very great saving of labor when small pieces of iron. magnetic properties Magnets are especially for an entire layermay usefid in loadingand unloadingsteel rails. PvHtt^ Ma^nd-ic ^. A cially commer- very preciable ap- savingof time and labor iseffected by their use.36 shows a lifting magnet in actual operation. 35 shows in cross-section a typicalCutler-Hammer lifting magnet. for they will pick up largequantitiesat every lift. to handle iron and CURRENTS ^Lifting magnets " used are steel in various forms. are handled. Without a magnet each individual piece would have to be moved by hand. They useful for handling steel billets in rolling are mills. It should be understood no work device. The LiftingMagnet. .*-^^ Non-Ma^tffhc Fig. because chains and slingsfor holding the load are not necessary. 37. " Magnetic separator. which in The the that the magnet itselfdoes littleor as a holding lifting. Formulae for the holdingforce of electromagnets are given in Par. Fig.26 DIRECT 30. such as scrap iron. 149.but merely serves actual work is operates the steel ropes performed by or the engine chains attached to the or motor magnet. Fig. . the flux in taking the shortest path tends through the upper half of the armature. unsatisfactory The magnetic circuit of a bi-polargenerator of modern design of the symmetry of the magnetic Because is shown in Fig. armature. circuit the flux divides evenly through the two sides of the armature. " Magnetic reduces the that the circuit and magnetic leakage to flux in the Ordinarilythe yoke field cores. It is to be noted that the Again the flux passing poles are alternatelynorth and south. field windings cores need a of a modern minimimi.both upon reaching the yoke through the field cores and upon reachingthe armature path and the cross-section of the made . polar complex magnetic circuitsof a multiFig. divides. It is to be noted it passes into the yoke. bi-polar generator. to This tends to crowd produce commutation. the pole shoes The long air path existingbetween Field WiEidfAf Toka Fio.therefore. 39. 39. only be one-half the cross-section of the Direct-current divides as machines of the bi-polartype are usuallyin small units. Moreover. 40 shows the more generator having eightpoles.CURRENTS DIRECT 28 of flux passingthrough the the amount duces. 41. 39 yoke need only be one-half that of the cores. " 40. incorrect by placingthe excitingampere-turns possible. 40 the magnetic leakq^geis very materiallyreduced Fia.This result is not secured as position of exciting coils. Fig. near in the the armature Edisonin as bi-polar bi-poL gle . Magnetic " Magnetic circuits of leakage produced by a multi-polargenerator. and Fig.29 ELECTROMAGNETISM In both Fig. It is to be understood that of itselfmagnetic leakage does not lower the efficiency of a machine. 38. resultingin a smaller percentage of the total flux passingthrough the armature. the yoke. They stillact upon but upon of their remoteness from largemagnetic leakage exists around the outside of the yoke and through the interpolarspace. since to maintain a constant ever. much heavier and more expensivemachine than would otherwise be necessary. the Thi"in armature. 41 shows the same generator of Pig. Howmagnetic fielddoes not requirean expenditureof energy. turn a increases the amount of Therefore a large magnetic leakage results in a field copper. generator as that in Fig. 40 but with the excitingcoils placed the magnetic circuits. . number of magnetic lines may in order that the necessary both the yokes and the cores reach the armature ciently must have suffilarge cross-sections to carry the leakageflux in addition because to the useful armature flux. To illustrate.30 DIRECT CURRENTS Fig. by electric an hours was will property the by friction into heat. coil of inducing known. loss energy a which resistance.but the across If. removed. the next magnetically of the lead in resistance. liquid helium " to tends therefore through passes in flume. well. a electromotive presence of absolute is which chapter. lead source The wire then being in indicates at the that the this extremely low temperature. in the at flow the prevent Resistance to acting. . and electric current the a Friction overcoming water amount an helium zero running is used loss of head. poor of this wire. if a represented by directly proportional AU^ at be may being expended would will be occurs with even a other some This and If straight. showed had short-circuited a lowest 273" in of resistance. This experiment ) of experiment. the in a force C practicallyzero of the some this friction. wiU current an the terminals across battery terminal a force the at circuit the upon obviously flow through at circuit the the electromotive the upon wh-e be connected a made flowing through current only not will current a The " circuit.for example.CHAPTER III RESISTANCE electric depends circuit impressed battery be contact poor point in electromotive same dissipated be tending to causing heat point of friction in mechanics. at sub- some able was diminution no been in removed. This energy careful in its iemperature.but the in or slight increase current the to in its effect street-car power pipe a the a circuit in which Liquid neighborhood resistance in show have induced The car.is called resistance. level track. in of time same after the of of has was ( Ley den. force properties drop in value. a Resistance. Electrical S3. friction tends a largely absorbed measurements As For on water loss of energy The circuit of water flow of the energy of current electric is converted car the impede to at or contact. resistance recent and the temperature . Kamerlingh-Onnes a 5 strength current the in the shown substahces Professor the heat likened example. considerable Also as dissipation. a uniform speed the moving prevent the moving loss is of when is 1 to produce "270" C.is . is a good insulator. Resistance body of but upon it. The used megohm.32 DIRECT CURRENTS times greater than that of others..silk. Wood. equal to 1. isthe unit ordinarily under these conditions.paper. also may classed be conductors.ebonite.) On the other hand. is a good insulator. cotton. Therefore both It is evident that reservoir B volume. but wood containingmoisture is a partialconductor. because pipe P' has twice This may be illustrated qqa millionth.The pipe P is twice as long as the pipe P' but of one-half the cross-section. may or good insulators. rubber.) one the direction in which i .000 (10^)ohms. among will allow a certain amount of current to pass and therefore are perfectinsulators.and is equal to (The prefix''micro" 35.000. Under these conditions the microhm is used the as unit. is the practicalunit of ohm 34. etc. not only " on The resistance of a its size and the electric current shape. and means Direction of nnn of Current. resistance. as dissipates The resistance of insulatingsubstances is ordinarilyof the to express magnitude of millions of ohms. flowingthrough ampere heat one joule of energy. be considered as nonconductors fiber. and glassor porcelain. the resistance of bus-bars and short pieces be so low that the ohm is too largea unit for conof metals may veniently expressing it. is many This into either conductors to the classification of substances stances leads or sulator in- Even of the best conductors. silver ordinary water the are and Distilled or pure water. The best conductors Carbon coming first and copper second. either dry or impregnated with oil. Unit of Resistance. pipes have the same will be emptied much quickerthan A. The " resistance and one also has such ohm that as resistance which volt is impressed across flow if one to ampere An is defined a value that one will allow its terminals. Oils.paraflSn. however. has appreciable one silver. given material depends an ohm (10""") . the best insulators known. as not metals.glass. flows through by the reservoirs and pipes shown in Fig. so that it is awkward it for second one this resistance in terms of a unit as small as the ohm. (The prefix''mega" means million.42. Twp equal reservoirs A and B are to be emptied through pipes P and P' respectively. dischargethrough different-sized pipes. 2 microhms. Therefore each per unit of Fia. successively. of equal Fia. 44. and the length. the resistance If. and this again makes the total friction of P' half that of -P if the cross-sections were equal. 43. " Rectangular prism as a conductor. Conductor ductor the same B but only one-half the cross-section. of a body or a substance the specified. of the same were length conductor A would have twice the 5. however.43) each of Now A has twice the length of conmaterial. to the end B. length of conductor is A unit Then if conductors A and B length of B. resistance of conductor However. " When Two " conductors volume.each centimeter on flows in the that the current a edge. that the resistance unit per It is evident. composed of two cubes. Fig. Assume the current direction of Ii from It encounters If it encounters of each 3 cube the a then the end flows must A through the solid resistance of each of two total resistance of 4 must be be 4/2 or cubes microhms. specifyingthe resistance direction in which 44. Water " contains the conductor of material. Further.Consider the rectangularprism of Fig. ' Digitized by CjOOQIC . even consider the two conductors A and B (Fig.33 RESISTANCE therefore oflFersless resistance cross-section of pipe P. 42. conductor A is twice the have 2 X 2 or 4 times the resistance length of Bj and therefore must twice that per of 5. amount same however. the length of P' is only half that of P. per cm.000ohm. or specific and A is 1 cm. 1 cm. or . on an edge and where ohms.between the two oblong it finds two paths in parallel. in this case k may be expressedin terms of an per cm.From 36. lengthof the But.and A. cube or in other units as will be shown later. path AS is 2 cm. in. the current flows in the direction of " "=a| R is the resistance in (3) L is the lengthin the direction at rightangles to the current of the current flow. is a constant of the material known as its resistivity resistance. Knowing the specific cube. the resistance of a wire. resistance in terms of the cm. ^ R=k. each surfaces C and D of the solid. cm. resistivity cube. or 1/580. of AB. The resistivity of copper is 1. A is the area flow. bar.the direction of unless this direction is obvious. In virtue of the two paths the resistance per cm. etc. cube. Specific be stated: of Par.724 microhms. the current flow should be specified the deductions Resistance or Resistivity.. and each having a length of 1 cm. 1X1 or B k is called the = resistance specific Jfc the of the substance.CURRENTS DIRECT 34 It.and inverselyas its cross-section. the substance in question If L is 1 cm. That is. square.therefore the path CD must have a 1 microhm. sequently Conor resistance of one-fourth that of path AB in specifyingthe resistance of a solid. the path CD is but one-half the resistance per cm. must have the form of a cube. It is evident that the cube is a perfectly definite unit of resistivity for the resistance between two oppositefaces is the same. 35 the followingrule for resistance may The resistance of a homogeneous body of uniform cross-section varies directlyas its length.may be readilycomputed from formula (3). in cross-section. in length. any The resistivities of various substances are given in Par. 1 sq. 43. . 100. may as of resistance circuit a of or a electric current.724 microhms per adopted internationally.61 = 680.The refined copper per cent.4 a Determine " (6) cross-section and L the conductivityof The *'^ = 0. the Bureau of measurements has recentlymade a large number copper.000 per cm. the length. 7. of conductivity 580. Until " recentlythe very per cent.5 in. in. cm. = 610 = cm. Per Cent.9 sq. The conductivityof aluminum is: thick. aluminum cm.54 = 12. Ans. and CURRENTS Conductance " be defined is the of reciprocal being that property material which tends to permit the flow of ohm is the reciprocal The unit of conductance is usuallyexpressedby g.000 39.54 X 2. and 20 ft. .594 microhms per cube cm.000 mhos/cm. an or ance Conduct- mho. has been fully conductivityfor careComparison to obtain at 20" C.54 X 12 X X ^ 2. conductivityshould be made of the of Standards upon standard mercial com- of sistivity re- 20^ C. In view uncertaintyof the qualityof his copper. sub- a per.000 mhos copper of conductance an stance. cube = cross-section of the bus-bar: A 0. 9-^ (5) also ? k' is the where cond'uciance specific A the uniform Example. k' The conductivityof the or wide. long. who careful measurements of the He found the resistivity resistance of supposedly pure copper. be Its recommendation 1. may per exceed cm. 0.6 X = The length L The conductance: g = = 20 354. to be 1.490 mhos. at 0" C. conductivityof copper has been based upon results obtained made in 1862 by Matthiesen. is 580.36 DIRECT 38. Conductance. bus-bar cube. The conductivityof aluminum is 61 per cent. mhos cube. 4 X 2. Conductivity.000 X that of copper and copper has 354. that the cube at cent. fifa. the total conductance circuit must be equal to the sum of the individual conductances. are in parallel. of sistances re- that is. . .-If a number in Series and 40. A " rod 4 ft. in ParalleL. FiG.. cm. is: (7) . In to be written a .133 = r. that is. is: That In a series circuit the totalresistarhceis the sum of the individual resistances. series. G = gi + g2 + gz+ . of conductances number " Conductances gfi.. conductivity = ri. (8) . of the totalresistance is equal the sum of the reciprocals of the individual resistances. 46. Tzy Ans.54 X " T" X Resistance at 20" C.724 Per cent. r2.0016X0. G = equation (8) may R' R That (9) ri r2 rz is: the reciprocal parcdlel circuit.740 connected etc. of 162 mils has conductivity? cm. the total resistance of the combination to " = ri + r2 + r. are in end. 0. 1. What 2. a " Resistances in series. If 45. Resistances end 99%. = 0.Fig.162 X = 37 u cube cm.ru^nf^r^^^Ai^ 0.etc.64)" 122 having sq. Since. + .45. Fig. ohm ^ (0.740 microhms. long and copper resistance of 0. or = 1. connected in of this portion of the parallel.RESISTANCE Example.000001740 = ^^^^ u ohm 122 1.133 = a diameter is its per cent. hWV\A/WV -"h R K- Fig.0016 a Cross-section Length 4 X = 12 per 2. 46. gr2. 0000007854 i"0. mil = j ^ (0.).875 mho.167 + + 0. of a cir. (0. mil.a cir. ri and rs.OoA peO-OW-*- " 0 (a) The square mU (b) The circnlar mil Fig.250 having 4 branches. mil is the unit with cables is which the cross-section of wires measured. Fio. mil is from mil dr.).are measured. The land.47 (o). for example. ^ 0. Fig. each in Fig. The shown square as = is thousandth one is side of which area of wire unit of wire cross-section. 0.38 DIRECT Fbr CURRENTS circuit liavingtwo a resistances in parallel. tables the circular mil is the standard The American English and a of inch. in. " Cross-section expressed in cir. advantage of the circular mil as a unit is that circular areas .001in. mils. just as the square foot is the unit by which largerareas such as floors. The and cir. 1. in. the jointresistance R for three resistances in -^. 6 and 0. Determine " (10) (11) + r2r3 Tzn the total resistance of the individual resistances of which ^=^+^+^ |+ circuit a are 3. or smaller a one area As than a 71* The area in sq. 48. 0.142 ohms. mil is 0.47(c). R = Ans.000001 A circular mil is the area of a diameter is circle whose and is usuallywritten CM.001) = sq. The Circular Mil. will be seen square mil. 4.001 square volt milli- a 0.333 + 0.875 41. In " the mil term Ho = volt.001in. respectively. ohms. ri + rj = the jointresistance is parallel R v^^V = + rir2 Example.125 0. means A mil mil is a square. 8 0. 00 one-thousandth. Fig.001-"i pH). (c) Comparison of the square mU and the circular mU 47..47(6). in.etc. an mil one A (0.001 X sq. may be summed obtain the number in two up rules: of circular mils in a solid wire diameter express the diameter in mils and then square To obtain the diameter of a solid wire having a circular mils.mils in A number Therefore 1. of cir.000(D^y = = D^ = (12) where The To Di is the diameter of the wire in inches.000. = = ^A certain wire givennumber of of the circular mils and the resuU has a diameter a (364. unit of resis- is the resistance of a cir. represents the cross-section of a wire having diameter of 1 in.4 Circular-mil-foot.rails.measured 39 RESISTANCE . 48.2294 Another in the English system.3648 Example. in^ - = a (0. milage? QQ wire root square of the (A. wire in mils. mils be written: may j^^.take the will be the diameter Example.640 cir. of given 364. is the diameter matter. A The area. D of the wire in mils.mils. in terms of this unit bear a simple relation very to the diameters. especially in. The area. The ratio of = a.100 cir. convenient tivity.mil a (1)2gq. Required: to determine its area in cir. cross-section of 62.000001 7 4 The generalrelation Cir. 0. in. j A " obviouslygives the of cir." cir. = ^ 0.640 42. Am.8)" " it.001)^ sq.G. " = 0.mils.- . What is its diameter? V62.000cir. mils.W.3648 in.) has in. Ana. 1. is its What mils 133.8 of 0. Ay in Fig.000. The = mils 229. 2500 ft.37 The ohms.mil it would a 25.0346 the have = 0..500 750.40 CURRENTS DIRECT This unit is the resistance of mil-foot. of 1 cir.-mil-foot of copper at in tion cross-sec- Fig. long? If the cable had cross-section of 1 cir. a copper cable. be expressedin feetand A in circular mds. of any length and size of wire be determined by formula (3). 20** C.L Metals 0. The circular-mil-foot. is 10. of Resistivities Cm.000 cir. = = = 10.-mU-foot (ohms) . may " Example. Table Aluminum Bismuth Copper (drawn) German silver la la Iron: Electrolytic Cast Lead Manganin Mercury Nichrorae Nickel Phosphor-bronze Platinum Silver Steel: Soft Glass hard Silicon (4 per cent. 2500 X 10.900 ohms. cir. 750.0346 ohm.000 used directly applying formula (3). work this resistance may (In practical -ift9M^'i frequently be taken as 10 ohms.000 . 49. mils.37 25.therefore.900 R or formula (3)may be R When However.) SlfE 3 the resistance Knowing this resistivity.37 2. must 48.) Transformer a cross-section resistance of is actually ohm 750.mil and resistance of a a lengthof 1 a wire havinga shown as ft.49. cube (microhms) Cir.000 CM. Fig. " is the resistance of What 760. If the 0" C.00427 0. For example. the increase of resistance will be 40 X ohms.427 17. 30 ^" ^ 1 + Ru 30 = = 27. Table 48 gives the temperature coef- fimdamental .00427 ^^'^^ ^^""^ LOSS X 80) = 37. is 30 ohms. This process of working back to 0" is a littleinconvenient. a is 0. At 40" C. a copper that assume every coil has a resistance of 100 ohms a at 0" C.427 or ohm. and at For Bo (1 + " aO (13) at the temperature t.Ro the resistance is the temperature coefficient of resistance at 0". for each degree Centigrade increase of temperatiu'e above 0". of the non-alloyedmetals increases very appreciablywith the temperature.08 117.427 of 1 per cent.08 = = 17. As the temperature of the windings of electric much higher than that of the surrounding machinery is necessarily airjit is important to know the relation between temperature and resistance. is found For resistance at known. The above is equivalentto saying that the resistance increases 0. The relation may be expressed as follows: 44.although it is and easy to remember. Ans. For degree increase of temperature the resistance will increase 100 X ohm 0. The What temperatures be determined.RESISTANCE 41 The resistance Temperature Coefficient of Resistance. definite temperature other than ordinarilythe resistance at 0" C. " Rt Rt is the resistance where 0" C. must first be some before the resistance at other this purpose formula (13) may ^" Example.00427 and for most of the unalloyed metals is sensiblyof this value. be put in the form iht = ^''^ electromagnetwinding an can of copper wire at is its resistance at 80** C? resistance at 0" C.08 ohms.66 0. " resistance of The 20" C.11 ohms. and resistance at 40" will be 100 + the 0.00427 X = 20 (1 +0. at these Ro Rn 234. fiw 30(1 + 0. equivalentto saying copper the (Actually behaves curve as if bends extremely low temperatures.50 + 234. _ Rm " = 30 30 Rio 234. 50. tt "{ o" -234.50. ordinarylimits of temperature.00393. Then = = - the resistance at 80** C.it will intersect 234.42 DIRECT ficientsof copper at the various temperatures other than 0**C. If the resistance of copper at ordinary temperatures be plotted against the temperature the result is a practically straightline.5" = o^ .5" = "o^ "o 234.5" + 234. temperature-resistance Fig. as shown by the dotted ing line. 50.6" + (16) U Applying this equationto the previousexample.07 " ohms.5" 234.5" + (15) (i Rt2 Rn 234.. from Table 48 is 0. The " CURRENTS temperature coefficient of copper at 20** initialtemperature The risein temperature 80** 20** 60**.) This gives a convenient method for determinrelations. that between it had 50. resistance at "234. table available the above Example. 45. .5" C. .Fig.00393 = X 60) 37.Fig.1 ohms. By the law of similar triangles.5" + tx 234. 37.5" + " o/^o 20" 80" on 30 j^FT-^ 254.5" zero This is Fig. Ans. (an easy number to " Fia. 50. " Variation in shown as of resistance with temperature. With this problem involves but one computation.5" C. Ans. remember). the If this line be resistance line at zero extended.5" + 80" 314. . of 0 0. 10 wire has a diameter of 0. (rule5.No.6 Weight of 1.W. Resistance of 1.6 times for every each successive gage number numbers. 0000 The example might have been worked more quickly by rule 4. of No. of 0000 0.25 0.050 ohm (rule3).000 ft.1 ohm (rule4) Resistance of 1. and a (2)The resistance (3) gage numbers.W. ft. 400 X 1. 2 and 3). The followto approximate relations make determine the weight or without it a comparativelysimple matter resistance of any number gage reference to the table: (1) No. 2 00 400 lb.44 CURRENTS DIRECT Gage (A.000 ft. = = = = = = = = = 2) .000ft. Resistance of 1. of the wire doubles with every increase of 3 1-26 the resistance increases v^ Therefore = (134)times for and (1. two (4) The resistance is multipliedor divided by 10 = (5)The weight of 1.000 ft. Weight of 1. of 0000 wire? follows: 7 4 0.G. 0." TheA.000 difference of 10 gage numbers.5 0. resistance of 1 ohm per 1 . 10 1 ohm. for every Example.(formerly Wire 49. 640 lb. The American ratio of cross" Sharpe Gage) is based upon a constant Brown ing section between wires of successive gage numbers. Weight of 1.050 200 lb.0625/1.0625 ohm (rules1 and of 0000 (rule3). The Gage " What is the resistance resistances will decrease No Resistance Resistance 10 1 as and weight of 1.000 ft.26)^ 1.000 ft.). 125 0.1 in.000 ft. of No.G.000 ft. 2 wire is 200 lb.25 1 000 0. EnglishUnits American The fundamental Copper resistivityused Solid^ calculatingthe tables is the International in Standard via.00393.7 per cent. 31.RESISTANCE 50. Standard Annealed Copper Wire. The temperature The 0.Hard-drawn copper may per The resistivity.89 grams NoTK 2. " S. " br ' From Pounds Circular per miXe may of the Bureau be obtained of Standards. 45 (meter. i^ by multiplying the respectivevalues abofC No.The " annealed copper. density cubic centimeter..28. or - at 20* ao = C.16328 ohm coefficientfor this particular resistivityis 020 is 8. higher resistivitythan resistivity.). Note Annealed 1. of the standard values given in the table are only for annealed copper correction for copper of any other of the table must apply the proper user be taken as about 2.(X)427. 6. " Working Table.0. gram) 0. . Wire Gage (B. NoTB 3. Conductors.is used more In a few instances it is used where a delicate but than . Copper. Bare Concentric CURRENTS Lay Cables of Standard Annealed Copper EnglishUnits 62. because of its high conductivityaii3""iQ^rate extensively cost. its use as a Although silver is conductor is very a better conductor limited because of its cost. ing highlyconductmaterial is necessary. such as in the brushes and occasionally in the commutator of watt-hour meters. " copper.46 DIRECT 61. the copper protects the steel from line conductor. and it can be readily as a any many soldered. long It is also used as make high tensile strength overhead ground wire on such spans an Its field is the transmission i . Aluminmn high voltage transmission Hnes. not easily abraided.high tensile strength. Aluminum but for the has same only 61 per cent. It is used to some extent for low voltage bus-bars as it offers much greater radiatingsurface than of the same conductance. Iron and steel have about 9 times the resistance of copper for cross-section and length. fused or welded to the steel. Further. lines. The advantages claimed for it are that it possesses the high tensile strength of steel. less than that of copper of the same conductance.not corroded by the atmosphere. other It has good qualitiessuch as ductility. its tensile strength less. where necessary. It is softer than copper. where its lightnessand large diameter are an advantage.and it cannot be readilysoldered. is The price of aliuninum copper by exposure held about to the 10 per cent. corrosion. of the conductivityof copper. The largediameter for a given conductance prohibitsits use where an insulatingcovering is is used extensivelyas a conductor for required. Copper-clad or tioA by galvanizing steel consists of a steel wire coated or covered with a layer of copper. The largecrossnsection for a covering given conductance prohibitstheir use where an insulating and the increased weight prevents their use in is necessary be placed on poles. In most where the conductors must cases view of their low cost per pound.47 RESISTANCE conductor than material. Iron and steel ordinarily be protectedfrom oxidaother protectivecovering. combined with the high conductivityof copper.it has about twice the con- of copper. It is not affected is much atmosphere. they are cheaper than copper sistors They are most commonly used as resimple conductors. ductance length and weight. as the same in connection with rheostats and for third rails of electric must railways. centimeter-gram-second solution electric of follows: as international eighteen millionths hundred flow etc. 1894." Qiuintity. "The of nitrate the is system of unvarying of silver at unit which ampere. " quantity of electricityconveyed the to second. 89. that second and potential and This foot. in than Force force to as resistance tend flow. expressed practical equivalent of passed through with accordance of current minute. called the electric an Electromagnetic is the current It as cubic The feet per shall one-tenth of the be by unit of electromagnetic imits and which when thousand one is the of the a and The unit of of flow the of later. such From as this definition is analagous cubic the Difference of of flow of electricity. but not it consists pipes. cur- in water a in one gram per second. Units. etc. for it through water electricityis When electricitythrough ELECTRIC THE that direction same IV the of rate of (0. potential difference of may when will volt voltage of a . and ampere as in many drop. the gallon. The is thi voltyand impressed cause now normal a is defined across current more Weston the of one an as is equal in ampere quantity one of water of that terminals ampere electric current rather electromotive unit one unit Electromotive specificallydefined cell.deposits silver standard The water. in coulomb The hydraulics. current circuit resembles a forced are vestigat in- recent infinitesimal of electrons these CIRCUIT known. (emf. as will be shown act. specifications. rate Congress. gallons per is defined ampere of current to ways The " represents the corresponds in hydraulics charges incompressible fluid would an Current. etc. acts results. H.CHAPTER LAW OHM^S The exact AND of nature indicate electrons.).) 01830 The of to cause which one a of emf. (See Par. or ohm international oi the ference Dif- " potential difference a amperes. of act an is known what travel unit of flow to the rate second. undergoes pressure 63. per Potential by the to it is evident expressed in coulombs be is quantity is the coidomb..001118) rent. the as in offlow of electricity. this pressure drop being uniform. Nature through through ohm. in Fig. that resistance which will allow one pere am- The its terminals. current cause closed system Electricity. Vi at in practically the generator to vz at the motor the same manner that the water pressure dropped in pipeFi (Fig.The flow of electricity " in many ways the flow of water of pipes. impressed across is specifically defined as the resistance of a at the temperature of melting ice (0" C). Ill flow if one to to flow. The water then flows out along pipe Fi to the hydraulic motor W. The terminal current now of the motor. 64. The line ab shows the pressure drop along the pipe. a pressure of A2 resistance of the pipe Fi. In virtue of the action a of the increased blades. the potentialdrops from resistance. The pressure in a boiler tends to cause to flow through the pipes.OHM'S LAW mechanical The in AND THE cause the dam tends to the flow of water.4521 grams a length of as has alreadybeen resistance. In Fig. the ends of between 49 CIRCUIT analogy of potentialis hydraulicpressure tends to ELECTRIC or behind through the penstock or steam through any leaks. Because of the friction loss in the pipe Fij the pressure at the motor less than A2. 52 the mechanicallydriven electrical generator G raises the potentialof the ciu-rent enteringits negativeterminal. For example.representinga net increase of pressure Hi. as from ing v\jv'2) etc.51 water enters P at a pressure the mechanically-driven centrifugal pump of mercury) above hi (representedby the length of a column the point of zero pressure shown by the line ho.) The generator.etc. In other terminals hz is slightly the frictional A3 is requiredto overcome words. the unit Chap. A voltage Because of the line .51).300 of a constant cross-sectional area and of cm. The defined in " international ohm column of mercury 14. 106. Likewise difference of potentialtends to Resistance. hi to " from V2 where vi to vi and V2 are potentialis ordinarilyassumed are measured the a the earth whose (The various voltages zero. of the Flow of circuit resembles a of volt is in mass.valves.its pump from pressure is through the pump A2. water cause The pipe causes of water pressure flow to a ence differ- The pressure. in raisthis portionof the circuit from vi to V2} produces with voltmeters potentialof increase in pressure vg vi line to the Li the + through net flows out measured "" = Vi. The hne a'b' shows the actual voltageat each point alongthe wire. Flow " " Flow of water of electric current through an feeder system. Pressure hi must necessarily flow back through the pipe F2.representing be greater than hi in order that H2. 62. This voltagedrop is uniform. V2 " Fig. the distance of a*b' from the ground line being proportionalto the voltageat each point. to overcome hi hi is necessary " . 61. the water enters the hydraulicmotor and in overcoming the back pressure of the revolvingblades its a net drop in pressure pressure drops from A3 to A4. and the connecting W Referringto Fig. an through a hydraulic motor and electric motor pipe system. 51. The pressure the water may the friction loss in the pipe F2. Fig.50 DIRECT vzia necessary CURRENTS to force the current through the line Li. . of +3 volts whereas the potential 2 or 1 volt higherthan of 3 Therefore the point c is at a potential When d. In Fig. 56.there same. The batteries Two " equal electromotive they because no current are having forces. The emf. level in the tank and in the reservoir is the water that is.and by a copper consequently there " wire can difference between a and b must through which be no potential Therefore points the ends of the copper wire. of battery Bi is 3 volts and therefore the potentialof its positiveterminal is 3 volts above that of its negative terminal.DIRECT 52 The pipeP. connected flows. electromotive unequal Fig. in virtue of c being at a higherpotential than d. will now Fig. the point c is at a potential of d is +2 volts. CURRENTS is pressure in each but there is no difference When the valve V is opened.likewise the + terminal of A 2 The its negative terminal. occasionallythat absolute potentialis of interest. batteries Two having forces. Measurement ^Voltageor potential measured It is only difference is ordinarily with a voltmeter. positiveterminal of ^1 has a potentialof +2 volts above its negativeterminal. of potential because there is no difference between a and 6. If closed. Fig. 56 the emf. 55. if the valve 7' ence level in the tank to fall. 66.no water them.no current will flow from a to 6. The voltmeter of potential difference now the - " . is opened. of battery B2 is 2 volts and therefore the potentialof its positiveterminal is 2 volts above that of its negative terminal. If this potentialbe assumed zero. has a potentialof +2 volts above potential negative terminals of both batteries are at the same of 2 volts. The negative terminals are at the same as potential. switch /S'is closed. each be at the same potentialof +2 switch S be volts.a current will flow from c to d. in pressure between flows from the reservoir to the tank. Ordinarily is the quantity desired. of Voltage and Current. 55 shows two batteries Ai and A 2 each having an emf. a differ- the two tanks will result and water of pressure between flow from the reservoir to the tank.allowingthe water However. Ohm's of connecting Ohm's Law a voltmeter that for and an ammeter. (17) R in amperes in a circuit is equal to the emf. measured with an ammeter. steady current circuit is directlyproportionalto the electromotive a acting on the circuit and is inverselyproportional " states a in the current force to the resistance of the circuit. When of water the ammeter is so connected. The current law be may expressedby / is in amperes. As ciu-rent Current is ordinarily is the quantityof electricity per second passingin the wire.the ciurent Potential difference be representedby either the letter"F" or "-B. justas a water the wires of the circuit and inserting is inserted in a pipe when it is desired to measure the flow meter in the pipe.the must ammeter be connected so that only the current to be measured of passes through it.OHM'S LAW AND THE therefore should be connected ELECTRIC or across 53 CIRCUIT between the wires whose potentialis to be measured. This is accompUshed by opening one the ammeter. the E is in followingequation if the voUSyand the resistance R is in ohms. " Proper method Law." V usually meaning terminal voltageand E electromotive force or induced voltage. may . across (SeeFig.) Never connect an ammeter of difference Ivoltmlter ^^Load Generator " Fig.the current passingthrough to the load is measured by the ammeter. 67. 57. of the circuit in volts divided by the resistance of the circuit in That ohms. is. the emf .57.57. the line. as shown in Fig. " The terminals of the voltage across What is 4 amperes. " are r- .i " i? thlS part of ^ the circuit.83 - Am amp.2 X 48 = 153.6 volts across field windmg Ei = IR2 " 3.2 amp.equation(17)becomes JS? "e^q /R = ^1-8. 58. is. This formula of emf. sources a generator field is 220 is the resistance of the field circuit? E -. i%igitizedbyCjOOQlc etc.6 V uct 1 the resistance in Voltage drops " across current SOUrceS r of emf. 55 ohms. will flow through the winding when it is connected across The " current 116-volt mains? / I ^ - " 3. stated in Par.the voltage across across voltageacross the generator terminals? ohms. An". provided the is steady and there are no '^~~ FiQ. = connected Ans. i " Wlthm j.CURRENTS DIRECT 54 Example. R . provided the current is steady and there That are no Example.2 volts (check). if several in series. _. 58.2x22 (18) -70. is.0 Also E I{Ri +R2) = - (22 + 48) 3. 224.if equation(17)be solved for the resistance the result " f = is (19) . a " f generator field and its rheostat.0 = Again. 118. j^i = /i2i = 3.) If the field current is 3.4 volts across rheostat Total volts at terminals. 39. the voltageacross any circuit ^^ is the to ^ equal prodP*^ That fj^Sx 48-163.the resistance of a circuit is equal to the voltage divided by the current. useful in volts and within the circuit. the fieldcurrent is very (See Par.and the the field winding terminals. 224. and ohms.2 A. " resistance of the field winding of a shunt generator is 48 ohms and the resistance of its rheostat is 22 (See Fig. 4 ^ ri + r2 That + u. By transformation.4 V. What resistance of the fieldwinding of a shunt motor is 30 ohms.. ic =s 220 = -^ " 1 68. The Example. The resistances sum Series Circuit. (20) . in amperes of the current 8. what is the voltage the rheostat.2 X 22 = 70. the total resistance is the As was of the individual resistances. j.) making resistance measurements. 59. across circuit of = ^1.OHM'S and LAW AND ELECTRIC THE 55 CIRCUIT the current R Example. " + ri r" relay is connected ^A 50-ohm + (21) rs + in series with resistance tube a The small pilotlamp having a resistance of 5 ohms. =^-^^^"^P- ^=50+30+5^-85 a forming trans- into resistances. r2. consistingof resistances ri. The Parallel Circuit" In Par. 59. operatingvoltage is 115 volts. 69. /a = current in r2. equivalentresistance be R 7 ^ = R I for 7i + 72 + 78 Substituting E ^-h"^7A) or l=i R + Ti l Ti + i n (22) . + /3 = ^ ^+ ^1 Let the total current Let the ^ + = r^ be / rz /i + = ^(i + \ri l r2 + i) rj /a + /s. 39. Then E h (equation17) = r2 E /3 = rz\ Adding these together: /. proved by be may E follows: Consider Fio. What current flows in this relay circuit? and with of 30 ohms a 115 116 . and Iz the current = in r%. " the Fig. + 7. A parallel circuit. and rz in Let I\ the current in resistance parallel the voltageE. . ". the relation of total resistance the circuit parallel proved by was conductances This equation Ohm's Law as to in resistances component Arts. Fio.) divides between of 12 amp. A current part passing through a branch having a resistance of 8 ohms. " a or (25) circuit of two branches.42 amp. That If but two resistances involved. in parallelacross a source. two paths in parallel.in a parallel as the resistances. Determine of 4. Example. and the total current " 10-volt 10 ohms in a circuit consistingof 4 resistances connected respectively. 60.125 0. inversely (Thisdoes not apply to the division That through the field and of current when the motor armature of a shunt motor is running. current passes through " each branch? .642 j^= Ans. 6. 0. are Ti If three resistances R are (23) + ra involved.are nected conresistances.10 + 0. Diyision Parallel of Circuit" Current in a In Fig.56 DIRECT CURRENTS resistance of a parallel of the equivalent is. the other How much branch having a resistance of 12 ohms.167 + 0. 60. 8. (24) = nrz+rirz+rzri Example. two-branch parallelcircuit. two Ri and i?2.25 = 4^6^8^10 R + 0.the reciprocal circuit is the sum of the reciprocals of the individual resistances.the currents are is. 6. in parallel across the in Division of current 60.642 mho = 1 R 1.56 ohms = 0. How Current in 2.6.+/.OHM'S Ji be the Let the 12-ohm LAW AND THE in the S-ohm current branch 57 CIRCUIT ELECTRIC and I2 be the in current branch.g. 4.0 X 6. and fia. the respectivecurrents found as follows can be shown J that _ J l^ ^ :=: I A current in each branch is given by \ : ^26) RiR% -f-RiRz -\-RzRil RzRi \ ^27) R\R% -\-R^Rz "h RJtil ^1^2 R1R2 (Note the cycUc order " a /a. ^-^ (1) (eq. /2 + current I I \ J^ the /i + = / \ Example.= I (1) from in (2) substituting h\^h 12 - f-i. R%. f.) passes circuitof three througha parallel resistances of 2.25) Also /.2 amp = 2 If the circuit consists of three (Fig. h " 4. - ^ J.6 ohms.8 7.4 and 6 ohms. respectively.0 does the current divide? ." Division three-branch parallel circuit. 7. = (2) 12 /. : Let / be the total current It be may H" R2RZ of the of 25 amperes + \ RzR\l /28) subscripts.61) branches Ri. ^2^8 ( \ in of current ei. 0 35 6 Current in 10 n = Current in 12 a = -r^ or 3.78 amp. 110.7 volts El = 6. ^A circuit may consist of Series-parallel of parallel resistances in series with other resistances or of resistances as shown in Fig.6 volts Et = 6. each group of parallelre^"^ into itsequivalent Ex sistances is firstcombined """"f" singleresistance by equation (22) and the groups " " ioii| |wA u"v.0833 + 0.09 amp.97 amp.45 = 35. as 32.54 X 6. Electrical Power. is then treated whole Example.56 " amp. Determine " circuit. = Ri Likewise -^+ 4 10 lii first the Combine into ~ the 10 and 12 resistances ohm 0. "" -j~- 2.39 + aKA ^ ' ^ 5 + mho 0.62. 41 7 in 15 Current a = -7^ = 2.54 unit power (check).45 ohms " combining the of three resistances into Rt group 110 110 5.53 amp.54 X 5.54 X 5. 6. lo 41 7 Current m 20 a = -^ Current in 25 Q = -"V 41 7 1-^7 amp. determine circuit shown Fio. the series circuit.10 = the in the in each resistance. = Total (check). E.1567 = ^T voltage resistance R\ a 0.0 E2 = 6. Series-parallelcurrent " total current each portion of the circuit. determine across 62. The Circuit.45 6-^""^P- r6784 6. groups In tUa case. watt and is defined fallingthrough a as " the The 6. = Zo Total 62.68 DIRECT CURRENTS 61. = 2.7 volts = Total volts (check).1833 = mho 1^ 5. 62. of electrical power developed by potentialdifference of one one volt. a in Fig.39 -- 41. is the ampere Watts in are . . 000 kw. total work done and is equal to the power multipliedby the time during which it acts justas distance covered is the velocity rate of motion or multipliedby the time.000 ft.000 watt-seconds. 2. Ans. The correct cents expression is per The '^electrical energy and energy is rate of power is sold for so many cents per kilowatt-/wmr. /0..-hr.000 ft. " If energy is sold for 10c per kilowatt-hour be purchased for 20c? This question as kilowatts may answered.-lb.60 DIRECT CURRENTS is the rate of doing worky Energy. = Ans. with horsepower. depending oil the kilowattSy similar way. energy is the velocityis rate of motion. it is assumed be that the is to be used for 1 hour: power 2 kw. 2 kw. "electricity kilowatt" is incorrect." is in volts.2kw. Power is the rate of expenditureof energy. Ana.-hr.)is comso monly purposes. available 20c/10c hr. To speak of a train travelingat a rate of 40 miles per hour gives no information the train travels. if " is in used. just as clearlyborne in mind. how (kw-hr.-lb.001 hr.to to the total distance which as of energy that speak of 50 kilowatts does not state the amount The statement is sold for so many is involved. joulesor 1 kilowatt-hour 1. = = = that the 20c could purchase any number time during which the power is supplied.).the kilowatt-hour (kw-hr.per mirivie and not to 33. the korsepower- .-hr.-lb.000 = X 60 X 60 = 3.and / is in amperes. A motor developingJ^hp.5 hr." illustrate: To Example./O. of work if allowed 8 minutes In When hour a speaking of work in connection is the unit ordinarilyused.-hr.OOlhr. Likewise. On the other hand. many it stands cannot If. difference between (orwork) should be Power doing work. since the time is not given. so of kw. Electrical " W E = 1 1 watt-seconds seconds. energy is the wait-second or joule.000 ft. is ordinarily The watt-second too small a unit for commercial the largerunit. 2 kw./l If used in 0..however. 4 If used in 0. horsepower is rate of doing work and is equivalent to 33. The unit of electrical energy 63. electrical Therefore or is equal to the product of electrical power and time. could do 33.2 kw.5 hr. in which to do it.600. -hr. the remainder energy. used energy supply lamps. and be used for chemical processes.2 Mechanical 65 Distribution system utilization) Small Lamps motors (to point of Light 2 (av.0 Turbine Mechanical 25 20.as chemical energy.conversely. X It is well known that heat may and electricalenergy. The energy is brought to the plant in of the coal combine The ingredients the coal.0 Generator Electrical 95 19.) Heat units converted 100. etc. 10^ watt-seconds.and large units.bus-bars.460 64" Heat and X 5 2. of the air.thus convertingthe chemical energy with the oxygen The ferred certain percentage of this heat is transThe expansion of the to the boiler and produces steam.460wat1"-hours = Ans. ^How hp. " 10 a developing motor hp. is heat in the wires.0 80 80.-hr. Ultimately all the may again as heat or else is converted into chemical appears to some energy other forms or of energy. operate motors. mechanical 61 CIRCUIT suppliedby are = 746 hp. 7. propel electric cars. complete cycle of energy transformation is well illustrated by a steam power plant.OHM'S Example. for 5 hours? " 2 AND LAW watt-seconds many 2 X 10 7.32 .0 Electrical 85 16. A and blades or through the buckets enginecylinders. into heat energy.converts the heat energy of the steam into me- in the steam of the This mechanical drives the generator. into electrical which converts a large percentage of this energy A portion of this electrical energy is transformed into energy. chanical turbine.X 3.5 0.condensers. EfELciencyof Energy Conversion Form of energy Coal Chemical Boiler Heat Efficiency (per cent.600 into mechanical electrical and ELECTRIC THE energy be may be verted con- that and. followingtable shows The 100 units heat modern power approximatelywhat becomes of each in the coal in the most efficient existinginitially plants. converted into heat.using superheaters. Finally.68 = Energy.) 10. (called the Mechanical Equivalent of Heat).2 watt-seconds or joules. 330.u.page 407.24 PRt = calories (36) 4. A. XXXIV page = = 3.2 where t is in Example. system the heat unit is the gram-calorieand is equal to the amount of heat requiredto raise one of gram 1 C. *See Appendix A.63^ (by R. unit of heat in the English system is the B. ^ water is equalto 4. I.34 Vol.-lb. many F.000 ft. very 8S4 Unltt i UaltslllO Mm Fio. is the temperature of the water raised by the action of the pump? of water " 10 per minute hp.000 8. E.62 DIRECT CURRENTS Fig.U. The " " TF - A PRt 0./ in amperes and R in ohms. Trans. E.t. per min. seconds. 63. 779. 400 gallons horsepower is delivered by a pump circulating How certain a cooling through degrees system. Thennal flow IM Its IW 108 T800 moo 190 1"K" B.u. pw MIb.G. (Britishthermal unit) and is equal to the amount of heat requiredto raise one pound of water 1" F. 330. 33.000/778 400 gal. Digitized by GoOglc . 424/3.T.S. Philip)shows graphicallythe flow of power It is apparent that from the boiler to the point of utihzation. is in the most modern plantsthe over-all efficiency even power low. = 400 X = 0. mechanical " and electrical transmission. It is equal to 778 ft. In the C. = 10 X = 424 B.13" F. Energy " 66. A gram-calorie By Joule's Law the heat developed in a circuitis: Units.336 10 1 A. thermal. Ans.per min.336 lb. . (1915).-lb.t. 000 CM.0862 ohm. of 250. the net voltage the voltageat the at the receivingend of the line is less than sending end by the voltage loss in both the (mtgoingand the be the drop in 2. 54.000 ft.0862 = 21. Load. LAW incandescent An " is immersed AND in small a W 63 CIRCUIT from 110-volt mains lamp taking 0. the voltage at the motor that at the bus-bars because of the voltagelost in supplying was the resistance From Table drop in the feeder. . shown is 250 amperes.5 amp. The feeder is connected negativewire)supplyinga to bus-bars having a constant potentialdifference of 230 volts. degrees per minute is the temperature many tank Neglecting radiation.by how of the water ELECTRIC THE raised? 0. Therefore return taken. maximum load on the feeder is 250 requiredto determine the voltage at the of transmission. long and consists of two 250. of water.000 66. containing 2.OHM'S Example. the effi-ciency It is and amperes. of cable must wire. " Voltage drop in a due feeder to a single load. " The conductors. As was in Par.24 = 0. be less must stated in Par. The feeder is 1. 0. of water.396** C. 60 X = 792 - Feeder Suppl]ringOne Concentrated feeder (consisting of a positiveand a Fig.0431 The By ohm. Potential Drop in calories per minute. the total resistance being 0. As than 64. 54.000 ft. Ana. equation(18)the voltagedrop in the line: current E' = 250 X 0.55 volts. 64 shows a a motor load.000 ft.000 CM.5 X X 110 792/2. the resistance of 1. 51. terminals motor "^woo^ : 10J8 Volts arop In + Feeder _|^_iiqjVollsdroplB "Feeder Fig. cable is 0.000 c.c. 65.4 output ^ ofc the 1Ime efficiency ^^ shown.6 - terminals is motor 208.and there is a uniform drop in each wire.000 CM.4 volts.64 the voltagedrop along the line is shown graphically.000CM. Potential Voltage drops in Drop supplies200 amperes 150 amperes to is maintained each in a a to a a Feeder at Diflferent Points.4 250 X = ocn 250 v" X ~7^^?r 230 cent. load 800 ft. the total line at supplying two SupplyingTwo loads. as watts. on. farther constant 300.8 volts." Loads 1 900.8 or With one concentrated given by the voltage at sending end of the line. this drop increasinguniformly to 10. = ^ -" = 90.64 DIRECT Therefore CURRENTS voltageat the the 230 21.determine and the efficiency of transmission. 208.2 = The power delivered to the motor The power deUvered . is 0.000X 0.6 volts tential difference between the two wires 500 ft.8 volts 219. The pomaking a total voltageloss of 21.0360 From = = 0. " 67. In Fig. from the sending end will be 230 - 10. Concentrated feeder 300.000 ft. The voltageat the sending end of the line is 230 volts. 240 loss cable Table 51. watts. 65 load 400 ft. The resistance of 800 ft.000CM.000CM. of 300. per of transmission is efficiency load divided by the voltage at the load the the -w"" I Bob I 300.000 CM.4 = to the line 230 = ^v.0288 ohm. 800/1. The 208. from the bus-bars. = Am. SOOA. 250 X -^^n 230 mput 250 X 208. FiQ.0360 ohm. Bars feeder load. a If the bus-bar voltage the voltageat volts. the resistance of 1. and In Fig. . ) The voltagedrop through a cir. a to assume a ^^"^ ''^''^' 1. 65.000 cir. load Ei 4. having one circular mil a With any a cross-section.2 - 219.001 cir. load to 0.-mil-foot.8 = graphically Fig. = Voltage at 150-amp. determine To Line loss to Pi Line the 200-amp. = 0.8 volts. voltage distribution along this line is shown The in 219. 7.-mil-foot carrying0. = Arts. load to (2 X 0. 0. load i^i Resistance of 240 = 20. load the 400/1. mil.0144 = E" the 150- to ohm.37 ohms.0144) 150 = Arts.0288) = loss from Pi efficiency: Total 200-amp.000 350 X of Feeders. 150-amp. cir . = Voltage at 200-amp.001 or ^ stated in Par.000 X 0. (Bus-bars and large feeders operate at a a In many Assume value of 10 ohms.001 ampere is: " Another drop of //? 0.0144) X (equation30). load to the E' THE 20.16 volts. the two wires. line loss P1+P2 = 649 7. mils per Call this the normal ampere per cir.001 X 10 carrying0.5 volts.each = 0. ampere. = (240 X 350) - _ " " 240 68. . 4.OHM'S LAW Voltage drop AND (2 X 0.0360 Voltage drop from 200-amp.709 - _ ampere.0288) 350 = ELECTRIC 65 CIRCUIT 200-amp. den- density very nearlyequal to this. 42 that was feeder to be a 76.290 84.060 + Efficiency losses input input 7.3 - 215.709 watts = or 7.060 watts ^ 649 = watts (equation30).-mil-foot of copper cases 7. side. = cable from one 200-amp.01 volt. the drop number = across its ends.32 volts.01 volt. If these be will also have placed side by will stillbe 0. load (350)2(2 X 0.709 kw. Estimation has itissufficiently exact the current densityin It " ^^ ^'^ ~ resistance of 10.01 volt between of = 0. current sity. load load amp. load (150)2 (2 = 150-amp. each of 1 The voltageacross cir. Further if the density is other than 0. be used. In Fig.000 CM.000 X ~ = 100.66 (b)jthe drop remains 0.\\ Pig.66 DIRECT ft. must The voltage drop across current the 1 Oir. the total be 0. smaller cable may 16 500.01 The the drop across wires may be separatedor they may be made into a cable.001 ampere Fig.001 ampere per circular miljthe voltage drop will be in direct proportionto the current density.01 The X 1. four conductors ea^h must be 0.001 current a wire will be ampere. Ans. If any a cir. number of cir. = becomes then X have densitymust A cable to operate at the normal 800 X allowable drop is 20 volts.001 ampere. voltagedrop shall not the power house is to take 500 amperes size cable is necessary in order that the 800 ft. 0.01 The voltagedrop per foot of copper volt providedthat the current densityis 0. volt. From the foregoingthe followingrule may be deduced: condicdor is always 0. In Fig. J Example. .-mil-ft.001 amp. conductors each added in parallel to the group of are carrying0.-mil-foot and each carrying0.-mil foot. from What exceed 20 volts? 500 The total voltagedrop 0. group Voltage drop in " is still0. HiL ^/.01 volt.001 ampere per circular mil.01 volt.01 volt.000 500.page 54. and length of one the ends of each CURRENTS of 0.004 ampere.000 CM. from A " motor 230-volt bus-bars.so 2 = a 16 volts. 66. 66 (a) are shown four separate conductors. This last follows from equation (18).66 (b)these same are grouped togetherand as each carries 0. . CHAPTER ELECTROMOTIVE BATTERY V FORCES" KIRCHHOFF'S LAWS 70. Battery Electromotive be connected the switch S the across beingopen, Force and Resistance. of terminals the instrument a If a certain vol tage now the instrument The a delivers kvvwvvvO Fig. 67.- -Connections for measuring battery resistance. will voltageV which E. ured voltage E, measthe batterywhen Tm. Battery switch the is less than di the be record '"^ meter volt- closed, allowing current I to flow, S Ne". a battery (Fig.67), willrecord E, If " no current, is internai voUage or the electromotive force of the battery; the voltage Vy measured when I flows, current a the is known as the terminal, value. particularcurrent age The difference between the open-circuit voltageE and the voltVy measured when current is being taken from the battery, of current is the voltagedrop in the battery due to the passage ance, through the battery resistance. Every cell has a certain resistbut partlyin the lyingfor the most part in the electrolyte, the external circuit is When battery plates and terminals. closed so that current can flow, a certain voltage is required tage to send this current justas volthrough the battery resistance, is required to send current through an external resistance. If the voltage-B,measured the at the battery terminals when circuit is open, drops to V when the circuit is closed, the voltage voltageof the battery for that 68 ELECTROMOTIVE BATTERY e (E = V) is " of the passage by Ohm's voltage drop through the /. current Let 69 FORCES the cell due cell resistance be the to the r. Then, Law, E V " e = Ir = (by equation 18) or r = = - (by equation 19) " I / E Ir V + == (37) (38) is,the internal resistance of the battery is equal to the open-circuitvoltage minus the closed-circuit terminal voltage the circuit is closed. divided by the current flowingwhen That Example. The open-circuitvoltage of when a current voltage measured What 1.98 volts. The is the internal voltage drop through JS; y " Then In r of 12 amp. flows is found resistance of the cell. The to be the cell = ^ = storage cell is 2.20 volts. a " terminal 2.20 1.98 " ohm. 0.0183 = 0.22 volt = Ans. making a bered character,it must be remem that under open-circuit conditions even the ordinary volt meter takes some is small current. (as in the voltmeter of this measurement current case of If the cell Weston a alone may capacity cell)the reduce terminal less,of voltageto a vajue one-half,or the open-circuit voltage. Under conditions voltmeter the the electromotive measure cannot the even these be used to force of the cell. rectly diMoreover, it is impossibleto measure the internal voltageof the batterywhen the battery dehvers current, for the voltage Fig. 68. The internal vnthin the cell itself. Fig. 68 "drop occurs resistance of a cell. " represents these effect on enclosed from but as The within so far as their external circuit is concerned. the in conditions a sealed box. the Its resistance cell itself and the sealed box. The A r connected cell then battery cell B is is considered as external to the may moved re- cell, be considered itsresistance having been replacedby r. resistance, connections are brought through bushings in the box to having no 70 DIRECT terminals a and 6. CURRENTS When being delivered is current no by the two terminals a cell,if a voltmeter be connected across and 6, the instrimient will measure the emf.,E. If,however, a current / flows,the terminal voltagewill drop from E to V, due to the voltagedrop in the resistance r. Under these conditions it is impossibleto measure E when since is flowing, the current the voltmeter outside the resistance, can only be connected through which the voltagedrop occurs. The voltage E and the resistance r are seldom constants but less dependent upon are or the current. more They are also affected by temperature, change in specific lyte, gravityof the electroetc. polarization, in Par. 71. Battery Resistance and Current. As was shown 70, the resistance within the battery tends to reduce the flow of current. the cellelectromotive If,in Fig.67, the switch be closed, force E will be acting upon of the internal a circuit consisting the " resistance of the cell r and the resistance of the external circuit jB. resistances The and r the circuit is their the total resistance in being in series, R The sum. ' The is current = ^^^^ TTH lost in the battery is power P 7V = E R becomes If the cell is short-circuited, and 7 zero = Under " r these all the electrical energy developed into heat within the cell itself. conditions is converted Example " ^A battery-cell having an of 0.10 ohm. What electromotive an ohm of 0.03 internal resistance is connected flows and current what is the to by the cell force of 2.2 volts and an external resistance of the battery efficiency used? as ' Power = o^j|^^-^*'^Po:o3"aIo = = (16.9)2X 0.03 (16.9)2X 0.10 8.67 watts. = useful power P is equal to battery loss. P ^"''- lost in the battery P' The = the = total power 2.2 X P = Oft 16.9 37.2 ft 28.6 watts. = developed by the battery minus = - 37.2 watts 8.6 28.6 = the ELECTROMOTIVE BATTERY 71 FORCES The be deduced: above, the followingrule may in a circuit is eqibdl current to the total electromotive forceacting in the circuit divided by the total resistance of the circuit, 72. Batteries Receiving Energy. If a resistance load be will immediately flow from connected across a battery,current the positive terminal of the battery and will return to the battery though itsnegativeterminal. As has alreadybeen pointedout, the battery terminal voltage will be less than its open-circuit value, of the due to the current the internal resistance flowingthrough of battery. Under these conditions, the battery is a source and is acting as a generator, that is,it delivers energy. energy From the " FiQ. 69. Generator " charging a battery. is forced to erder at the tery, positiveterminal of the batthe battery will no longer be supplying energy but will be suppUed from some be receivingenergy. This energy must other source, as from another battery,or, as is more common, from a generator. The cell shown in Fig.69 has an electromotive and a voltmeter F, connected across force of 2 volts, itsterminals, If current indicates 2 volts when electrical energy, flows. current no If another of source direct-current generator, supply a potential difference of just2 volts and its + terminal be connected to the + " such as a terminal of the battery and its terminal connected " terminal of the battery, as in the shown V will stillread 2 volts and the ammeter the battery neither delivers is noted other circuited. than Under those these nor noted A the voltmeter figure, That is, willread zero receives energy when conditions to the the and no battery stood battery is said the effect opento be "floating." If,however, the voltageof the generator be raised A will indicate a current flowing from the the ammeter slightly, 72 DIRECT + terminal of the CURRENTS generator into the + terminal of the battery, direction justoppositeto that which the current had when the The voltmeter will no longer read 2 batterysuppliedenergy. in excess volts,but will indicate a potentialdifference somewhat a of 2 volts. What actuallyhappens analogy. Fig. 70 shows a be illustratedby may a mechanical standing on the track. A force of 400 lb. is necessary to overcome the standing friction of the end of the car a force F is applied. the track. At one on car Before the force F can move the car its value must at least equal F is exactly400 lb. the car will not move, 400 lb. When just car as " Force necessary to start a flowed into battery when the generator voltage was just of the battery. equalto that ^^^^^^ 70. cm-rent the 400 Lb. Fig. no car. When the force F exceeds the force effective in lb., however, the car will move, by which F exceeds producing this motion being the amount 450 lb.,400 lb. of this is utilized in over400 lb. Thus, if F coming the 400 lb. opposing force due to friction and 50 lb. is effective in moving the car. In the case of the batteryno current will flow until voltagein of the 2 volts is produced by the generator. Thus, if the excess 2.0 volts of this is utihzed generator voltagebe raised to 2.4 volts, 400 = 2.0 volts of the to "buck" in sending current the into the / assumes its volt is effective Thus, if the cell resistance = Q" 4.0 amp. = that the resistance of the leads is Therefore,if resistance and cell. 0.4 will be be 0.1 ohm, the current This cell and JB? is the electromotive V the terminal force of voltagewhen negligible. a battery,r its current flows in at positiveterminal, E V ^^-Z^ " I = (40) r and That E = V - Ir (41) nal is,the electromotive force of the cellis less than the termi- of the resistance drop in the cellitself. voltageby the amount These equations should be compared with equations (37) and Digitized by (^OOglC (38),respectively. ELECTROMOTIVE BATTERY 73 FORCES the cell is receiving electric energy, as conditions, is the case when a storage batteryis being charged. 73. Battery Cells in Series. Strictlyspeaking, a battery consists of more unit or cell. However, the term than one also to mean a singlecell,when this cell is battery has come not actingin conjunctionwith others. their electromotive forces are cells are connected in series, When added together to obtain the total electromotive forceof the battery and their resistances are added together to obtain the totalresistance of the baMery. Thus, if several cells, having electromotive forces,Ei, E2, Ez, E^j etc.,and resistances ri, r2, rs, r^, etc.,are connected in series, Under these " , the total electromotive E force of the combination Ei + E2 + E3 + ^4, etc. = (42) the total resistance is and r + n = Equation (42) assumes " is so an that forces ^ preceded by El + across + If any force opposes is connected then by equation (39)the series, = all connected additive. are be equation (42) must external resistance R / cells are the (43) r^y etc. + rz its electromotive that so its voltagein If + their electromotive that connected be r2 a the Four + R ri + is current E2 + Ez + r2 + rz + sign. cells in Ea, etc. .^v ^^ =: r cell others, minus these to r,, etc., + R cells having electromotive forces of 1.30,1.30,1.35, and 1.40 volts and resistances of 0.3,0.4,0.2,and 0.1 ohm, respectively, are What connected in series to operate a relayhaving a resistance of 10 ohms. flows in the relay? current Example, " dry 1.30 + 1.30 + 1.35 + 1.40 5^ ^ 0.3 + 0.4 + 0.2 + 0.1 + 10 = 11.0 A 0.486 amp. Ana. of n equalcells in series has an emf. n times batteryconsisting but has the current capacityof one cell only. thai of one cell, in 74. Equal Batteries in Parallel. To operate satisfactorily electromotive parallelall the batteries should have the same force. The behavior of batteries having unequal electromotive forces can be treated as specialproblems (seePar. 78). " 74 DIRECT Fig.71 shows CURRENTS each having an batteryof six cells, a tive force of 2.0 volts and that the emf resistance of 0.2 ohm. a electrons oIt is clear of the entire batteryis no greater than the emf of cell. The current, however, has 6 paths through which one any to flow. Therefore,for a fixed external current, the voltagedrop in each cell is one-sixth that occurringif all the current passed through one cell. If the internal resistance of one cellis 0.2 ohm, the resistance of the battery as a whole must be 0.2/6 0.033 . . = ohm. ";-2v. Jff"2V, + E'Vf, + JE7-2V. + 4.^"2V. + "7-2V. ''ie-o.s "Jt0.20. "K0.2fi r"o.2Q Fig. 71. "r-t).2Q "rs-o.2n Parallel arrangement " of equal cells. across Example. If the external resistance connected the battery in Fig. 71 is 0.3 ohm, what flows? current Resistance of battery 0.033 ohm. 0.2/6 " = ri, r2, resistances 2.0 ^ = 0:033To:3 ^ ^"^P- ^ = 0333 ^ om ^'^' ^^^' ^^'^' / equal but the resistances of the cellsare not all equal,but by consideringthese rs, r4, etc., the battery resistance r is found (equation (9),Chap. Ill,page 37). as being in parallel If the emfs. are of = 2.0 ^7 the terminals are 1 1^1,1,1,, 1 1 = r fi r^ 1 (45) f-etc. Ti Ti each having battery consists of 4 cells connected in parallel, electromotive force of 2.0 volts,but resistances of 0.30,0.25,0.22,and an the 0.20 ohm respectively. If a resistance of 0.5 ohm is connected across terminals current does of the battery,what current flows,and how much the battery terminals? What is the voltage across each cell supply? Example. " ^A -^^^ofe+ois+o^+oi^^^-^^^^^^1 0.0593 = ohm. 16.87 2.0 2.0 / = = 0.0593 The + 0.5593 0.50 3.58 amp. terminal voltage El = IR =^ 3.58 X 0.5 = 1.79 volts. Ans. Ans. 76 DIRECT The resistance of each CURRENTS ri r' is the resistance of where Since there combination Example, an cell. the resistance of parallel, of the cells of Fig. 72 have current the whole an emf. of 0.9 volt and If the external resistance R is 0.5 internal resistance of 0.08 ohm. what (by equation43) be must Let each " mr' = one in rows n are be must row ohm, flows? 4 X , /=j I 0.08 3.6 0.9 "_- = . . ^ 6.4amp. Ans. "-^^ 0.5 + o (a) To obtain the best economy, group the cells so that the battery resistanceis as low as possible. This usually means a large nimxber of parallel connections. Under these conditions the life of the battery will be prolonged 76. but Grouping of Cells. " the initialcost is excessive. (6) To obtain the maximum current with a fixed external m resistance make the internal resistance ("r') of the battery equal to the external resistance. This is not economical,since only half of the energy developed by the battery is avfiilable in the external circuit; the other half islost in the cells themselves. Under these conditions the batterydelivers the maximum power. action for To the intermittent obtain (c) operation of quick relays,beUs,etc.,group the cellsin series if possible In the example of Par. 75, how obtain the maximum current? Example, The " total battery resistance " 0.08 must should the cellsbe arranged to be equal to the external resistance. ELECTROMOTIVE BATTERY -^0.08 Solving 0.5 = m best Ana, 11 + = 77 FORCES in parallel. series,and two rows if connected in (Eleven cells in series would not operate satisfactorily with the parallel remaining nine cells in series.) The is ten arrangement 77. Kirchhoff's Laws. possibleto solve cells in By " circuit networks many it is of Kirchhofif's Laws means would that otherwise be diflScultof solution. sum of the of wires,the algebraic currents at a pointis zero. (2) The sum ofall the electromotiveforcesactingaround a complete circuit is equal to the sum of the resistances of its separate parts each into the strength multiplied of the current that flowsthroughit, the total change ofpotential around any closed circuit is zero. or (1) In any branchingnetwork in all the wires that meet first law The leavinga junctionis equal to the total If this not were that It states is obvious. current total current the tion. enteringthe junc- so ^^^ would accumulate electricity at the junction. The law is illustrated by Fig. 73. Four currents, Ii, I2, I3, and junction J4 The 0. flow currents meet at Xfs ^ ^^+4a the first three Umard ^^ 1^^ the j,^^ ^3 _ j^^^^^^^.^^ j,.^^j^j^^^.^ g", have junctionso plussignsas add to the quantity at the point 0. they flows away from the junction,so has a minus from the quantityat the point 0. Then I1 + Assume that Ji = Then and /2 + 5 amp.; 5 + 8 + /3 72 - = /a- /4 = 8 amp. 17 = last current The sign as it subtracts (48) 0 and J4 = 17 amp. 0 plus sign indicatingthat the flows toward the junction. The second law is but another application of Ohm's Law Iz = 18). +4 The amp., J4 the basis of the law is obvious; if one current starts at tion (equaa cer- 5 Volt drop in (1) 10 B (2) (1) RmHU ""-1 n 0.a6 Ui=lA B2p2A v. This second law is illustrated by the followingexample.74 (6). In there is a 10. Therefore the net potentialat B is but 9. 10-6 passingfrom A each opposition. 1. having electromotive in series together) and in drop of potentialdue at flow there to the current occurs a simultaneous flowingthrough the 1ohm resistance of cell No.CURRENTS DIRECT 78 and follows continuouslyaround the paths circuit.the batteries is 10 J Consider respectively. " batteries Two and 6 volts and are connected Determine Since internal resistances of 1 and 2 ohms force of the two The current and the voltage at in ^=1 electromotive 6 " = net motive electro- 4 volts* 4 the = + 2 + 5 point A ^. of the circuit until the startingpoint is again reached. 8=^'^ ^^P- being reference potential.volt rise in potentialdue to the of battery No. (a) Voltage relations Fig. every SialO v. necessarily must force encoimtered of electromotive sources voltagebeing given its proper sign.he must with which he started.volt cuit. but around the circuit to 5 force as in the direction of the current 0. Blie aoe to E\ ^0.5 volts greater than that at A. external resistance of 5 ohms.5. an batteries act two forces of 10 opposing (their+ terminals connected in series with the current the electric circuit. Therefore pjotential again have the same pointin tain the a in this passage be equal to the voltagedrops in the resistances.6 Amp. and there is " . In passingfrom B to C there is a drop of 6 volts due to passing from the -|-to the terminal of battery No. an (Fig. ^. 74). 74. 2. part of the cir- is. as is shown in Fig. 1. there is a drop in potentialof 2. When point A is reached the potentialhas dropped to zero.5 X - = = 5 Total + 4 + ( - 4) 0.5 volts due to the current of 0.5 X 1 0.5 6 " 1 " +2.the voltagedrops. These points are illuby Fig. '' 1 No.BATTERY ELECTROMOTIVE 79 FORCES drop of 1 volt due to the current of 0. '' No. A voltagedue to passage through a resistance in the direction oppositeto the current flow should be preceded by + sign.5 volt -- 4. On the other hand.0 volt - = " 2. Therefore the sum taken with their proper of the Ir signs. when passing from the + terminal to the terminal.5 X 2 0. A rise in " to the example. and Ez are con- For " " j " " . should be precededby a + sign. 2 5-ohm = - = res. voltage A drop in voltageshould be precededby a sign.'s ^i.5 volt - 1. direction as the When going through a resistance in the same current.is equal to the sum drops. signsmay be troublesome and is a frequentsource If. - = drops 0. Kirchhofif's second law to specific problems the questionof algebraic of error. 2. the followingrules are kept in mind no difficulties 78.0 volt - 0 = In the applicationof Applicationsof Kirchhoff's Laws.5 ampere flowing through the 2-ohm resistance of battery No.5 ampere flowingthrough the 5-ohm resistance. a in This is further illustrated by the electric circuit shown Fig. 1 2 Total = = forces + - + Ir 10 volts 6 volts 4 volts Cell No.the potentialdrops so that strated a sign should precede this voltage. in passingthrougha baiteryfrom the + terminal.however.so that this voltageshould be preceded by a sign. 74. E2. of all the electromotive forces in the circuit. " should occur. 75. This is illustrated as follows: Electromotive Cell No. This also further a the makes net potentialat passingfrom C In to A C = 9.5 = volts.the potentialrises so that this voltage should be preceded by a + sign. Three batteries having emf . 75. an equation may be written El- + Startmg at I.R. E2- I2R2 + - LRi = 0 / and passingalong the path febcdf: Ez + IzRz " " I2R2 "f"E2 = 0 "r. Example.6) - (/gS)+ 2 - (/il) =0 in Fig. " Fig. I1- + since Ii is assumed to I2- h toward flow 0 = the junction and I2 and Iz the junction. directions for the various currents assumed indicated The battery resistances are asby the arrows. This may be two currents. obtained junctionas b. Application of Kirchhoff's " Fig. to determine With these three equationsit is possible away Kirchhoff's equations for the determination of three Three The third equations are necessary. are Consideringpath ahcday + 4 - (/1O. - Fig. are assumed neglected. Startingat the point a. sumed negUgibleas compared with the other circuit resistances.80 DIRECT nected shown as in differentparts of the network Rij R2j Rz. Ra' are to CURRENTS The of resistances. from the three currents. " Application laws. identical with that shown The battery resistances and compared with the circuit resistances. Ri R. . 75. 76. and applying Kirchhoff's second law the path cibcda.-4V.76 except that numerical to be small shows values a network are used. by applying Kirchhoff's first law to some gives but unknown of laws. path febcdfystarting -3 (7. - 7. currents + V.6-^ is not the current will minus sign a -V\AAA 7. Similarly. + - 7. FORCES 81 6 = U) at /. 4 + " 3-^ solved. + 1. - 0 - or 7i 7. - - 2 0 - 1 - (fi) junction 6. foimd when at K the of actual direction of proper 0. the question of assuming the often arises. = - 6 6 combining with (B) and Current.57i +37. 78 Amplication " chhoff's direction that they all meet in Fig. ^j-2 tion direc- ^Thisis illustrated by the three Ix current assumed equationsare Example. 77. and at the 37. of Par.+ 7. = (C) Substitutingh (C) in (A) 1.) + 37. 7i + 7. 0 37. \^ "8V. - - 37.57i 1. + 7.1) + 37. current be assumed may direction.BATTERY ELECTROMOTIVE 1. 77.67. + 6 = = 0 course of Kir- laws impossible .57.startingat a.5(7. 4. In the " solution of this A j- _i ^ ^ type of problem. h - 1-r^ ing assum- Fig. + 2 + 7. be to the have the such " current have a :i-r^ 0. This condition point (" as is shown is of Considering circuit abcda. that The to flow in either this direction.57. are paralleled.000 CM.000. 2. Kirchhoff's Applicationsof Kirchhoff's Laws. Ans. Further " considerations. a 1. where power In practice.200 ft. Kirchhoff's laws are rarelyapplieddirectlyto electric railway systems./z. 78. therefore toward /2 + /.etc.a 240. 0. is fed to the loads through electric railways.000 feeders are paralleled.two CM. " = Ans. by a ring system of feeders. = 0 = 0.000.volt sub-station at A suppliestwo distributing A and By a distance C. Similarlycircuit fehcdf.starting /a 3 + - /a The three currents - 3/2 - 3/2 + 2 /i. laws might be appliedto problems involvingdistribution systems. since the feeder layout in such systems is usually determined by various operating 80. between distance of 1. Between b feeders of 800 ft.etween A and C.. followingproblem illustrates the possibleapplicationof The these laws.. however. Ans.78. signs before 1 2 and The minus currents were Iz indicate that the assumed directions for these two the actual directions of flow. Only occasionally is it necessary a these laws to power and lightingsystems. Fig.5 amp. 77. since the widely fluctuatingloads which are their location make it impossibleto formulate constantlyshifting to apply definite problem. Substitutingand solving /i I2 /s = " 3 amp. Fig../s all flow /i + 1 - = 0 junction d.82 CURRENTS DIRECT at /. Fig.5 amp. Exam-pie. different feeders and from different sub-stations. " centers B and In . direction to flows in the opposite that this current signprecedingI\ signifies The the + indicated by and that assumed arrow.three 1. " Ring-feeder system. . and be connected deflection BATTERIES SECONDARY AND solution. primary strip. terminal that Simple " approximately now + terminal a 79. may be 84 repeated with various metals. concerned. immersed plates be 79 in that Batteries.however. ^ -Sulphuric "AU"A'/^^MMMM'Ai^MVA^/y}A (a) (5) FiQ. of the strips._-_ sz. 79 (6). the " This copper zinc. copper Voltmeter i "fER^^^S-5^ Copper- Copper Dilute _. copper will be voltmeter appreciable difference no one of of strips or copper sulphuric acid dilute a If two " to the terminals (a). no a ciable appre- This observed. Fig.the voltmeter exists. voltmeter. be replaced by will indicate difference to the shows is zinc in order so far the that the the positive to the The experiment above needle volt. . showing one It will be necessary of as cell. shows potential exists between of the the strips.^. voltmeter voltmeter and may circuit is external to will deflect and that a the connect the read zinc up potential to copper the scale. .Fig. If.VI CHAPTER PRIMARY Principle of Electric 81.::irz. carbon or lead may be substituted for the copper and a potentialdifference will be. 79 (6) its terminals (Fig. if current be taken from the cell shown in Fig. may (sal ammoniac). when consideringsuch an electrolytic cell.zinc sulphate. Furthermore. Fig. Other acids such as hydrochloric.although it will not be of the same value combination.ammonium such chloride common as be sulphate. chromic.and potentialdifferences will may For be foimd to exist. as an acid. Likewise other metals it was for the copper-zinc as be substituted for the zinc. particular tically is current loss in all cells the flow of accompanied by a weight of at least one of the plates. but in praccell.etc. 80) current current be taken considerable from the cell under proper conditions and time. salt solutions be substituted for the sulphiuic. The electrode at which The a the solution anode. vrithin the cell. Again. This is true not only in the case of this . The metal stripsor platesof a cell are called 82.. solution used in a cell is called the electrolyte.but two conditions are necessary. (2) They must be immersed in some or salt. (1) The platesmust be of different metals. Definitions. however. metal " electrodes.SO). the cell through the zinc. the zinc platewill diminish in weight. In order to obtain a difference of potentialbetween the two plates. If current for enters is the (as the zinc. such electrolytic solution.alkali. to the the zinc when external circuit is the copper is positive when to the copper considered.PRIMARY SECONDARY AND 85 BATTERIES example. Fig. the current will flow /row the zinc through the solution to the copper as shown that current flows from zinc to copper For the reason in Fig. it is not sulphuricacid be used for the solution. copper.or even may salt (sodium chloride). Energy is stored in the cell of and the electricalenergy is delivered at the expense chemically. 80. copper necessary that used. etc. found to exist between each of these and the zinc..but the zinc is electro-positive the platesand the solution alone are considered.80) is the cathode. and the electrode at which leaves the solution (as the copper.current by connecting a resistance across and into will flow from the copper through the resistance AB Inside the cell.zinc is said to be electrochemically positiveto Therefore. and the electrodes which In a secondary cell the electrolyte undergo change during the process of supplying current are restored electrochemically by sending a current through the a cellin the 83. this change being accompanied by a decrease of chemical energy Therefore system. Primary Cells. energy Such cellsand cells or batteries are divided into two classes: primary secondarycells. Hence: An electricceU or batteryis device for a transformingchemical into electricalenergy. from time to time to renew primary cell it is necessary and the electrod^ the electrolyte which goes into solution by fresh solution and new plates. In 80. chemical a into current. 81 that and generating an electromotive force and of such combinations only a limited number practicable. delivering wastage of the materials when . ^pP^-o o Ottthode Anode 3^ LAAAAr-" '//////^////^//////X/. " Current-flow in a single cell.86 CURRENTS DIRECT the platewhich of the goes into solution. " are Although it of metals combinations many was stated in Par. solutions so are a commercially good cell are as follows: (a) There the cell is not must be littleor no current. Fig. That is. there reverse direction.respectively.one plateis either oxidized or converted into another chemical compound. is converted energy the cell delivers when electricalenergy.The general requirements of of capable forming a cell. which reduces the every the terminal voltageto drop magnitude of the current and causes when current is taken from " was the cell. tive Increasingthe size of the cell does not increase its electromothe force. The crossthrough which the current flows inside the largeas is practicable. V. at least for any appreciabletime. Fig. 85) would be excessive.Thus. with a greater current capacity. Such resistance lies in the in the contact surface between the electrodes and the electrodes. and the electrolyte. cell or batteryhas an internal resistance. 84.and therefore the battery would be capable of deliveringonly a comparatively small a " moderate electromotive 87 BATTERIES SECONDARY AND current current.otherwise the battery cannot not supply even values of current. materials.Also the crossarea section of the platesmust be largeenough to carry the current to the cell terminals without excessive drop in voltage. the resistance of the cell may be diminished area by decreasing the distance between the plates. practicable. Internal Resistance. even were no away (see Par. The cells are bucking each other.PRIMARY (6) The to enable force must the cell to deliver a be of such reasonable amount a magnitude of energy as with flowing. and in the electrolyte itself.because both the copper and the zinc would waste the batterydelivering Polarization current. moderate the cell shown in Fig. 79(6) would not be As an illustration. (d) The internal resistance and the polarizationeffects must be excessive. as . This resistance may electrolyte.This means large of electrodes in contact with the electrolyte. of the cell in the same be reduced by changing the dimensions way as would section of the be done path cell should be made for any electric conductor. Little is experiencedin making this voltagedrop negligible. diflSculty It will be appreciatedthat largerelectrodes mean a largercell. up of the same differingmateriallyin size. (c) Frequent replacement of materials must not be necessary and such materials must not be expensive. This electromotive force depends only upon material of the two electrodes. As pointed out in Chap. This reduces the length of the path through which the current flows within the cell and correspondingly reduces the cell resistance. but made 81 shows two gravityieells. In addition to increasingthe of the electrodes. 88 CURRENTS DIRECT terminals is. AB represents the voltage drop due to the internal resistance force . 81.ammeter. the fall by connectinga cell. their + terminals are joined and their are joined. external resistance as in Fig. 82. When the switch S is closed. Fig. E. of terminal of electromotive If " voltageas voltmeter. " Drop the cell electromotive of voltage in a cell due to polarization. as a follows: open-circuitthe voltmeter will indicate Time Fig. 82. Equality " 85. a test current and an the results will be somewhat When the cell is on forces be in made is taken from cells of to unequal determine sizes.current will flow and the The distance voltage will drop immediately from OA to OB. 80. Fig. representedby the distance OA. A galvanometer G connected in one of the leads that no current flows from the largerto the reads zero. indicating that " smaller cell. Polarization. cathode or positive opposes that of the cell. It glassjar. These effects two explainthe of many types of cells after time. Zinc Stilplmte Solution The bubbles be hydrogen may removed chemically by bringing oxidizingagents.The porous cup is placed in a solution of copper sulphate with copper sulphatecrystalsin the bottom of the jar. some reduction they have in the current delivered capacity ciurent for be for Polarization. further drop of voltageis due to polarization. When the cell delivers current. " Daniell cell. Fig." This 86A. practically covering appear upon As time it. These They contact bubbles cause a have effects: two substantial surface between increase in the the cathode and the Hydrogen actingin conjunction with the plate sets up an electromotive force which resistance at the electrolyte.even though the current be maintained constant. elapsesthe terminal voltagewill be observed to drop still This further. Daniell cell. some detail. 83. If the platebe roughened.into Remedies intimate " contact with the cathode. These hydrogen bubbles may removed mechanically by brushing them off or by agitating the commercial is impracticable under electrolyte. the bubbles form at the and come to the surface projections more readily.inside of which is a porous cup containing zinc sulphatesolution or a solution of zinc sulphateand sulphiu'ic in this The anode acid. is a two-fluid cell having The copper zinc and as electrodes. Fig. 83. or negative electrode is immersed electrolyse. such as chromic acid or manganese peroxide. small bubbles of hydrogen the positiveplate or cathode. hydrogen readily combines with the oxygen of these compounds to form water (H2O) This method is used in the bichromate cell. Cell.PRIMARY of the cell and SECONDARY AND this has been 89 BATTERIES considered in earlier. consists of a .This conditions. in the Le Clanch6 cell and in dry cells. which is of copper. and the copper electrode of when thin sheet copper. is made of stripsriveted together and placed in the bottom of the cell togetherwith copper sulphatecrystals. very Due to capillaryaction the electrolytetends to creep up poured .and metallic copper out of the copper comes sulphatesolution and is depositedupon the copper electrode.which CURRENTS cathode. ^The gravity cell is similar to the Daniell cell. the cell is set up initially. upon The cathode. The porous keeps the two solutions separated. This is surrounded by a zinc sulphate solution." . The cathode will therefore gain in weight whereas the anode will lose in weight. This copper becomes In the operation of the cell deposited in any way. The copper sulphate is the heavier of the two The solutions and therefore tends to remain solutions should be in at the bottom.84.copper will be sulphate solution comes it should be removed if by chance deposited. The solutions are kept separatedby gravity. This cellis designed for use in a circuit which is kept continually The copper If left idle the electrodes waste closed. copper is in a copper sulphatesolution. As the cup there is no polarization.1 volts.rather than a porous cup.except that gravity. This cell is shown in Fig. The connection to the copper is usuallyan insulated copper wire fastened to the copper and carried out through the solution to the top of the jar.90 DIRECT plate. bottom The anode of the cell. the electrodes should be reshould be thoroughly washed. " . is depended to keep the electrolytes separated. The and the porous cup electromotive force of this cell is about 1. is zinc. A solution of copper sulphate is then poured to within a few inches of the top of the jar. When the cell is moved time. This is the reason for having the zinc electrode massive. the zinc goes into solution as zinc sulphate. Gravity Cell. carefullyfor if the copper in contact with the zinc. There should ravi ce y j^^ copper sulphatecrystalsat the g^j^g^yg 86B. taken is out of service for some away. is usually rather massive and is cast in the form of a crow's foot and hung on the top of the jar. surrounds the porous cup. . The per is to bring mangamost method of reducingpolarization common nese zinc. resistance^Obviously if two of the above quantities It is a matter IbRe^third is readilyobtainable by Ohm's Law.arid the zinc. The cathode CURRENTS is molded Carbon and the anode is amalgamated ammonium or electrolyteis sal ammoniac circuit work chloride.4 volts.and are known. and reproduceresistance standards. such as ringing door-bells. The electroternal force is 1.is shown in Fig. Its uses are for intermittent work. This readilywhich unites the hydrogen bubbles to form givesup + with contact oxygen water.but because of the drop due to its in1 volt not over resistance and that due to polarization. This type of cell is suited only for open motive because of the rapiditywith which it polarizes. In Clanch^ type of Le one pencilzinc cell a is suspended in the center cylinderof carbon and dioxide. dioxide The into intimate Terminal " Terminml with the carbon.. bent into cyUndricalform. voltage. the top of the cell is dipped in prevent the solution "creeping.DIRECT 92 tion. An improved manganese type. and to the fact that it contains no injuriousacids or alkalis. to make of no great difficulty be able to . In this form a hollow carbon cyUnder is filled with manganese dioxide. " It is essential in work practical to reproduceaccuratelystandards of current. Weston Standard Cell. to the small amount This cellowes itswide use to its simplicity. of a The Fig. surrounds the carbon cylinder. the porous cup cell. 86.telephone work. 86. of attention that it requires. and open-circuit telegraphwork. being separated therefrom by rubber rings. 89. 1 pint of concentrated tion solu- of sal ammoniac A more to To produces zinc chloride crystalson the zinc and carbon.-Porous cup hollow solution should consist of 3 Le Clanch6 cell. cell should be allowed in planning an installation. ounces water.'' paraffinand the top of the carbon is covered with a black wax. etc. " standard Weston cell.PRIMARY SECONDARY AND 93 BATTERIES than metals in stripsand in nothing more and calibrated. Such standards mounted other forms. carefully definite are permanent and their resistance remains constant invery standards such as standard A are of either current than maintain reproduce and to or voltageis much more is the standard of resistance. the polarizationeffects.87.fThe its materials cell depends upon concentration of the force of a a diflScult and motive electro- purities. top of the celland In the bottom is the anode. was standard the be it to placeswith at various Clark a at different times reproduced and for cathode of cury.ataadanL_ standard cell. are the held in bottom cell located at the bottom this is mercurous sulphate of a porcepositionby means lain and packed with asbestos. The electrolyte . merMrM^i] anode an of zinc. in one cross-section of the Fig. cell. It is difficult. In the Weston as a vent of the other amalgam. their im- the temperature. changed very appreciablywith the temperature and that this change lagged behind the change that the electromotive were in force temperature. to select cell materials such will enable as high degree of cell the first of cells to prove successful. expanded This is substituted for the zinc of the cadmium cell.. by another porcelaintube packed with acts for any leg of the This is held in place asbestos. A Clark is shown of paste. therefore. materials tube. of cadmium of Weston portableform is mercury cathode H-tube. electrolyte. The objections to this cell an 51K^rtTir}" Fig. and rouii Sollphiila electrolyteof mercurous sulphate and zinc sulphate. leg of an These tube extends gases H-tube that are The Above at to the formed. the two. it has been found more maintain a voltage standard rather Of isobtained in voltagestandard This the practicableto produce and than a currenJ^. commercially had This a a The accuracy. 87. 0001 amp.000. It is possible to reproducesuch cellswith electromotive forces differing by only a a case few parts in 100. by tembut corrections can be accuratelymade. The leads from the cathode is cadmium sealed into the tubes at the bottom. " . are sealed with in wood and cork. the electromotive force should appreciablecurrent be taken from the drops. 90.94 DIRECT CURRENTS sulphate.portable. The unsaturated type of cell rather than the normal cellis used almost entirely ib practical as no work. the cell is used without deliveringcurrent. A certificate should each one giving its electromotive force. They are not as accurately reproducibleas is the normal cell. than If 0. they are rapidlyreplacingother types of cells.0186 volts. The word ''drycell" cell that is dry will deliver any is reallya misnomer. In and the unsaturated cell. The cell is made in two forms. left in the solution. The cell must be in such a manner that it delivers no appreciable used. the normal celland the unsaturated or secondary cell. for no of dry cellsbecoming In fact the chief cause current. current.its concentration crystalsare is substantiallyconstant cells at other temperatures. Dry Cells. Such have practicallyno temperature coefficient. of the so-called Poggendorf method described By means in par. Dry cellsare a modification of the Le Clanch^ cell and as they are very light. accompany which usuallyis about 1. Its electromotive force is affected slightly perature. The The the anode and top of the cell is entire cellis mounted with binding posts at the top.and convenient. 125. it is evident that if any appreciable current be taken from the cell its terminal voltage will The terminal be quite different from its electromotive force. In the normal cell. therefore. appreciable exhausted is their actuallybecoming dry. more time. and metal wax.cadmium sulphate crystalsare left in the bottom of the solution so that it is always saturated. but when the circuit is again opened the electromotive force slowlyrecovers its initialvalue.the solution is saturated at 4*^ C. cell at any is taken. voltageof any cell differs from its electromotive force by the IR drop due to the cellresistance. As the resistance of a Weston cell is about 200 ohms. Not .paraffin. PRIMARY AND A cross-section of 95 BATTERIES SECONDARY typicaldry cell is shown in Fig. non-conductingmaterial such The anode consists of zinc is lined with The some of paris. . always set in close-fitting The electromotive force of a dry cell is about 1. of it should if in a cell is to deliver an good condition. 88.. with used at all. " The compound. The depolarizingagent.made in the form of a cylinderwith an open top.even new though the outside of the cell remains 18 months. The binding post is to the soldered a top of the zinc. " Sectional view dry cell. It fillsthe cellto within about an inch zinc of the top.is mixed manganese with finelycrushed coke and tainer pressed solidlyinto the conbetween and the the Blotting Paper carbon terial non-conducting ma- which lines the zinc.is added and the cell then sealed with or Fig.4 volts with time.. 88. and the mixture of coke. with perhaps a little sulphate.5/0. value of 1.and the cells are cardboard containers. The when The so method short-circuit it a year to internal resistance of and increases to several times that important except as of the cell. and acts as the container of the cell.1or 15 sistance re- when amp.which surrounds this rod.1 ohm this value with time. blottingpaper or plaster carbon rod. zinc is idle. varies in The rod itself various shape among Sealing Compound It is located manufacturers. The anode is sheet zinc.5 volts when but this drops to about 1. a as carbon. powdered dioxide. A instantaneous new after effect is largeas compared polarization the internal resistance is not useless practically an a low value of internal indication of the condition for testing the condition through an ammeter. tar some wax frequentlylacquered. etc. axiallyin the zinc container and the binding post is secured to the top of it. even cell is A if not the cell is about 0. Sal ammoniac. continuously.. up of the zinc deliveringappreciable current the terminal voltage is very nearly 1 volt. As is well known. purposes. it is not suitable for a storage cell. but the active materials go into solution and do not all return during the reverse cycle. lead-lead-acid type and the nickel-iron-alkali type. One of the chief causes of a cell'sbecoming useless is the using as a result of electrochemical This allows the solution to leak out and then becomes worthless.96 DIRECT When the current new. The life of to actions in the cell. BATTERIES StorageBatteries. field is limited to supplying moderate currents intermittently. the of . They are used extenfor door bells.but the two differ from each other in the manner The materials of a primary cell which are they are renewed. and for many instruments.the cell materials are reto their initialcondition by sending a current through the cell in " a reverse direction. Therefore if a the electrochemical a cell must remain cell in its operation gives oflf that it cannot be brought usuallyin the form of gases.the Ufe of such a cellwould be limited. in the storage cell. as There are but two forms of storage cells in common use. electric bells.gas engineignition.1 amp.whereas. back to its originalcondition with a reverse current.telegraph other flash lamps. so material. In both these cells the active materials do not leave the electrodes. used up in the process of delivering current are replacedby new stored materials. A storageor secondarycell (sometimes called an accumulator)involves the same principles as a primary in which cell. but they are capable of supplying very small currents of the sively magnitude of 0. buzzers. For this reason productsresultingfrom the dischargeof such within the cell. STORAGE 91. CURRENTS under these conditions may reach even When 25 amp.telephones.but the results are a temporarily by usuallyfar from satisfactory. dry up and the cell cell may be prolonged introducingfresh solution. dry cells have many Their applications. The Daniell and gravity cells are both reversible and hence are theoretically capableof being used as storage cells . the Le Clanch^ cell be used as a gives off free ammonia gas and therefore cannot storage cell. For example. SECONDARY 97 BATTERIES ^The principleunderlying the lead cell by the followingsimple experiment. given off from each plate. Two may plain lead strips(Fig. to change from solid metallic lead to spongy will be . " Forming Positive Plate the plates of an elementary lead storage cell. These are connected in series with an incandescent lamp suppliedfrom 115-volt direct current mains.PRIMARY 92.but it will be found that a much from one come plate than the other. A careful examination.and the other apparently will not have changed its appearance. will show that the metalUc lead at the surface of the latter platehas started lead. When Negative Plate Fig.89) are immersed in a glassof dilute sulphuric " be illustrated acid. The Lead AND Cell. After a greater number short time one platewill be observed to have changed to a dark chocolate color. 89. or from a current flows through this cell bubbles of gas battery.however. have become now lighterand will more nearly resemble its initial lead color.even ciurent be is sufficientto exhaust the cell in a very short time.5 volts. 89 the cell*will indicate about across the voltmeter 2. that is. polarization This overcome This the periment simple ex- illustratesthe principleunderlying the operation of lead storage cells. . is of sufiicient magnitude to operate a small buzzer for a veryof energy that such a cellcan deliver short period.75 volts.98 DIRECT CURRENTS the current is flowingas shown When connected in Fig. of 0. When through such a cellthe metallic lead of the positiveplatebecomes converted into lead peroxide. After a short rest the cellwill recover slightly and will again deliver current for a very brief period. When no positiveis converted to the peroxideand the negativeto spongy lead by the action of an electric current.and the cell w^Ul now This current found to be capable of delivering a small current.when both are lead sulphate.the excess in charging the cell being necessary to resistance and them. As the cell dischargesthe voltagedrops off slowlyto about 1. When the two lead platesare the same electrochemically. the two platesbecome dissimilar and an electromotive force is about observed internal electromotive force exists between volts. The platewhich is a dark chocolate color in the above experiment is the positiveplateor cathode and the one which is partially converted to spongy lead is the negativeplateor anode.1 volts.after which it drops more rapidlyuntil it becomes zero and the cell is The color of the dark brown platewill apparentlyexhausted.1 effects. The principleof the cell is the same that of the primary as cell.but the amount the small current taken by the voltmeter is very limited. The bubbles which were noted come mostly from the negative the current is passed plate and are free hydrogen gas.4 volt 2. If the interruptedby pullingthe switch the voltmeter be reading will fall to about 2.but is converted from solid lead into the form which is softer and more than ordinary porous spongy the cell is dischargedthe lead peroxideof metallic lead. current the flows. When the positiveplateis changed to lead sulphate and the spongy lead of the negative platebecomes a sulphateso that they both tend to become electrochemically equivalent.whereas the negativeplateis not changed chemically. . plate. 90 is made by this The plate is first process. passed under revolvingsteel process may wheels which surface into its convert rows. The serves as a . adding This certain The process.these firmlyembedded to any and in the great extent. type of Plants type^ is shown Another Manchester of lead and antiniony is grid made active material consists perforated. weakens process As the mechanically. corrugated lead ribbon. spirals expand and become griditselfis not acted the lead Therefore when more upon button. the cellis charged. which A spiralsand pressed into the perforations of the grid. Plants the active material is then formed negative plate is peroxide to spongy The process. upon Fig. CURRENTS is slow but be accelerated byacids to the sulphuricacid during the forming Gould plate shown in Fig. the in Fig. but plate. The oxide per- is coiled has into a greater vol n Fig. The of a. Gould 90." ploughed plate.100 DIRECT material. certain of it are not this plate tions por- acted by the wheels. Plants process.91. from 91. " Plants tlmn mo (Manchester) positive group which it is derived. reducing by The electrically by the made from the positive lead by an electric current. These portions act as ribs which givesupport and mechanical strength to the plate and tend to prevent buckling. ridgesand fur- increasing the surface of the area plate. form the " Pasted of a or " This type of plateconsists of a skeleton into which lead oxide is positive and paste. this. 93. 1. for from charge. The negative plates. Faure Pasted or Plate.together with its lesser size. applied in the The on paste the 92. greater life than support.400 complete cycles of charge and disThe negative should have about 25 per cent.cost.should be good ordinary Plants positive. battery is positivegrid is converted then charged. lead-antimonylattice work Fig. due to a more rapid shedding This lifeis approximatelyone-fourth that of the active material. It is therefore useful where lightness and compactness are necessary. The pasted type of positivehas a much shorter life than the Plants type. as ignitionand startingbatteries for gasolinecars. etc. that on .especiallyfor short periods.92. It has less overload capacity than other types and possibly the life is slightlyless.800 to 2. The if properly cared for. such very in electrical vehicle batteries. The chief advantage of the pasted plate is its highoverload capacity. peroxide and types of pasted into negativegridinto spongy lead.and weight for a given dischargerate. Two plates are shown in Fig.PRIMARY mechanical AND SECONDARY 101 BATTERIES The advantage of this type of plateis its rigidityand mechanical strength. the erosion of active positiveplate the iron-clad exide has been developed.^^ " of an In order to Iron-clad Exide overcome cell. filUngthe space between the core and the small that the The perforations are inner wall of the tube. so peroxide does not drop out readily. Its positiveconsists of a lead-antimonyframe which lar supportsa number of perforatedhard rubber tubes. 93. An ordinary pasted plate j" use(l for the negativeplateof this cell.102 DIRECT CURRENTS of the Plants plates.would be unequal on the two sides of the plate and buckling would result. material from the . An irregulead-antimonycore passes through the center of each tube and device for the current. Cells having a pastedplatefor the negative and a Plants positiveare common.which occurs peroxideon charge.the expansion to be worked one on any of the positives when it is converted to the of the active material. Cut-away " '^Iron-dad Exide. Although expensive. ^ n"irlitf" plAli Wood vpficcr t"p4rator ^4"g*t"vfplaTc Fig. In all batteries there is one more negativethan positiveplate. to be worked This allows all the positives both sides. Were on side only. The peroxide is a collecting as serves pressedinto the tubes. emergency periodduringa temporary shut-down of the generatingapparatus. twice the and at less than the one-hour current that the Plants plate can rate this ratio becomes greater. and lead-lined wooden used only for cellsof small capacity. The of the lead liningmust be sealed by burning the lead with seams be used. 93.this type of cellhas It isused usage.charging and discharging.which rest on the bottom of the tank. probably not come be strong. (See Fig. principally iron-clad exide. Solder should never The wood flame. (See Fig. The platesof this tjrpeof battery 94. batteries and portable batteries. floor area is very valuable.and well made. Tanks. of an SECONDARY AND PRIMARY a long lifeand BATTERIES can stand considerable to operate electricvehicles. Glass jars glass.100. a non-oxidizing should be painted with an acid-resisting paint.For a given floor area the pasted plate can dischargeat the one-hour rate. though continual.) In the lead-lined tanks. For merely regulating on duty. StationaryBatteries. They are lined with sheet lead. When glassjars are used. Earthenware tanks have been used more as an experimentand will The wooden tanks must into general use.% in.) The platesof like polarityare burned to a heavy lead stripor bus-bar to which the current-carrying lead is either burned tween bolted.is given in Fig. the Plants plate is preferable. thick. the plates are suspended by projecting lugs which rest on the edges of the jar. An occasional application of linseed oilwill prevent decomposition due " to the acid.earthenware. the platesare similarly suspended upon two glassslabs. The containingtanks are of three generaltypes : tanks.such as asphaltum. are as they are expensiveand have not the requisitemechanical strength in the largersizes. stationary Storage batteries are divided into two generalclasses.Where a batteryis installed for overload for a very short to carry an enormous service.cut away to show the 103 rough A view assembly. There should always be a liberal space beor the platesand the bottom of the tank to allow the red lead . depending may ing the nature of the service. be either of the Plants type or of the pasted type.94. the Faure or pasted plateis preferable. involvonly moderate. This is a very important factor cated in congested city districts where such batteries are usuallylo" and where 96. After being received. To prevent the positiveand negative plates from coming in contact with one another.104 CURRENTS DIRECT the plates. " Assembly of a wooden separator. All short-circuiting to reduce types of stationarybatteries should have a glasscover evaporation and to interceptthe fine acid spray which occurs during the chargingperiod. " ^Lead-lined storage been wooden cell.'^ Orftiflfor jcnigi^i .several types of separators have been tried.The wood. suspended between the plates. tank Fig. after being treated.They are speciallytreated to remove ingredients that would be detrimental to the electrolyte. 96. the rods are not a complete barrier beplatesso that the expansionof the active material on either The the positive or the negativeplatemay cause a short circuit. as they then decompose readily. is not attacked by the acid. Separators.L-UL t I'.but these are unsatisfactory there is stillopportunity for bits of peroxidedropping because from the positiveplate to lodge between the platesand cause a tween short-circuit. Moreover. 95. most These are very satisfactory separators are made of wood. These separators be allowed to become should never dry. offers too much resistance to the of the perforations limited area without peroxideto accumulate " passage of the current to the active material. Glass rods have .they should be kept wet very . thin and are grooved vertically to permit the circulation of the electrolyte. 94. """'"J Hupponirnf Separ^tui^ Fig. Very thin perforatedhard rubber is still but this is unsuitable for largercells as the in use for small cells. (See Fig.0 1. and a graduated tube which floats in the liquidas shown The bulb floats in the liquidwhose specific 96.300 for pasted be made from acid concentrated plates.210 for Plants platesand not higherthan 1. " scatter of specificgravity in of heat is evolved This results in if the water is added the Part Acid 4. The specific gravityof a solution may be determined directly by the use of a hydrometer.95. SECONDARY AND 105 BATTERIES In largersizes of batteries the separators are held in placeby dowel pins. acid. acid and of steam water being generated should be avoided container and are even cause as it sonal per- injury.3 Measurement largeamount mixed.84) by pouring the add into water in the fol" ratios: Parts One Specificgravity 1. This solution may lowing (oilof vitriol sp. Electrolyte.210 4. gr.280 2.break the a This stationarybattery. This consists of a weighted bulb in Fig.240 3.PRIMARY until installed. A Water a when largeamount to the acid. 1.200 1.75 96. may to Volume Fig. gravityis to be .4 1. The should be chemically pure electrolyte sulphuricacid.) 97. When fullycharged the specific gravityshould be 1. 97 is used. SpecificGravity. 3 12 98.hydrogen is given off at the negative plateand oxygen is given to the positive plate to convert it into the peroxide. 98.160 to 1. " Syringe hydrometer. 97. Fig. the small hydrometer floats and may read directly. 98 shows the change in specific gravityduring charge and discharge. This relation is very important. is an accurate indication of the condition gravity of the electrolyte the of charge of battery. " of specificgravity in Variation 6 4"^^^^6 a 7 8 stationary battery. To determine the specific gravitywith such batteries.210 when fullycharged as " . and the specific gravityis read at the point where the surface of the liquidintercepts the tube. Such a tube may be left floating permanently in stationarybatteries in a representative cell called a pilotcell (Fig. The more specificgravity will rise from the complete dischargevalue of 1. When the batteryis charged.96). which means concentrated.as the specific 0 FiQ. the syringehydrometer shown in Fig. The electrolyte that the solution becomes and more givesup water. The small amount of Uquid and the inaccessibility of vehicle and startingbatteries make the use of such a hydrometer impossible. Fig.106 DIRECT CURRENTS measured. The syringe contains a small hydrometer and when sufficientliquidis drawn be into the syringetube. . Vehicle Batteries. the battery a full charge. into and Lowering position. 100. To put back in service. 100. " Stationary battery in position.108 DIRECT CURRENTS before the battery is ready for service. If the battery stands over a long period without being used. and allow them to stand 12 to 15 hours.210 and charge for 35 hours or more rate or its equivalent.If the battery is to remain idle over a long period Fig.fillthe battery with the electrolytehaving a specific at the normal gravityof 1.which is a non-conductor. 99 " . plates Fig. vehicles and " In the for automobile design of batteries for starting it is necessary pelling proto . electrically Therefore the battery should be given an initial charge at the normal charging rate for about 40 hours or more. Siphon off the water and the cells T'vdll stand indefinitely without injury to the plates.then siphon off the electrolyte. be reduced the active material becomes more less converted or into inactive lead sulphate. Therefore a batteryif idle should be charged occasionally.and so is difficult to reduce electrically. it is impracticable to the followingprocharge it periodically cedure is necessary Give to prevent sulphation. which may be saved Fill the cells with water and again used. 280 and 1. They are then packed tightlyinto a hard rubber jar as shown in Fig. for burned called lo (he ' assembled at" "element" s'uppottingthe element "pjce veliicle cell. These are made extremely thin and are insulated another by very thin wooden from one separators. the specific of the electrolyte is as high as 1. where this type high dischargerates which occur of batterystarts a gasolineengine. of an This in the cap ate Exide seitarators. j . and because of the necessity for a high ampere gravity capacityfor the weight. 101. called the btidee Sediment Fig.the of electrolyte amount is very small and therefore it is necessary to work it between wide limits.the lower limit being 1.PRIMARY SECONDARY AND 109 BATTERIES high discharge rate with minimum weight and used for both positivesand size. Further. "posiare strap. Therefore pasted platesare negatives. of permits the replenishing allows the gases to the escape. called the tive as shown. . 101.185 and the upper of the 1. are as "negative group Both Rib or which is closed with and electrolyte Because a " a vent Assembly cap. shown.300. There is a hole in the top of the jar obtain very a "Tilhr When used sliJi) connectors'* or cells connect a "oell connectors" When side placed called to by side is "side connector"" used to cells connect placed end to end is called 'end conn"-ctor'" an Soft lubbet r"f"" Sliap used to Hold-down connect used pLiies of keeji wood in a groui) separators fioro tloaiing Pobiiive plate of Perforated to wiH)d sniouth side placed setiarator neJtt robber placed with negative plate separator next Negative plate of The colur posiiive plate (wcKivi-d Hard brown dark a lubher to a tiray oi slate color jar when burned to the positive i"late".280 and 1. when Ihc strap. and eroups shown. This jar is sealed in with an asphaltum compound to prevent the liquidsplashingout. eroup" The negative plates.300. a startingbattery having an 8-hour able to . more current. Because of its ruggedness. Discharge rate. after apparently having become This is due to the free solution finally penetratingthe pores of This the active material. 93) is used to a largeextent in electric vehicles. However. for the electrolyte As the space is very limited in vehicle falls quiterapidly. are For rates for very short dischargeat enormous instance. it would not be able to deliver 64 amp. After such a battery has stood a short time it will be found to have recovered to some ing extent and is therefore capableof deliverexhausted. 101.4 amp. The number which may the voltagewhich is desired. Below is given a table showing the percentage capacitywith various dischargerates. Practicallyall batteries have a nominal ratingbased on the 8-hour rate of discharge.the ''Iron-clad Exide" (seepar. continuously for 8 hom-s.110 DIRECT individual cells are The and CURRENTS mounted beside one another in boxes connected togetheron top by lead connectors of cells be burned or held by lead nuts. for 8 hours. frequentadditions of water are necessary.4 amp.so that the level of the electrolyte batteries. Consequently it is not possibleto reduce all the active material during the short periods of discharge. Thus. for 5 hours ( 320 ampere hours) but only 88 per cent. or for 5 hours. The normal chargingrate of such a batterywould be 40 amp. hours Percentage of capacity at 8 8-hour 5 3 1 rate : Plants type 100 88 75 50 Pasted type 100 93 83 60 fallingoff in capacity with higher rates of dischargeis due to the inability of the free solution to penetrate the pores of the active material. if a Plants battery can deliver a current of 40 amp. in such a unit depends upon Vehicle batteries are usuallyshipped assembled. the battery will have a rating of 40 X 8 320 ampere-hours. Rating of Batteries.charged and so that they are complete with the electrolyte ready for use when received. a preliminarycharge is advisable. is called the 5-hour rate. or crates are " = = of this 56. 56. Batteries intervals. Although the above battery is just capable of delivering40 amp. If doubt exists as to the polarityand direct current not available. which shows the chargingof a 6-volt starting determined that the mains supbattery. 102. two ends main is voltmeter is which a of the wires which connect the acidulated water or in glassof slightly wire. " Charging a starting battery from 110-volt mains. The charge may be started at the 3-hour rate and ended ing up the water at not less than A into the 8-hour rate. when doing startingduty.) If the platesare of the pasted type about one-half when should be reduced gassing the current siderable beginS. trated This is illusby Fig. of charging 102. dip the mains to the salt water. example of the constant current rate is the charging of low voltagebatteries from 110-volt mains. (See Fig. 98. Charging. gassing the battery to become causes heated. When Bubbles form about the negative using batteryinto a . the acid is carried out in a fine spray by the bubbles and active material may be carried from the platesby the mechanical agitationof the bubbles. It should be definitely ply common and it is also necessary to know positive. is often called upon to supply450 amp.SECONDARY AND PRIMARY 111 BATTERIES rating of 10 amp. 102. hydrogen and oxygen. In the constant current method the current is kept at itsnominal 5-hour or 8-hour value until the gassing period begins.the constant " method. ^There are two general methods and the constant potencurrent method tial a battery. In addition.for gassing representsa waste of energy because a conportionof the chargingenergy is used in merelybreak- Pio. The chargingrate with Plants platesis much of the in excess above. 103 shows the connections of the set when the battery is being charged. (the 8-hour nominal rating). The booster ordinarily consists of a low voltage. Therefore the total voltage will be 2. batteryfloatson constant potential bus-bars. The constant per cell when there is no series resistance in the circuit. Fig. As an example. method of chargingis to be preferredas potential the charging current automaticallytapers off due to the rise in the cell electromotive force as the cell approaches the charged The source of potentialshould be about 2. high to force " Booster method of chaiging a storage battery. rating.5 volts.ready to take load as occasion demands. driven by a shunt motor.3 volts condition. The booster suppliesthe remaining 16. battery. 103. . it is necessary to have a series booster for raisingthe chargingpotential to a value sufficiently When a Fig. necessary the bus-bars can supply 110 volts.66 kw. The charging current will be 320/8 or 40 amp. The voltage of each cell should be boosted to 2.3 X 55 126.3 volts on charge. The booster raises the voltage just enough to send the necessary current into the battery.000 0. Of this 126.55 cellsare that the battery has a 320-ampere-hour Assume necessary.112 the CURRENTS DIRECT constant charging rate chargingone must reduce the the battery approaches the fully charged method current as of condition. consider a 110-volt installation with a floating battery.separatelyexcited shunt generator.5 volts and its ratingwill be current into the = 16^X40 = 1.5 volts. As the average cell voltageis about 2 volts. so rapidly when the charging rate is reduced toward the end of because of the lesser IR drop in the cell itself. discharge ifthe batteryis used to supply incandescent lamps. This final rise of voltage also indicates The terminal 10 012S466789 Hours Fig. dropof voltageat various rates of dischargeis shown in Fig. at the beginning of charge and rises slowly to about 2.6 volts.as The terminal voltage is about 2 volts is shown in Fig. completion of charge. 104.4 volts.AND PRIMARY The total power SECONDARY utilized in 126. 104.however. This last rise occurs in the gassingperiod. 104. afterwhich it rises very rapidlyto 2. 40 = 5. that the cell is nearing the . It is this rise of voltage which automaticallycuts down the chargingrate when the constant potential The voltagedoes not rise method is used. The charge. It will be noted that the battery voltage curve at the "-hour which is a very distinct advantage rate is fairlyflat. " Voltage curves on charge and dischargefor lead cell.06 kw.5 X 113 BATTERIES charging the battery is. 1.000 voltage of a cell rises on being charged. Capacitiesand Weights of Lead Cells. 0.as the spray which is carried out of the jarson charge settles on horizontal surfaces and attracts racks wooden other moisture. flame should be allowed in the installed in the In room.280 - F. Battery Installations. well-ventilated rooms. Temperature. As hydrogen room addition and to no the gas is of stream a given off. All wooden should be of acid-resisting surfaces should be covered with asphaltum paint. The.) The jarsare set in glasstrays containingsand. Specificgravity Freezing temp. the acid in the air will corrode the copper. 1. largerbattery jars should be set on porcelainpedestals6 in. Below are given the relations of weightsto kilowatt capacityfor the various types of cells which have just been described. per " . air Therefore sweeping along the it is desirable to have floor. which are in turn set on glassinsulators. (See Fig.no switches should danger due to be the arcing at the switch contacts. The floor tile or vitrified brick. 106. Above 70" this increase is of the order of from degree Fahrenheit.180 - 1.so that if a battery is well charged there is no danger of freezingin the temperate 104. The room should be well ventilated. or so above the floor. Below is given the relation between the and its specific freezingpoint of the electrolyte gravity.0 per cent. " zone. " be installed in be mounted on painted with asphaltum paint.200 - 1. It will be noted that the freezingpoint is very considerablyreduced values of the specific with increasing gravity. Batteries should Small glassjarsmay dry. 100.5 to 1. 6** 16" 5r 90** the higher temperatures the rate of diffusion of the acid throughout the pores of the active material is increased so that the ratingof a batteryincreases very appreciablywith increasing At temperature.240 - 1.114 DIRECT CURRENTS 103. . 116 DIRECT CURRENTS stampings. It is to be noted in the above read from Positive an + Edison reaction that the and left to negative storage cell. 106. . " Assembly. Steel washers The between the platesact as spacers. nickel-plated. 105. plates removed from Edison battery container. " plates of GNiOa 3Fe = Fe304 + 2Ni304 + 8K0H and read rightindicates discharge. The chemical reaction in the cell is complex. leftindicates charge. gravity of the solution does not change during charge specific or discharge. The platesallhave a perforatedlug by which they are fastened togetherwith a steel bolt and to a binding post. in Both the positiveand the negative platesare shown Fig. 105. Fig. in Fig. quantity of potassium hydrate solution both sides of the equation. but its nature is indicated by the followingchemical equation: NegativePlate Positive Plate 8K0H The + above from rightto Fig. The bolt is threaded and steel nuts clamp the platestogether.containing iron in a very finelydivided form. positiveand negative plates are insulated from one another by hard rubber grids.and also that no water is formed. These steel frame for supflat pockets are mounted on a nickel-plated port. 106. This indicates same (KOH) appears on between the electrodes that ultimatelyall the reaction occurs Therefore the themselves. The positive cell assembly is shown An Edison and negativeassembly is placed in a corrugated. PRIMARY welded SECONDARY AND steel tank.This valve should never encrusted with a potash deposit that it sticks. " Charge or Discharge 6 5 4 3 Hours at Normal Voltage changes during the charge and Rate discharge of an Edison cell. In the top is a valve which allows the to escape gases Fig. nickel-plated The individual cells are 12 Fig. shown in Fig. 107. Charging and " . because become suflScient to cause th^ in wooden usually mounted racks. Five " Edison storage cells mounted in a water may be tray. 108. The binding posts are insulated from the cover by hard rubber bushings. The Edison cell is rated on the basis of a 5-hour charging rate. Fig. 108 shows typical for the Edison battery. be allowed electrolyte. the cells being connected together by as steel connectors. It will be charge and dischargecurves 107. 117 BATTERIES top is then welded to the rest of the container. the internal pressure may sides of the container to bulge. added to to the become so The during chargingand through which 107. Discharging. Moreover. In spiteof the usual precautions. The Edison cell has many advantages. there is no sharp voltage the completion of charge. and They are also used in various types of electric trucks and for In automobiles they are not generally battery street cars. The specific changes but gravity of the electrolyte noted per slightlyso that it cannot be used to indicate the condition of charge^as with the lead cell.only freshly distilled water should be used in replacingthe electrolyte. It is light. For example. used for starting. as their comparativelylargeinternal resistance does not permit a sufficiently high dischargerate. Edison cells are used for vehicle lighting and boats. based upon The figures the capacityobtainable on normal are charge: " The efficiencyof a Efficiencyof Storage Batteries. The platesdo not buckle and the active material does not ''flake" or drop from the plates.2 volts cell. 108^ Applications. is changed to potassium carbonate very readily.rugged.it is advisable to give an overchargein order to be on the safe side. stand for a long time in a dischargedcondition without and can chemical deterioration. If doubt exists as to the rise near condition of charge. as tap water usually contains carbonates in solution. The overchargedoes not injurethe cell reduce the efficiencyalthough it may slightly The electrolytein an Edison cell evaporates rapidly and As the electrolyte frequent additions of water are necessary.the electrolyte is slowly converted into potassium carbonate by contact with the air. a normally dischargedcell is charged at a uni109. storage batteryis the ratio of the watt-hour output to the watthour input.and it should be replacedby fresh electrolyte every 250 complete cyclesof charge and discharge.118 DIRECT CURRENTS that the average voltage on dischargeis about 1. Below is given the relation between the battery weight and capacity. " . also much used in motor are ignition. 3 volts.both with the temperature.104 and 108.7 per cent.3 6 = X X What is 552 445 Efficiency = One often hears ^^ of the or 80. cent. This does not represent the true efficiencyas the cell actuallywill not be completelydischarged.much of the active material has not been reduced.the efficiency be charged at the 8-hour rate conditions. As amperes the ampere-hour do not represent energy. watt-hour efficiencyis due to the great the voltage of charge and that of discharge.95 volts. energy.and somewhat As high charge and dischargerates produce relatively high PR and is lowered under these polarizationlosses. For a complete cycle the wattsize is about hour efficiency of a stationary battery of moderate The watt80 per cent. Figs. The cell Is then for 6 horn's at voltageof 2. a cell may and dischargedat the 3-hour rate and have an apparent efficiency as shown or in of 60 per cent. to store energy. average an completelydischargedat Watt-hours output input a uniform rate of 38 voltagebeing 1. Watt-hours 119 BATTERIES = 38 X 1. for 6 hours.and after a short time the cellwill be found to have recuperated to a considerable extent and to be able to deUver it appears more to be.95 X 6 =445 = 40 2. of a battery'sability is not a measure efficiency be found In the above example the ampere-hour efficiency may follows: as Ampere-hours output Ampere-hours input "= 38 X 6 = 228 "= 40 X 6 = 240 Ampere-hour efficiency ^^ = The much lower difference between 95 per.even though Owing to the inabilityof the free acid to permeate the active material. at the 8-hour charge and dischargerates. The of a storage batteryis of the order ampere-hour efficiency of magnitude of 95 per cent. Further.PRIMARY SECONDARY AND form rate of 40 amp. of charge and discharge. ampere-nour of efficiency a storage Dattery. the average the efficiency of this cell? amp. . The efficiency of a storage battery varies with the rate. are as the of batteries should be efficiency.as well given due consideration. distribution of power are Note. Assume The principle that it is desired to copper platea carbon dynamo brush. For the Edison cellthe amperehour efficiency is about 82 per cent. Electroplating is a very important electricalindustryand is closely related to the subjectof batteries. for the Edison The ampere-hour and the watt-hour efficiency cell are less than for the lead cell. The one of the factors to first costs and the maintenance high so that these factors. 109. and the watt-hour efficiency about In 60 per cent. conditions. The portionsof the brush to be platedare immersed in a solution of copper sulphateas shown in Fig.120 DIRECT CURRENTS largestationarybatteryis about 86 per cent. selecting be considered. 109. This is due partlyto the fact hour of efficiency that the Edison a cellhas lower electromotive a force and the IR drop is proportionately greater. " Copper plating bath. 1 Electroplating. A copper stripis also immersed in the solution and is connected of a dynamo or some other to the + terminal of direct current source supply. Pars." Fourth Edition. is very simple.Copper Plated Fig. XIV. 110. of storage batteries in the generationand considered in Chap. the watt-hour efficiency may high as 95 or 96 per cent. Googk to . 186 complete discussion. is but the efficiency a battery. for " "Standard a more Handbook. The article to be plated is iSee 206. under the same Where a battery merely ''floats'' and the cycle of charge and dischargeis a matter of minutes be as or perhaps of seconds even. Section 19. " ^The uses -aaM^ . of the surface to be plated. close togetherthe depositwill not be uniform. Acid is added to the solution to positing. etc. Electrotypingis another common example of electroplating. Copper platedon surface. The only opposing electromotive force in the bath just described is the IR drop in the solution.silver. tin.several are connected in series. Under these conditions the current and the will carry copper from the solution depositit on the carbon brush. This may be reduced by but if the electrodes are too bringingthe electrodes close together. Under these conditions.PRIMARY connected to AND the SECONDARY 121 BATTERIES negative terminal of this supply. When practicable. Nickel. in wax with the type or objectto be reAn impression is made produced. acid is formed in the solution. zinc. the solution in time becomes contaminated If an inert substance by the going into solution of the anode. The amount of metal depositedper second isproportional to the current. in. ments refineto be observed.zinc is carried is depositedor plated into the solution as sulphate and copper from from its sulphateon the positiveelectrode. per sq.. It is later backed by type metal to give it the necessary mechanical strength.02 amp.however. It is not necessary that the anode be of the metal which it is desired to deposit. as anode. The current should be such that the density is about 0. be depositedby the use of suitable baths and electrodes. The current flows the zinc to the copper within the solution. gold. such as carbon is used. This copper which leaves which is carried from the solution is replaced by copper copper strip(the anode) into the solution so that there is no change in the solution itself. Other metals may be used. prevent impuritiesfrom de- cyanide solution of copper is found to give better results than the sulphate. The surface of the wax is made conducting by applying of is then thin this coat a graphite. Because of the nature of electroplating baths. . A low voltage and high current generator is generally In practicethere are many used for platingpurposes. may in which the source A gravitycellis an example of electroplating A of current is derived from the bath itself. they are naturallylow voltage devices. Under these conditions the coil has placed itselfin such a positionthat its flux is actingin the same 122 . that shown in Fig. This tendency of the coil to turn is shown in Fig. " Magnetic field produced by an instrument coil.CHAPTER VII INSTRUMENTS ELECTRICAL AND ELECTRICAL MEASUREMENTS If a coil like Principleof Direct-current Instruments. 111. If the coil carryingcurrent be placedin a magentic field. poleof the coil will be attracted toward the south poleof the magnetic field and the south pole of the coil will be attracted to the north pole of the magnetic field. 110. I). 110 carries a current. 17. " the coil will tend to turn in such a direction that: The resulting magnetic fielddue to both the main fieldand that of the coil will be a maximum (seePar. Ill (a)where the coil attempts to turn in the direction indicated by the arrows. Ill (6). Chap.and the north Pig.a magnetic field results (Chap. If the coil is pivoted and free to turn it will reach the position shown in Fig. II) with a north and a south poleat oppositeends of the coil. . flux the flux tends to enter the radially. A plane mirror is mounted on the . The of a DIRECT bobbin. linking the coil is inthus making the galvanometer more sensitive. methods of reading the deflection There two common are the coil system of a galvanometer.112 an bobbin aluminum bobbin will be considered later. 112. 112.124 CURRENTS with or without coil may be wound is usuallyof fiber. When the moment force and due moment to of the storing re- the turning the current equal. Any turningof the The coil is in the produces torsion filament which opposes the turning of the coil and is called the restoring force.- -Principle of the D*Arsonval galvanometer. all practicalpurposes galvanometer deflection to the current.as shown in Fig. is proportional This of the as one phosphor-bronze filament usually serves leadingin wires carrjdngcurrent to the coil The other leading in wire consists of a very flexible spiralfilament fastened to the bottom of the coil. 113). the polesof a magnet a soft iron core is usuallyplaced and Fig. The duced length of the air path is reso that the amount of creased. the galvanometer assumes a steady deflection. are For FiQ. or phosphor-bronze. The addition of this core results in two distinct advantages. The advantage of Between (Fig. The of aluminum.This last effect core makes the deflections of the galvanometer almost directly proportionalto the current flowing in the galvanometer coil. coil pended usually susby a phosphor-bronze filament. of Effect " core the magnetic upon value of this deflection is determined in the telescope. time unless it starts to swing. As the the scale. the beam of lighttravels across deflects.ELECTRICAL and the can scale a INSTRUMENTS and AND telescope are 125 MEASUREMENTS mounted 3^ about from m. " and use A a lamp its Telescope and concave field of by filament is scale method of means mirror image focused on a the cross hair eter galvanom- distance placed some on a ground glassto of reading scale graduated in centimeters galvanometer. which a mirror 114. galvanometer. 113. 114). is fastened. One method is in some way mirror " is to attach an air vane to the coil. a a galvanometer. The Coil Core Fig. Damping. the from FiQ. When the mirror turns. it will continue swingingfor some of damping retarded or damped. The reflection of the scale in the mirror be seen with the telescope(Fig. If a galvanometer coil. This air vane is enclosed so .which is hung freely. the reflection of the scale in the mirror deflects. method Another is to moving system. the motion currents put CURRENTS DIRECT an a If the coil be wound of the bobbin aluminum an on swinging trical is elec- bobbin. In either of case two a common galvanometer may be protectedby the by-passesa certain known current from the galvanometer. Galvanometer Shunts.and may result in a injury to the galvanometer. When galvanometers are used to detect small currents as in null methods (see Wheatstone " "2" ^^[JJvvvWWVWAAA/VNA^ (a) GAlvanometer (") Ayrton shunt FiQ. The same result may the main be coil. through the magnetic field will induce and these will be in such a direction as to itself. shunt. within This opposes obtained by the motion of the coil. or even by short-circuiting 113. comparatively large current This causes violent deflection of the coil. electricload on the moving coil as in an electricgenerator. types of shunt.126 that it restricted space and damps any method of the coil. 115.the apparatus may be so far out of adjustmentthat a flows through the galvanometer. Ayrton Shunt). Bridge). In certain other measurements the current that it is desired to measure with the galvanometer be so large that the deflection is considerablybeyond the may scale. " Types of galvanometer shunt shunt. The most satisfactory swings in movement damping. or proportion of the use the a resistance which . bindingshort-circuited copper coils on by shunting the galvanometer externallywith a resistance (see it. There are One type is shown in Fig.115 (a). galvanometer current for fullscale deflection. For inif the galvanometer is to measure rent. Fig. to one-tenth current 7. = Ig = / = circuit current. ^g as = of /.etc. ro (1) and = 7-7.Ig must if all of the current be one-tenth T The shunt the shunt as their current the value / passed through the That is. shunt resistance. But These time. at la J- current are versely in- Hence: J-0 /o\ .is of such a value that it shunts ^f 0 of the current away from the galvanometer when it is pluggedacross the galvanometer. 115 (a).ELECTRICAL INSTRUMENTS It consists of three or AND 127 MEASUREMENTS four separate resistances which are plugged adjusted a galvanometer one are so in value that with a given current to be measured the successive stance. (2) the galvanometer respectiveresistances. Jfo the external curthe top resistance. To determine the values of these resistances proceed as follows: across the Let Rg To which reduce galvanometer resistance. Rt the it would = galvanometer deflection have galvanometer. == shunt current. /. -galvanometer currents are in the ratio of 10 to 1. resistance of 600 sistances re- its deflections in the ratio of to reduce 100 to 1 ? Ayrton Shunt Ri = R2 = -^ -QQ- The " = 66. If the shimt has a resistance of only 5 times that of the galvanometer the sensitivity will be reduced only in the ratio of 6 to 5. " the current ^An ammeter is an electricalinstrument which flowingin an electric circuit. the shimt is adjustedto (See par. regardlessof the galvanometer resistance. to 6. (2) A fixed resistance is shunted across which givesa constant value of damping in open circuit ballistic measurements. ^A " should 10 to 1 and CURRENTS galvanometer has a it in order shunt What ohms. One line terminal is permanently connected to one terminal.) When this deflection for give the maximum galvanometer deflection. 159. the galvanometer deflection will be Hooo of i^s maximum value. There were early types of ammeters. 6. 116 shows a typicalinstrument of measures .06 ohms. the galvanometer. Ammeters. The advantages of the Ayrton shunt are : (1) A shunt is applicableto any galvanometer. where If C be moved A6 is Koo of the resistance AB.the maximum is it would be were of the sensitivity by the addition of the shunt.C. where resistance Aa value of external current not used. Ans. the galvanometer is shown in A permanent resistance A Bis connected across terminals. Fig.128 DIRECT Example. galvanometer is reduced 114.etc. That is less than is. the deflection of a pointer attached to the plunger might be made to read amperes. Ayrton shunt Fig. If point C the same the shunt be moved to a. and the other line and* can be connected line current to the maximum deflection is obtained when C is at B.7 = ohms. the so by restraining upon of the plunger by gravity or by means motion of a spring. Hooo *^" total resistance AB. which is not usuallyobjectionable. is movable With a fixed various pointsalong AB. the galvanometer deflection will be Jfoo of its maximum value. most of which many depended for their operationupon the pullexerted by a solenoid of pullis dependent some on type of iron plunger. 115 (6). end of this resistance. The amount the current strengthin the solenoid. Ans. principle structed galvanometer. uniform the D'Arsonval galvanometers. a given a higher for values of current than for increasing values. 9 Digitized by (^OOgle . This damping is due to the because of its cutting the set up in the aluminum currents magnetic field. reading decreasing (2) The weight of the plunger makes it impossibleto mount the tion moving system so that the fricis negligible. 117.-Mov^entof a Westoninstru^nt. Weston. The moving 117. Coil ismade of silk-covered The aluminum bobbin. measure- instrument. Edward into almost universal instrument is based of theD' Arson val Fio. and violentlyon sUghtly fluctuatingloads. galvanometer. netic which for current or results in hysteresis lag. scale for indicatingthe essential parts of the instrument are shown in Fig. Two pole pieces the in horseshoe soft-iron fitted to are poles magnet and a is held between core cylindrical these pole piecesby of brass. For direct current the Weston developed by has come The use. The lengthof a ^i " ' \ air gap is very much i shorter than is usual with / Fig. ments.ELECTRICAL INSTRUMENTS this class. but it is so conthat it is easily portable and it is provided with a pointer and deflections of the moving coil.also makes the instrument highly damped. very wire wound copper on an aluminum fine bobbin. the on 116. " Early of type plunger ammeter. This gives a strip air gap and a radial field. As in the D'Arsonval essary.a permanent magnet is necThe beingmade form. Such instrument is not AND instrument 129 MEASUREMENTS is due: (1) To maginaccurate. besides supporting the coil mechanically.(3) The error fluctuates an damped. any tendency of the coil directA typical Weston Fig.it is supported at the top and bottom by hardened steel pivotsturning in cupshaped jewels. This method of supporting the moving coil is almost frictionless and makes the ment instru- the portable. in amperes Because of the or as the radial the deflection of the moving coil field. whereas D'Arsonval galvanometer is not The so. of Weston Weston portable galvanometer. 118.usually sapphire. uniform graduhas substantially ations. 119. which causes a spiral spring needle the leave to its zero to coil or uncoil. Although lacking the a are . in this type of instrument is practically ing proportionalto the current in the movment so that the scale of the instrucoil. is not level. This is carefully by very small counter-weightsso that the whole moving element holds its zero if the instrument even positionvery closely.which may be " in volts marked case may be. 118.will not cause light and delicate position. Fig. Instruments of this construction having very weak springsare often used for portablegalvanometers. The top and bottom springs are coiled in opposite directions so that the effect of change of temperature. " The internal instrument shown in Fig.one the at flat spiral top of the coiland the other at the bottom. current the springs. is led in and current out of the coil by two springs. which connections is desirable. The pointer moves over a graduated scale. to turn is opposed by these two milli-voltmeter. These the as springsalso serve controllingdevice for the coil. A very aluminum pointer is attached to the moving element to indicate the deflection balanced of the coil.130 DIRECT Instead CURRENTS of suspending the coil by a filament. To Upper Spring Sprius To Lower That is. . " For full scale deflection the drop across a shunt is about 50 millivolts. 9 from 4500 as negligible most An cases to 200 to amperes.By the law of divided circuits: Ish Rm Im R"ah . current.in current. In as a divided Fig. No. practically. to the current instrument readingsare proportional For this reason the ammeter itself (Pig. compared and shunts. The current taken. 1 from 25 No.i^^and Im be the instrument resistance and the instrument current respectively.If Rsh is constant.132 where DIRECT Ith and R^h CURRENTS the shunt are current and the shunt ance resist- respectively.118) is often marked "Milli voltmeter.so that the to the current in the shunt. shunt also be considered circuit. 121. so that it is almost always Fig. 6000 with the line current ammeter Ammeter " the main equalsthe its shunt may Therefore. amperes. and let. the voltagedrop across the shunt is proportional in the shunt.a be the shunt resistance and the shunt current respectively. by the instrument itselfis usuallyabout 0.01 amp. 122 let Rsh and 7. the the line current is 90 amp. X 4 = The volts 0. an of current Division " between its shunt. the instrument An ammeter is calibrated should with an external shunt of scales or Ikrge number given that the instrument instrument current terminals are Assume ranges. instrument "' 122. such as main manganin. A low adjustableresistance Fig.050 volt across or 50 the ment the instrumillivolts.is.the current divides between shunt inverselyas their resistances. be assumed 90 the a current? in the line differs from may and resistance of 4 ohms.0125 0. instrument. a must ratio. and ammeter resistance change appreciably with the temperature. the shunt Dividing this voltageby the shunt resistance. 4 ' /" 0. The resistance of the leads connectingthe shunt to the instrument should remain and the leads with which constant always be used to connect the Ihe lugs and binding post contacts shunt to the instrument.it should be made a does metal not whose either means Rm l!2="i operates at a higher temperature than the of This the change must in change always divide between the that instrument amp. and shunt 133 MEASUREMENTS AND INSTRUMENTS ELECTRICAL the shunt current by small very a equal. Then.0125 may current .118) is connected inside the instrument.0005 a What is the value of the instrument the current As the two amount. the current accuracy. For 0. is a example just gives full scale deflection when is 0. By varying this resistance the instrument is adjustedto itsshunt. same AAAAAAA- shunt Rih Fig. be made in the to have amp. " that Assume instrument an resistance of 0. has that ohm.0113 and the shunt resistance of must in the shunt and the resistance of the all at or the As not that both the fixed ratio. The resistance of the instrument circuit should also reconstant. (thespiral. should be kept clean from oxide and dirt. the instrument That Example.0005 In. . circuiting 116. . In the smaller sizes of instruments only and of use it 100 amp.all the shunts shown 5.050). An ammeter shunt.) The moving usuallywound that of the ammeter a in anameter concerned. lies in the principaldifference. The posts of millivoltmeters and voltmeters are of much lighter construction and the metal posts are covered with hard rubber.005 ohm be substituted. as it should have as low a resistance as is goes in series with the line. external shunt is optional. having a resistance of 0. An ammeter can resistance is introduced To protect anuneters be made for shortfrom heavy currents. that of an voltmeter so does far as the not ment move- (SeeFig. the moving coil of Because of its comparativelylow resistance. By the choice of suitable shunts the same be made to give full scale deflection with 1 amp.000 amp. external to the instrument account on of its size and its heatingloss. the shunt may be obtained with 10 the 50 millivolts drop across 0. an as thereby obtained. manner of connecting the instrument to the circuit.117. mostly for insulation purposes. higher resist- however.the shunt is usuallyplaced within the For instrument. and with may in Fig.it is connected directlyacross desirable that the voltmeter take as littlecurrent as is practicable. Therefore a 10 scale ammeter (10 X 0. provisionmay them when readingsare not being taken. etc. usually be distinguishedfrom a voltmeter by the fact that its bindingposts are heavy and are of bare metal. ^The construction " differ materiallyfrom and magnet are coil of the voltmeter finer wire than The into the circuit. As a voltmeter is the line to measure the voltage. instrument results. that when it is connected. 121 For instance.134 DIRECT The CURRENTS then deflects full scale with instrument 100 in the amp.005 amp. line. except in the case of an instrument having an external shunt.. is of with and so turns more has a and of ance. very Uttle additional so practicable. Any instrument when connected in a circuit should disturb the circuit conditons as Uttle as possible. If shunt a = could be used scales the with same instrument scale is one different many internal or between ranges 50 and 100 is usual to have the shunt the amp. Above an and to 50 amp. up where desired. Voltmeters. Another result is showninFig. This is shown By current Ohm's the instrument is to Law the proportional through be graduated in the voltage. to connect a high resistance in in Fig.9900- L^y/VVW^^VNA/WWVVWVVVVNA^ |148a)j . = = ^ / As the instrument be that resistance of 20 ohms. the voltmeter -ufison- -14. Assume in that an instrument gives full scale deflection with 0.so that the instrument scale can volts. same instrument also have a full scale volts. the circuit must total resistance of the instrument V B = 150 -V 14. If it is and that the coil resistance is 20 ohms. this means necessary." The range of a voltmeter having its resistance incorporatedwithin the instrument.01 amp. 123 (6).500 ohms. Wind method of securingthe same 20 another resistance equal to 1.980 ohms has additional 0.ELECTRICAL INSTRUMENTS 135 MEASUREMENTS AND the line.01 a are If it be desired that this deflection with 15 15. This last method is advantageous as it permits also injuryor repair independentadjustment of each resistance. A B 160 16 i i 0 16 160 (6) (a) Fia. " .123 (a)) that the resistance OB = q-^t = 1. moving coil. then the full scale. series with the moving coil. in of connectiDg resistance Methods a voltmeter.000ohms.980 ohms may be 15 tapped so (Fig. Multipliersor Extension Coils.as it cannot. 123. 123. desired that the instrument indicate 150 volts.480 ohms and cojinect it from a binding post to the junctionof the resistance and the moving coil.500 1. The resistance required is easilydetermined.the resistance of 14. " in one = resistance does not affect the other.be connected directlyacross would ordinarilytake an excessive current and might be burnt Therefore it is necessary out. and this tap can be brought to a binding post. . may be 116. 000 As resktance a external resistance should be connected = the 68. a wire CF attached to AB. = Ans. or They are usuallyplaced within a perforated.the resistance of the instrument jRm. The equation giving the relation between the resistance of the multiplierjB*.000 ohms.68.000 Ygg 17. which the current passes. 124.000 " 51-. now already within be added are 17. There type of instrument is another which pends de- instruments.000 = " i7. 17. ^ Instruments.the action of the instrument depends on the electromagneticaction of a Fig.box and the terminals brought out to binding posts. 17. instrument.000 ohms.000 to the used in this instrument. for its indications upon A diagram of this instrument heating action of the ciui'ent. and the multiplyingpower M is as follows: sometimes extension manner are coils.124.000 ohms ohms must External is X is 17.ooo 117.the resistance of the circuit must As the instrument 000 of in series with it so that its range (6)600 volts? Therefore. through is At C. the added 17. = resistance wiU be. Example. be. necessary.000 ohms already has 34.000 ohms. 17. the through current same X 2 = 34. Ans. " Braun Principle of Hartmann hot-wire and current.000 + 17. The multiplyingpower is marked of the multiplier near a terminal. instruments fore hereto- considered.136 DIRECT increased by the CURRENTS of external resistance connected use in series with the instrument.000 resistances external at 300 be doubled. Hot-wire In the . In the above problem of the (6) the multiplying power " is as multiplier ^ follows: 61. A " has 150 scale voltmeter (a) 300 volts? (a) In order volts as to maintain 17.000 ohms. M ^t-^!^ (49) = Example. called mnUipliers. AB is a fine wire of platinum-silver is shown in Fig. the .000 - total resistance must (6) The What the instrument flows at 150 volts. a is very small. When a current flows through AB^ the heat expands the wire ABj reducing the tension in the wire CF. For this reason this type is very useful in radio telegraphy. its indications of if the frequency is as are a shunt independent not used. Such instruments affected by temperature and do are not hold their calibration for very long periods. Therefore. V is the that portionof the circuit and / is voltageacross the steady current viously. Let it be shown . fluctuations very slowly so can Another advantage of the hot wire type of instrument is that it can be used for alternatingas well as for direct currents. Obthe voltage V may be measured with a voltmeter. and is held in tension by the springH. and the resistance R computed. Voltmeter-ammeter portion of an of Resistance Method. flowing in that portion of the circuit. the pointerP over Wy moves When current used as an anmieter. the pulley W.by Ohm's resistance of any Law. When is connected in series with the wire AB. sistance high re- This type of instrument is *'dead beat. It is often used as a transfer instrument to measure alternatingcurrents in This type of instrument of direct current.for work they should be calibrated at the time of using. This fiber. and allowingthe spring H to pull the silk fiber to the left. 125. it is very sluggish in its behavior and only reaches its ultimate deflecton after This is an lapse of considerable time. a shunt is necessary unless the used as a voltmeter. " The electric circuit is. advantage in the of fluctuatingcurrents as the needle follows the measurement be accuratelyread.the where current / measured with an ammeter.ELECTRICAL INSTRUMENTS AND 137 MEASUREMENTS At This passes around Ej on CFj a silk fiber EH is attached."that is. accurate the ELECTRICAL MEASUREMENTS Measurement 118. is the 110-volt supply. actingon the pulley the scale. requiredto determine the resistance R in the circuit of power The source in Fig. terms is particularly useful for the measurement of high frequencyalternating currents. " 24 amp. must it is desired to know as directly Therefore.126) meter through which the current is led to the specimen. Fig. R across take The excessive current. terminals are connected well inside the terminals BB (Fig.79 ohms. Example. be connected the resistance of this directly portion of the circuit only. terminals are determine requiredto of interest let it be voltmeter transferred conditions the voltmeter from across reads 91 volts and the resistance of R the to across ammeter R\ still Therefore: Ql /2'=|^3.138 The CURRENTS DIRECT small and if connected resistance R is comparatively volts would 110 across to insert it is necessary the current. The voltmeter What (Fig.however. the contact resistance.792 = ohm. the voltmeter eUminate this error due to contact resistance. = It is sometimes desired to measure resistances of such low value their terminals. 19 volts when of the resistance the ammeter R*t resistance: The i2 ^i = 0. reads 125. As the volttakes but a very small current. an resistance R' in series with R to limit a voltmeter. connected directlyacross that. 125) is the value of measuring method Voltmeter-ammeter " reads resistance. 24 As R'.if a voltmeter were which be comparativelylarge. may and might even would introduce considerable error exceed in To magnitude the resistance which it is desired to measure. small sharp pointed con- . Under a matter The these reads 24 amp. . having resistances of 100. is the resistance of the voltmeter. . {a) Fig. . 127 (b) shows the applicationof this method in megohms of the insulation resistance of measurement Example.140 DIRECT the same are as i must current CURRENTS flow through each so that the voltages follows: F2 Fi where F2 - iRv - (1) (2) iR = R. high they are usually expressed 1.1 . to the Fig. 127. 0. These about six times as great as can be obtained with give a sensitivity the ordinary 150 scale voltmeter.000ohms). What cable and = _. 1. The direct nected con- cable is voltmeter is the insulation resistance of the cable? 120 ^ A terminal lead-covered side of the line other 10 volts. iim. R This method R^y^I^ = (60) of measuring resistance is particularly useful in determininginsulation resistance of dynamo windings^cables. a is connected 100. For this reason special150 scale voltmeters. Dividing (2) by (1) and solvingfor iJ.000-ohm.000 ohms (one-tenthof a megohm) are available. One cable. It will (1 megohm be seen from equation (50) that the greater the value of Rvy be measured the greater the resistance that can by this method. voltmeter a line it reads to = - :r^ 10 10 = . 127 as across of the voltmeter a is then of the (6). " such (h) Measurement of resistance resistances are very by the voltmeter method. As etc.000. current connected now " When reads the 120 of core to the a volts.1 the sheath in Fig. megohms. 128. corners connected are batteryB feeds the diamond. are viously Ob- battery and the galvanometer may be interchanged without affectingthe relation given in equation (51). 10.Also the currents /i current passes through the galvanometer. If the galvanometer Fiq. M or rheostat and N arm. and the unknown from Current other two the Across a make two a a to form diamond. of the To a resistance X and N are fixed value resistance. 1.000 ohms. is galvanometer. etc. as no If the points a and b are at the same the voltage potential. 100. The bridge in its simplest against other known form.usually 1. 128. ob and: drop oa IiM hX (1) of = = = = Also the voltagedrop ac be and = hN And since /i = = I4P Is and I2 IiN = = IA I2P (2) Dividing (1)by (2) M X ^hP'^'N P IiM hX (51) which is the equation of the Wheatstone called thQ ratio the arms and P the balance Bridge.ELECTRICAL 120. a opposite corners two o and c the some and measurement. The going Bridge.the Wheatstone Bridge Wheatstone methods method is 141 MEASUREMENTS AND INSTRUMENTS " in which one the unknown resistance is balanced resistances. potential. The P is then adjusted until arm the galvanometer does not deflect. current no be flows through it and therefore the two points a and b must at the same h and h /4. . ." Elementary Wheatstone bridge. does not deflect. M arms each set at connected 6.P. is shown in Fig. Three known resistances ilf iV. In distinction to the foreof measuring resistance. and 1 ohms respectively. iV. and consists of P as in and cut are CURRENTS DIRECT and a of resistances number pattern of Wheatstone 1.000-ohmcoil.110 number of such values that with be made equal to any whole plugs infinity that the bridge ( )and a 10. common consists FiQ. 100. 129. and N " Massachusetts to 1 ohm P may Institute of Technology consists of three of 10. ranging from 5. 129. The infiniteplugsmean circuited at these points and by their position be open can be made the 10. and arms in which manner in The P on the coils in these ferences difthe arms out of circuit. a part of iV or ohms.000-ohm coil may a part of P.000. M of three resistances of 1. Af.142 The not many differ in types of Wlieatstone Bridge found from principle lie in the bridge as well A that positionsof the in the in shown practicedo Fig. plug type of bridge is shown in Fig. 128.000 ohms the proper combinations between 1 and 11. respectively. 00 Between the outer ends of N and P are two .000 ohms bridge. 100. resistance lies between By removing the two 2-ohm and the unknown resistance is narrowed down a 2 plugs and then a 1 between To get a more 2 and 3 ohms.000 ohms unplugged all the time reducing the shunt S.000-ohm plug and the galvanometer deflects to the right. By successive trials. of these plugs. that 1.ELECTRICAL unknown The AND INSTRUMENTS resistance X be connected may the infiniteresistances. 129. As the principle of error in this type of bridgeliesin the contact resistance source to fit tightlywhen used. across any so. By inserting the 1. is less than facts are determined.761 ohms X = ^P = and when the -^2. thus giving a wiping contact. remove around = From.the infiniteplugbeing removed.761 ohms. When it is desired to insert a resistance the plug is removed. these two observations. cut gaps in heavy brass or using the bridge.they should be made and simultaneously This is accomplishedby exerting a slightpressure As dirt twistingthem. to precisevalue the ratio arms made be changed.000 ohms etc. By proceeding in this manner. a balance in P. obtaining a balance the batterykey should always be depressed before galvanometer key. indicating in P is too large. vanomete 0). In this type of bridgethe resistance coils are connected across compositionbars. of error the plugs should be oxide are and a frequent source kept clean. so that the current in the bridge has time to reach In the ohms . 2 and 5 ohms. galvanometer circuits and a shunt Connect resistance.000 ohms.and when it deflects to the right the 5.761=2. it is found that the galvanometer does until a 2-ohm This means reverse that the unknown not plug is removed. the placing keys in the battery and in the the galvanometer to protect it from deflecting violentlywhen the ratio arms Make M and N the bridge is considerablyout of balance. which one of Between the unknown resistance may also be connected. each 1.depress first the batteryand then the galthe The is Now observed to deflect left.000-ohm plug and removing the value of P is too large. galvanometer the 6.000 left the value of resistance in P is too small. to key.much time followed in obtaininga balance. With the galvanometer well shunted and all the plugs in P (Res. In is certain unknown be saved if a systematic procedure may Assume that it is desired to measure a bridge as shown in Fig. 200 ohms. a 1 to 1 ratio. The unknown sistance re- galvanometer deflects to the 5. This is repeated with 500 ohms. and when it is desired to remove a resistance it is short-circuited by the plug.000-ohm plug the galvanometer stilldeflects to the right. M is now and 1 ohm must 2. These plugs have hard rubber tops and are tapered. in P. Then: is obtained at 2. ifit is found M 143 MEASUREMENTS across advisable to do and P is another infiniteresistance. Instead of using plugs. 130. 100 cm. It is obvious that nine coils per decade be quickly obtained.so are not so likelyto be mislaid or to become dirty.a dial arm cause type used in rheostats is employed to select the required resistances. sufficient for obtaining any desired resistance. group 10-ohm coils. resistance units of the resistances The consistingof ten are 1-ohm rheostat arranged in groups coils. has the Only one plug per necessary. 131 shows a dial bridge of the Leeds " Northrup type.the next of ten 100-ohm decade is This arrangement decade. constant a CURRENTS DIRECT in is shown of the arrangement Fig.100 cm. Fig. 132. The Wheatstone of a Slide two Bridge.in which slider which moves over slide wire is the balance a German a simplified is obtained silver or by means sistance manganin re- typicalslide wire bridge is shown in Fig. balance Arrangement " of rheostat arm resistances in a decade bridge. long.is stretched tightly heavy copper blocks CD. a 130.it is a simple matter to see that the few plugs used are and fittingtightly.the dial bridge. of manipulation this type has come Care should be taken to keep the dials and contacts free from dirt and oxides. The " Bridge. Beof its ease into extensive use. convenient type principlehas been extended to an even more similar to the of bridge. between resistance wire A J5.there is less probabilityof error in reading. Each group is called a coils. A meter scale is wire. The decade 121. ten njiKnTLnHrQI^ rWi rivi rWl rTn rWf rWl rWI n"i ""V1 rwi 100 100 100 100 100 100 100 100 100 100 iHnHunjinrt^ fwfl rWI rVVi rfW rWl WYl rVtl IWl rVi flT% 1111111111 FiQ. although ten coils per are decade can often are used. apart.etc. The Wire A . advantage that the plugs are always in service. an convenient more arm Otherwise value.144 introduce A P the electromotive force of self-induction may error.the next of of one equal resistances. 145 . 10 131. " Leeds AND "" Northrup MEASUREMENTS dial bridge.ELECTRICAL INSTRUMENTS Fig. Rib connected between D and E and X between C and E.146 CURRENTS DIRECT placed along this wire. (100 Bridge: the law of the Wheatstone Z is the distance " the resistance of I is Ir and Then of the wire is that of the remainder By Then wire. resistance resistance fl. no TiQ. 132. along key K' is movable is the key K' the scale and when pressed a knife edge makes The rest of the bridgeconsists of a heavy contact with the wire. a known though X. The slide wire is not as accurate as the coil bridge. alof R and X are interchangeable. to the other end K' from a length of the 100 of the scale. the positions The galvanometer is connected between the key K' and E and the battery terminals are connected to C and D. A balance is obtained by moving K^ along the wire until the galvanometer shows A contact deflection. end of the scale one (52)becomes ^ = (52) l)r (100: ^^^ '(100n - (52)may also be written " R This is equivalentto statingthat when the slide wire is divided into two X ^^*^ 100^/ a parts which balance are is obtained to each other as is to R.because the .and the unknown copper bar E. " Slide-wire bridge. from Let I be the distance in centimeters to K' when unit per balance is obtained. Let X cancels out and be the resistance *- R Ir r r l)r. . The cable Varley loop is also used to locate similar in principleto the Murray loop. the The CURRENTS X This other ^. togetherat B should make good connection.000 ft. point Murray loop test. assumes is the same. assumed the two ratio arms of are a . A ratio and be used instead of of a bridge box may rheostat arm obviously. The slide wire is split into two sections which are to each the two lengthsof cable on each side of the fault. faults.the resistance of so the conductor is increased and location of the fault may result. : " " = rrrr 600 2. In Fig. is grounded at some A between stations. long consists of two conductors. One conductor Example. with a 100-cm. " It is bridgebox being necessary. in Fig.148 DIRECT this resistance.is connected as in Fig. A balance is firstobtained by means Let r be of P. L is the where as ground does long as the conductorIf the conductor is broken with both ends lyingon error any is not broken.a Varley Loop. the distance X to the fault may X L (L- + V be found as a false follows X) : (55) I length of one cable. slide wire bridge. the slide wire. 123. It is necessary that the batteryand the vanomete galturbances disthe order avoid to positionsshown. A cable 2. 133 to locate the fault. in occupy in the galvanometer due to earth currents. produce resistance of the fault to in the measurement not ground. the resistance per foot length per conductor.133. uniform. from Z' = 15 Z = 85 the station at which the measurement is made.as contact resistance at this point may introduce an appreciableerror. Solving(55)for X. = (56) that the resistance per foot of both conductors The jumper tieingthe cable ends and is uniform. 134. The connections shown bridgeand P is the rheostat arm. M and N are The however. " A balance From is obtained at 85 = How the station is the ground? far from equation (56) L X cm.000 = ft. with the switch S at a. INSTRUMENTS ELECTRICAL (It will be noted that bridge. test. to one X) - be found it isnecessary the switch S is thrown A together form X 149 MEASUREMENTS AND Then of bridge.but rather the to the fault.) of R in Substitutingthis value (57) R/2L(2L X) P + RX/2L M - ^ N Solvingfor X. ' '_2L/NR M R\ MP\ - N + (58) I This equation gives the distance in feet equation is frequentlygiven as follows: NR ^ In this resistance If Af = case + Rx is not the distance = which is simpler in form than ^ The (i? - (58) . This throws both lengths Varley-loop " arm -{-rX positionb.) and P M ^r(L +L N Before X can P Fig. of cable in series and 134. the fourth made is then Call this resistance R. (59) N to the along the grounded conductor iV in equation (58) X the fault. (60) . of the total loop arm a the resistance per foot of cable R r = 2L is not (This measurement or if the resistance per foot necessary the total resistance of the cable is alreadyknown. To obtain this. of the (57) to know r. makes them simple bridge measurement resistance. MP - M to p) fault. the connections in Hg. A low 135. described in Par.P 221. shown ance switch at (o) and Af 1. iV 1. over was obtained when Af 10. be secured from direct Such potentialmay usuallynecessary. not sufficiently To make the measurement. is also A considerable source of potential. In locating a fault by the Varley loop test.a balance was 2. although dry cells.150 CURRENTS DIRECT Example. from 100 to 500 volts.800 ft. and testsilver chloride cells. and Instilation Testing. 134 were Each conductor is 2. With the used. long. " Measurement of the insulation resistance of a cable.both at the factory 124. insulation resistance after installation may proper indicate imhandling or faultyinstallation. P was found to be 137 when a bal10. In " cable is installed. obtained.135. The voltmeter method in many applicable cases. after the A low value of insulation indicate that the insulation is of may an sistance re- inferior grade.A simplediagram of connections is shown in Fig.21. current mains.000. A known usuresistance. is one The method of substitution. iV then these Switch 8 is thrown Under to (6).000. 119 is . making R " = = = = = " By equation (58) the distance in feet ' ^ to the fault '" "" iirC'"^ Toio = "" ^'^""^^'"') " ^- to measure practiceit is necessary the resistance of the insulation of cables. a sensitive galvanometer isutilized. conditions. tube batteries connected in series are more satisfactory. but where the is insulation resistance is high even a high resistance voltmeter sensitive. v^ Ayrton Shnnt Battei%SI FiQ. 1 megohm (100. the unknown resistance can be determined. 0. When = The cable is until a now reasonable deflection is obtained. As the currents in the two cases are inverselyproportionalto the circuit resistances. placingthe cable in circuit. The 1/Si.because the unknown of megohms and the known make times smaller than Z"i that it would many This to obtain possible results under these conditions be in the hundreds resistance may This would resistance is but 0. deflect ofifthe scale unless the galvanometer were low value as 0. ohm. Pig. multiplying power of the shunt equals Mi described in Par. Let Di be the deflection with the 0.1 ^ M2D2 (61). resistance X is then substituted and the galvanometer readingagain noted. This wire is then removed. and the constant determined.1 megohm. the galvanometer deflections being used rather than actual values of current.1 = g (61) it would ordinarycircumstances not alone.1 megohm is leftpermanently In . the cable is firstshort-circuited by the wire shown dotted.1 meginstead of substituting practice.1 ^ I2 = 0.135. so be is difficulty by overcome the the deflection D2 not be readable. Ths 0.0001.is firstconnected in the circuit The unknown and the galvanometer deflection noted. of the use the 0. D2 and the value of the shunt M2 now The = S2. Ayrton shunt only is in circuit.1 megohm and D? be the deflection with the unknown D2 0. current h^MiDi I2 Therefore the unknown Z = M2D2 from resistance.ELECTRICAL INSTRUMENTS AND 151 MEASUREMENTS ally 0.is (62) the cable for the 0.1 megohm the galvanometer sensitivity ordinarilyis such that it would shunted.000ohms). Its in the circuit in the two cases justed ad- the shunt into the circuit and introduced ing Call this read- multipljdngpower is I//S2.1 X Under accurate resistance. Therefore the shunt is adjusted to some Call this readingof the shunt Si and the galvanometer deflection Di. 113. 0. precautions must be taken to insulate thoroughlythe apparatus itself. Due the cable to become totallydischarged. 136. through discharges the galvanometer. Fig. time this IX.) It takes time to charge the cable. Hard rubber posts should be used for supports and. When in position (a)the circuit is closed through the cable. As it is often inconvenient to wait for the galvanometer to reach a steady deflection.decreasingcontinuously. 136. wherever possible. Chap.152 DIRECT CURRENTS in circuit to protect the galvanometer in case of accidental shortcircuit of the cable.which is chargedelectrostatically. Its resistance is usually not appreciable compared necessary to that of the cable. the switch S is thrown When to (6) the electrostatic charge in the cable rushes out through the galvanometer in the reverse to absorption it requiresconsiderable time for direction.so that no correction is ordinarily for it. " Charge and discharge curves of a cable. (See par. key S is ordinarilyprovided. This is also shown in Fig. In making insulation resistance measurements.136.so for some A switch or . charging current flows. 153. When thrown over to (6) the cable. This is shown in Fig. it has been arbitrarily agreed to take the deflection at the end used in of one minute as the value to be determining insulation resistance. . When the switch (a) is first closed there is a rush of current which charges the cable electrostatically. giving the relation of the galvanometer deflection to the time. X = = The length is greater than it is for the is inverselyproportional area leakage fore length. less than leakage current that Ans. VI. flows through the wire AB. (a) (b) The because ^.0 volt. 0.1 ' 20 X of to Therefore = " .200-ft. the voltagedrop through each^resistA C willbe 1 .0 Ans. . is its insulation resistance? (a) What (6) What is its insulation resistance per mile? Ml = M2 = 1/0. 136 was 2. There2. If 0.1. measurements the so should made are 153 MEASUREMENTS through the air rather than be allowed The ground. Let a storage cell Ba supply Let the wire ABhe current to a wire AB through a rheostat R. Chap.1 Dt (from curve) =11 cm. path _. The 0. leakage path cross-sectional of the the resistance per mile R = 1^ 182 = 75. of the 2. length is directlyproportionalto the length the resistance of this the length of cable.000 =0. Its standardization measurements for making accurate standard cell. megohms. making the total The standard cell is conresistance oi AB nected equal to 15 ohms. will be 0. . divided into 15 divisions each of 1 ohm resistance. The Potentiometer. 1 volt and the voltagedrop across ance " Digitized by VjOOQIC .0001. 20 the shunt and cm. obtained curves deflection with The read read the shunt insulation whose When 0. Example.200 ft."^ 182 megohms. " resistance per mile will be the amount of the cable.ELECTRICAL INSTRUMENTS the leads should be carried to rest with insulation resistance varies temperature. long. for the mile . cable The " tested for insulation. The potentiometeris an instrument of voltage. (See depends primarilyupon the Weston Par. POTENTIOMETERS 125. with its negativeterminal to the negative terminal of the storage cell and its positiveterminal is connected to the tenth 1-ohm coil C through a key and galvanometer.) The principle is as follows: motive in Fig.000 10 1/0. .0001 10. 89. 137(a) that a standard cell S has an electroAssume force of exactly 1 volt.200-ft. 136 Fig. .1 cable the was in shown are megohm only was in circuit was in shown curve Fig.1 amp.10. the on AND temperature be mously enor- which at carefullydetermined the and stated. " B".11.S . 137(6).1 current will flow through the standard cell circuit due amp. " Simple potentiometer. (c) 137. reverse be marked some measure is known is connected in volts as unknown to be less than to the end A shown.S . the galvanometer one direction.S1.4 . is connected direction.1 . electromotive 1. .21.1 Under these conditions the current in AB zero.. If the current is less than 0.9 . to the voltage AC being either greater or less than 1 volt. the standard cell emf. If. R i\^ 0 current - . the galvanometer deflects in and if it is greater than 0. positiveterminal of the electromotive force through the galvanometer and key to a movable The . deflects in the volt. Let Therefore it be force E A B may required to whose value negative terminal Fig. R S Fig.0 1. Obviously it is possibleto so that the galvanometer deflection is in AB adjust the current is exactly0.4 R 4il + 1Ji (N the wire A-B (o) Standardizing (b) Measuring an unknown emf.7 .1 amp. of the wire Its AB. each resistance in AB is 0.1 amp.5 volts. is in exact oppositionto this as 1-volt drop.1 and the potentialdrop across amp. the current in AB is not exactly0.however.154 DIRECT If the key be depressedno CURRENTS will flow through the galvanometer.0 1.8 . . A contact T is movable on ^4. M 139. R2 inserts less moves over resistance and depressedwhen the 15 contacts. The resistance K in circuit.9 of the current OB^ when the is automaticallyput from plug at K is changed.0 volt cell exactly as in added resistance -40 is necessary to allow for voltage. correspondingto 0. an excess settingcan Fig. and M' moves double-throw double-pole. Ri.constant. standard The cell has that instead so Fig. the load on By this arrangement. the battery.1 volts.5 adjustment is 1. 137(c))changes the connection of the galvanometer from the standard cell to the unknown three galvanometer keys. . accessories. and Ro. emf.-P.0 so that be made correspond with the electromotive adjusted are Leeds to cell used.1 volt. " in voltageslightly connecting the standard excess of 1.D. which a " M to and JIf' are balance the Northrup potentiometer without the movable unknown emf.-T. and therefore keeping the total potentiometerresistance. Ri should firstbe depressedas it inserts a high resistin series with the galvanometer and prevents a violent deflection if there is considerable unbalancing. of resistance wire mounted represents 0. the voltagedrop is 5. (D. in it when across of 11 turns Each turn slide wire CURRENTS DB ohms. A over there is no resistance in series with the final balance Ro which is is obtained. force of the standard contacts. There are ance R2.)switch (correspondingto Swj Fig.100 divisions. each the slide wire. the entire wire is divided into 1. A resistance S shunts 0.01 volt and This slide wire consists on marble a cylinder. 137 this small the of (a).156 DIRECT the As amp. A volt box is merely a very high resistance from which suitable taps are brought.0 volts and the potentiometerreads 1.5 to 15 volts are connected multiplyingfactor in this case being 10. and the movable across directly terminal The of the volt other terminal remaining terminal of the volt box contact K. 140. AB If no will be If leads be carried from AD. AC. a. and 10. To Potentiometer E. box Therefore 118. being calibrated it should be connected in parallel If the voltmeter reads 119. to have a resistance Assume the " Volt JL .184 is 100 X the correction to the voltmeter 0. This is illustrated by AD the resistance AD. 139. 127.4. = are voltmeter One connected of the voltmeter connected to GH " a is a resistance connected terminal and one to the end G of this wire.184 volts.000 ohms of 4" 5 A Fig. Fig.if a voltmeter is V with AD. so Therefore. the The Drop Wire. An external view of this potentiometeris shown in Fig.6 volt. voltagesfrom 1. the voltagedrop across across Box AB current ^^%^o. - In a similar manner. with the Potentiometer.wire connections.((00 ^ J5$ J G leaves the wire at Koo that = 140. For the measurement of potentialsin excess of this value a voU box is necessary.ELECTRICAL INSTRUMENTS AND 157 MEASUREMENTS readingson the potentiometerare all made one-tenth their previousvalues.6 volts only.F. Termimdfl drop.the true line voltage across the voltmeter will be 1. across the line. B. since the potentiometerprincipleis an oppositionmethod that no current is taken from B. Voltage Measurements tiometers ^Potenare designedto measure potentials up to 1.ooo to the potentiomete the potentiometerwillmeasure J^oo the voltageacross AD. By slidingK along GH are any .M. " Volt-box AB and '" resistance of 100 ohms. resistance is then measured of the potentiometer.1.ohms.etc..F. and rheostat to control the current. a potentiometeris designedto voUage: It also be used " ure meas- by merely Let an unknown current / flow through a applyingOhm's Law. 128. 0. for adjusting of the volt box. 141.the The voltageacross the standard proper polaritybeingobserved. but is merely a convenient means the voltage. ft. since for this part of the circuit both the voltageand the resistance are known. in order is connected also with are a current of an and a potentiometer. the voltagedrop across known ured. determine its errors. The ammeter in series with the standard resistance. may to current measure Therefore: R The of method making the It is desired to know the exact To FiQ. to the operation It is not necessary GH is called a drop wire. resistance R. two in Fig. Terminals Potentiometer Calibration to measurement smaller as a Standard resistances rule.0 volt drop.158 DIRECT CURRENTS desired When used in this manner. passingthrough the am- with ammeter provided with four terminals current is shown E.two heavy ones bindingposts for potential.M. justbeen pointedout. by means Standard resistances are decimal usually adjusted to even such val^es as 10. If E. if any exist. The As has of Measurement with Current Potentiometer. The for two potentialbindingposts are connected to the potentiometer. Thus . voltagemay be obtained. They are ordinarily rated to carry a current that will give 1.0.01.be measthe current / is immediately determined. " meter.. 1. 141. 5/15 at Ammeter amp. etc. etc. be used. calibration would An instrument curve. 142 in provided with they (a) is cool resistances type shown a the 0.01 ohm. Knowing tliktthe potentiometer is Umited to 1. haying a 143. amp.5 volts.1 ohm. 1.5/100 Likewise a = 0. 1. = resistance. are often immersed set in a " Standard largercurrents. fifteen points on the scale and the correspondingcorrections each point are plottedas ordinates.it is easy to select the proper Fig.015 15-scale instrument 0.INSTRUMENTS ELECTRICAL the 1 ohm keep the can Fig. carry motor-driven Fig...01 ohm would require1.000amp. require 1. rated for ohm. of 100 ohm. (The instrument read- When or would " standard instruments are .000 To in oil. The (a) 0. resistances.001 1 amp.001 in (6) is ohm. and The more. they should be checked at ten calibrated. 159 MEASUREMENTS AND 0. water jacket.are included within the unit itself.. oil bath water-jacketed stirrer.. the stirrer. The type shown (6) Self-contained 142. range 0. 144 (a). Certain precautionsmay essary in measuring the power. = of Power.and proper correction made.160 CURRENTS DIRECT plottedas abscissas. knowing the voltmeter resistance. If the voltmeter by the dotted line in Fig. measure the power is connected taken by an candesce in- as shown lamp.)As ingsare etc. Since by means the power is the product of the volts and the amperes {P BJI). may introduce a very appreciableerror into the That is. There are three methods of be calculated.the current taken by the voltmeter is In other words. is 50 4. however. measured = D C r-VWW^ Correct : Am Ainineier meter Incorrect Volt meter (a) High Fio. to multiply the volts by the amperes it is merely necessary to be necobtain the power in watts. 143.143). Measurement " Direct current power is ally usu- of a voltmeter and an anmieter.this voltmeter current. in by straightlines as shown the correct when current instrument an successive points For instance. to connect Fig. being registered is a load connected in parallel with the lamp. included in the measurement. 144.it is customary to scale errors.(Fig. The voltmeter lead may be connected as shown by the .0.. 129.the voltmeter by the ammeter. the instrument scale is subject reads 50 amp.the power taken by the voltmeter will be measurement. although of itself small. As the current taken by the lamp is small. The voltmeter power may eUminating this error. when the ammeter The voltmeter may is being be open-circuited the read if it is certain that this will not alter the voltageacross lamp.8 amp. " (b) Resistance Correct and incorrect methods in power Assume that it is desired to Low Resistance voltmeters of connecting and meters am- measurements.8 50. 120 and watts.05 = = 41. if a low resistance CD is beingmeasured.12. _ : 0.35 by voltmeter ^ = is the true if the voltmeter power power taken loss isneglected? 42 watts. it reads 120 the voltmeter is connected inside the ammeter the lamp Apparent Power the power taken by a 40-watt tungsten and a 150 having a resistance x)f 0.. pivoted coil M.3425) apparent power is negligible.000 ohms are used for the measurement.and the addition of of the low voltmeter preciable ap- This will not introduce inside the ammeter.15 ohm measure 0.5 scale ammeter scale voltmeter by .an measures error power of 0. 2 per a outside the ammeter.9 watt. A lamp. The coils FF are wound with comparatively few turns of wire which are capable of carryingthe entire current of the circuit. It is desired to " sistance re- and having reads ammeter what power taken a = 0.as voltagedrop in the includes the now is connected case to the current reading is ammeter negligible. 120.OOU True to lamp =41. this last error negligible. = _ What amp. but its readingis too high by the true voltageacross As the resistance of the lamp is drop through the ammeter.25 X 1 he wattmeter It cojisistsof fixed coils FF and 120.05 per directly . = The Wattmeter. 11 a free to turn . now read: : (0. connected the small very reading is largecurrent a required resistance. in this error be be may outside the ammeter.15 X 0. within the magnetic fieldproducedby coilsFi^as shown in Fig. In this last case the lamps. for the measurement very a voltmeter The voltmeter should ammeter. appreciableerror.35 is the apparent 120 X 0.144(6) the resistance is necessarily meter the drop across low.INSTRUMENTS ELECTRICAL 161 MEASUREMENTS AND through the voltmeter is not reading the the ammeter. 130.Fig. for presumably an the introduced.145.1 power voltmeter introduces The If connected The voltmeter will now the read + cent. When volts and the resistance of 16. and if the voltsolid line that the voltmeter so does current not pass .05 34. However. is usually high and that of the ammeter low. " in this error will the ammeter case. The precautionsshould be observed also in making above measurements Example. which cent. = _ lo. II. the watthour meter must take into As power is usuallysold on consideration both of these factors. versed re- readingsshould be taken. 63.many an energy for . The field of the coilsFF is proportional to the current and the current in the coil M is proportional to the voltage. The Watthour Meter. that is. page 60.162 DIRECT CURRENTS moving coil M is wound with very fine wire and the is led into it through two control springsin the same manner The current isled into the coilof is connected ammeter a Weston instrument. dollars may depend upon the accuracy of basis. in series with the load in the is connected. " The watthour meter is a device (See Par. line in series with The same current that The fixed coil manner moving coilis connected as an the across manner as a high resistance R in the same voltmeter coil is ordinarily connected. Therefore the turning moment of the circuit is proportionalto the power and it also depends on the angular positionof M with respect is taken into consideration when the scale is to FF. 131. the wattmeter is seldom used for As it is subjectto stray fields. measurements. high degree of accuracy obtainable by the use of the voltmeter direct current and ammeter. The wattmeter extensivelyfor alternating than for direct current. QQQ^ Fig.) As energy is the measuring energy.Ill.Vol. which a marked. A more current complete description togetherwith its uses is found in C'lap. Owing to the 145. product of power and time. " ^The iodicating wattmeter.both the current and voltageshould be reversed and the average of the two readings is used more used. . of coil F' connected F' is so connected This in series with the that itsfieldacts in the same direc- . practically which is constant. To meet this condition shaft. their retardingeffect is proportionalto the speed of rotation. in other words. the torque acting on the armature to the product of the load current and must then be proportional the load voltage or. line the so right-handside of that they aid each rotates. tional As in the load current passes the armature. in series with resistance. This disc aluminum disc D is pressed on the motor an In the poles of two permanent magnets MM.is a much lightloads the effect of friction.Neglecting the small voltagedrop in FF. line wire. greater proportion of the load. Friction cannot be entirely meter even armature is with the most of the meter careful construction. operate light during at it is desirable that the is accomplishedby armature. means due error to friction be eliminated. is connected proportionalto the line voltage. A shunt circuit is tapped to the upper line on the left-hand side. As the ordinary meter mayof considerable the at loads a portion time. rotates between cutting the field produced by these magnets. As the strengthof these is proportionalto the velocityof the disc and they are currents acting in conjunctionwith a magnetic fieldof constant strength.164 DIRECT CURRENTS greatlyexceed the rated current terminates at the upper binding post of the not the These meter. other and It firstto the armature. From the brushes the line passes through coil F\ and through a resistance R to the lower This resistance R is omitted in certain types of meters. must be a retardingtorque acting on the moving element which is proportionalto its speed of rotation. the effect of friction is Near the rated load but negligible. so is fulfilled. they supply the field in which the armature The other line wire runs straightthrough the meter to the load. eddy currents are set up in the disc. through the silver brushes By which runs rest the small commutator on C. coils FF are on wound This meter. power is to register there It can be proved that if the meter correctly. and there is no iron. through FF. the line.the current in the directlyacross As to the load current. that the condition for correct registration eliminated in the rotatingelement. the magnetic field produced by these coils is proporcircuit.retardingits motion. it is proportionalto the passingthrough the meter to the load. which increases friction and causes to run the meter more slowlyunless F' is readjusted. This equationmeans that the meter constant . The moving element turns the clock work of the meter dials through a A to rotate.wear in time. To reduce friction and wear. as a small error in the largersizes may ultimately the difference of many dollars one the other. it is important that they be kept in adjustment. as incorrect. The element rests on a jewelbearing /. pivot. The jewelis supported on a spring. continuously.146(a). The coil is movable so that its positioncan be so adjustedthat the friction error is just compensated. a mean To The power and over a by a caUbrated revolutions of the disc D The ammeter. is as follows: WXH where =^ (63) KXN TT is in watts /f is in hours *' constant^' usuallyfound K is the N is the revolutions of the disc.become may. the rotatingelement of the meter is made as hght as possible. meter on the disc multipliedby the revolutions of the disc givesthe watt-hours registered by the meter. Even if the initial Adjustment of the Watthour Meter. which is a sapphirein the smaller sizes and a diamond in the heavier types. Fig. roughening of the jewel. 146 (5) shows the interior view worm of Thomson a watthour meter. and the gears G. is largelybased on the regto consumers As the cost of energy istration of such meters. such on pittingof the conmiutator. A hardened steel pivot rests in the jewel. " This isdue to many causes. or way adjust the meter it may be loaded as shown in Fig. the revolutions of the disc.change in the strengthof the retardingmagnets. the time is usuallymeasured in seconds.in with a meters. the registration of a watthour meter adjustment be accurate 132.ELECTRICAL tion that due as INSTRUMENTS AND to coils FF. 165 MEASUREMENTS Therefore it assists the armature it is acting Being connected in the shunt circuit. periodof time which ismeasured relation between most by the load is measured taken watt-hours and are meter volt- counted The stop watch. In time the pivot becomes dulled and the jewel roughened. When checkinga meter. The gear ratios and clockwork take care of the dial registration. etc. and is found to be in error near lightload. brought within 0.5 An".4 X 40 X up slightly. 0.4 amp.166 DIRECT CURRENTS Equation (63)then becomes t is the time where When in seconds. JNTX Ji: X ^ 3. The lightload adjustment (made at from 5 to 10 per cent. rated load) is effected by moving the friction compensating coil F\ If has been the meter is slow the coil F' is moved in nearer the armature.600 ^^^ ^ V The of the meter cent. and if the moved farther from the effect of the meter the center. Per cent. regis- Near full load the adjustments to be made.4.6 revolutions in 40 disc makes the seconds.074 . oe- ' = = 98. In the test of a 10-amp. With a meter There magnets are that the meter means are are moved may is' X 1.5 per cent. slow and should and be speeded careful adjustment. is running slow the magnets two nearer retardingcurrents the magnets What '^ calibrated indicatinginstruments easilybe volts 3. from (64). and . of accurate tration.the error is obviouslydue to friction. Let the average determined watts and ammeter readingsbe TFi. accuracy constant 9.4 X 0.600 _ ~ 100 This average 1. watthour 53. intermittently A run of about a minute givesgood results. of the meter accuracy = 9. If the meter moved. = ^ " . The watts average from the corrected voltmeter by the indicated as during the meter same periodare. ammeter are read while the revolutions of the disc are being counted. accuracy per is W/Wi 100 meter Example. ^ is 1.6 T. a at this load? 116 Average standard watts TTi meter from watts (65) Average ^ The are the center is of the disc where reduced.5 per cent. 53. is the meter the voltmeter and tested. is running fast If the meter correctlyadjustednear full load. and amperes during this period are 116 volts and having " of the per cent.090. so that the meter at lightload. " Diagram of a 3. Other 147. upon a " watthour The meter. meter is It does . should be re-checked at fullload and then again BU8 148. affect the fullload adjustment slightly Load Neutral Fia. + \ Fig. " Astatic heavy Types of Watthour designed to register energy current Meters. three-wire three-wire system.ELECTRICAL if the meter This INSTRUMENTS is fast it is adjustment of F' may AND 167 MEASUREMENTS pulledout further from the armature.wire watthour meter. the fieldin which in the rotate armature magnets the are rotates the other armature effect will be nil. 147. the One below the conductor. 148. creased strengthof one is in- the other is decreased. to the meter In the former the meter case does not registeraccuratelyunless the voltagesbetween the two outer lines and neutral are equal This error is usuallysmall. There These is above armature and the a single other is Any strayfieldwill presumably strengthen one the field in which magnetic field created by two rotates strengthof so surrounded it will weaken ing that the result- retardingmagnets. shown as or is omitted. as the meter differ materiallyfrom that the two in CURRENTS shown connected are The in in Fig. 146 except oppositesides of the line be connected circuit may armature be connected across it may the outer is used the neutral connection If this latter connection to the neutral wires.168 not DIRECT coils FF shown Fig. . The meters already described should not be installed near bus-bars carrying heavy currents because the strengthof the field and of the retardingmagnets may meter be affected by eliminate the effectof stray fields an astatic is used. To type of meter spindlewhich heavy conductor. are as sets of placed that if the so these magnets are much as by an For further tection proiron box. There are two armatures on the stray fields. Fig. similar. The surrounding air and the insulatingsupports for the wire have an extremelyhighresistance. for example.CHAPTER THE 133.the air itselfis a fairlygood magnetic conductor. 169 errors of considerable . This paths in the same way is niustrated by the fact that even in the best designeddynamos from 15 to 20 per cent. that any leakage current which escapes from the wire is negliso gible compared with the current flowingin the wire or conductor. Magnetic paths are usuallyshort and have largecross-sections in proportionto their length. flux may when they are several feet suflScient to magnetize watches even known distant from the machine. If the magnetic of circuit and the linked with this properties a ampere-turns circuit be known. In the magnetic circuit there is no known insulator for magnetic flux. The VIII MAGNETIC CIRCUIT Although the general nature and characteristics of magnetism were discussed in both Chapters I and II. The electric current has been considered as confined to a path. the magnetic flux can be calculated in the same Magnetic Circuit. that the current manner " be calculated in the electric circuit may if the resistance and circuits are In this respect the two voltagebe known. a wire. Therefore it is impossibleto restrict magnetic lines to definite that electric currents are restricted. They are often so complicatedin their geometry that only approximations to their magnetic resistance can be obtained. of the total flux produced leaks across air paths where it cannot be utilized. The presence of this leakage and its intensityis often be detected with a compass.which makes itdifficultto attain the degree of precisionin magnetic calculations same as are obtained in electrical calculations. In fact.no quantitativerelations were considered. This often causes magnitude in magnetic calculations. The magnetic circuit differs from the electric circuit in three respects. " subtracted. result is produced by 15 amperes The same flowingthrough 100 If any turns. The magnetomotive force of a circuit is measured by the work done in carrying a unit north pole through the entire circuit. The gilberts gilbertis seldom used in commercial work. oersted is seldom name used work.47r7iV = = 1. The permeance " of the reluctance ((P = -^)and of may a circuit is the be defined erty of the circuit which permits the passage of the as cal recipro- that prop- magnetic flux .500 ampere-turns. Under MAGNETIC UmTS Ampere-turns (IN). It is directlyproportionalto the ampere-turns of the circuit and only differsfrom the value of the factor 0. Reluctance cuit. in the electric circuit. Magnetomotive force tends to drive the flux through the circuit and corresponds to emf.4t 1. (mmf.4t or 1.257 IN. magnetic flux and correspondsto resistance in the electric cir- Reluctance of The " unit of reluctance is that of This unit is called the oersted.they must be 134. ampere-turns act in opposition. in commercial Permeance The centimeter-cube a of air. ampere-turns by the constant Magnetomotive Force " = F 0. but the name The unit of magnetomotive force is the gilbert.170 CURRENTS DIRECT tric ordinaxy conditions of use the resistance of most elecconductors is substantially constant. ((P). magnetic resistance of materials. varies over The magnetic extent the magnetic historyof the material. Correction for The the effect of temperature changes can be accuratelymade. on resistance of iron may easilyincrease fiftytimes when the flux alters from a low to a high magnetic density. although temperature changes may cause variations of several per cent. 10 amperes flowingthrough 150 turns give 1. is resistance to the passage ((R).267. and the amperes flowingthrough these turns.however.267. is not constant but This resistance depends to a large wide ranges. also F). acting circuit are obtained by multiplyingthe ampere-turns by on a 0. That is. The ampere-tiu'ns acting on a circuit are given by the product of the turns linked with the circuit For example. . proportionahtyis unity.. two means a /a times air. if the path has a lengthof 1 cm.since the reluctance of a long and 1 sq. cm.having a permeability Moreover. On 149. li (Ri where ii = length in consideration. cm. sists of a (a) Path whose reluctance (") Path is 3 oersteds. in iron. the other hand. of simple magnetic Reluctance " paths. the reluctance of the path through which the flux passes is one-third that of one cube alone. cm. 1 cm.inverselyproportional to Fig. cm.149 (6). lower reluctance. cross-section is one oersted.172 DIRECT CURRENTS path in air having a lengthof 3 cm.provided the maintained were the be same between poles faces. whose reluctance ^z is oersted. as shown in Fig. its cross-section and in series.this path is equivalent to as three centimeter-cubes placed in series.The reluctance is proportional to the lengthof the flux path. inversely proportional to the permeability of the material. or 3^^ oersted. As the total flux must through each cube. Fio. the = Aim of that uniform circuit under part of the cross-section in sq. in the jSgure. and a crossHsection shown of 1 sq. if these paths were ju. and a cross-section of 3 sq.Ai = cm. The reluctance is inversely portional proto the cross-section of the path. of . the flux would in value mmf . it is evident that the total pass successively reluctance is 3 units (oersteds). Reluctances " of constant path in air Hence. The 160. reluctance its This The of any portion of a circuit is proportional magnetic to its length. the flux density and the previousmagnetic history. steel to the magnetomotive in simpleform.151. The total permeance (P and reluctances in = (Pi + (P2 + combine parallel 1/(R (P3 + (P4 justas resistances in parallel. If 173 CIRCUIT /xi permeabilityof that the = magnetic circuit consists of several parts in series as shown in Fig. 160. portion of the circuit. " = 30 Gilberts Magnetization relation of the flux in iron force cannot be 40 per curve or Cm. l/(Ri+ 1/(R2+ 1/(R3+ 1/(R4 = Permeability of Iron and Steel. expressed It is necessary to show Such curve. for cast steel." by a curve called the "magnetization Abscissas for one grade of cast steelis shown in Fig.THE MAGNETIC that and portion of the circuit. this relation . ordinates are the correspondingflux densities (^). The 151. a curve and are magnetomotive force in gilbertsper centimeter (fl"). The permeabilityof iron or steel depends on the quahty of the material. " H Fig. 136. the total reluctance is: a (R = (R? + (Ra + (R4 Zi/AiMi+ /2M2M2 + /3/ASM3+ U/Aah^. Permeances permeance (Ri + = in parallelare (66) added together to find the total in parallel added togetherto are justas conductances find the total conductance. is practically a straight Beyond B the flux densityincreases much less rapidlyfor a given increase The in magnetomotive force and the iron approachessaturation. Fig. permeabilitycurve ordinate is obtained for this same steel. 152 shows Each 162.000 16. ^The relation between for the magnetic circuit. pointC. It will be noted that the permeability It begins at a comparatively low varies over wide range. a at the point p.magnetomotive force. ^ (R the gilbertsper cm. cm.since "f" ^ B. is also equal to the lines per sq. Law H^ Magnetic Circuit.000 Sq.increases to a maximum to about by dividing5 by for each value.. Cm" per Permeability curve for cast steel. and then decreases value. 0 - ^ H.000 Density - Linei 20.174 CURRENTS DIRECT From to B the A curve line. even The iron is then said to be saturated. in leoo 1400 PERMEABILITV CURVE CAST STEEL 1200 f-iooo I s. .and reluctance.is the "knee of the ciu^e. where the bend in the curve is very decided. = (67) = cm. 151 is called the normal saturation or induction curve.being a centimeter-cube.so "^ since the cross-section of the cube is 1 sq. in air 0 H/Gi. 164 shows normal induction curves grades of iron. 151. point of the curve in Fig. (R is unity. = in Hand air.. The type of curve shown Fig. ^ 800 eoo 400 200 0 2000 4000 6000 BclElux Fia. and of the " resistance for the electric circuit. is identical with the relation between current. " the 8000 12. emf. flux." Beyond C the flux can be increased but slightly with a very great increase in the magnetomotive force. for other commercial Fig. one-fifth its maximum 137. Magnetic problemscannot used in Par. FiQ. Fig.476 "" ' 1 800 1. 0. 153. This is due . in. in. permeabiUty of rin" flux in the the also the flux density. 137. Arts.54 cm. from equation(66) F1+F2+FZ + OAirlN .0443 + 0.64 X sq.29 X 0. Fi.etc.0 1.7 = 2.476 2. 153. Error. U Ai " = From 1.7 1.140 lines (maxwells). 2. Example. the method " cm.in series and magnetomotive forces Fi.. equation (68) 471 0 with ringmagnet.2 A. (gausses) sq. 0.700 lines per of Trial and readilyby lines per sq. (68) _ . Assume determine Neglectingfringing.29 sq. The flux density: B " 1 140 ~t~nQ " = 138.2 X = cm. 250 the turns of wire.5 amp. = 2.64 He = 46. Method be solved 884 6. current flows. 800.64 X = 1. 471 = = 0.THE The 176 CIRCUIT MAGNETIC to the magnetomotive jlvxis proportional forceand inversely to the reluctance of the circuit.4jr X li = 18 in. ^The " through which a the iron to be Ring-type electromagnet.29 X 0. and F = 0.369 1. proportional If the magnetic circuit consists of several distinct parts having reluctances (Ri.is wound 471 = 46..5 X 260 18 X - Ke in.. cm. " of 1.6I2. 810 maxwells 2. 2. The iron ring of Fig. 152. are substantially As new the value of = m 139. 152 = + ^^ 0. permeability. Ampere-turns.13 X 2.123(Ra=^2|:^= ^^^ = ^ 0.176 DIRECT to the fact that the CURRENTS permeability(which is a variable but is given in the problem as a constant value of 800) is not ordinarily similar to those and curves known until the flux densityis known Therefore the perof Figs. Assume that the permeabilityis 800. Determination shown in Par. IV.290 gausses. that the voltagedrop per unit lengthof a conductor is independent of the total current but depends only upon the current densityand the resistivity of the conductor. " whose ^' 18.950 maxwells.123 2. 163 and Par. 137 is made of cast steel is given in Fig. 2.0365 + 0.180 gausses.123 2. the last two values of flux and flux density correct. of " * = T- . Example. = the permeability at this density is 980. In a similar the magnetomotive force per unit length depends only manner the fluxdermty and the reluctivity of the material. This is upon proved as follows : Writing equation (68)for one portionof the circuit. meability is not As the answer usuallynecessary known until the in turn depends to resort has been answer the upon to trialand determined.13 ^' value of Therefore (Ri permeability.54 1.0446 B From must Fig. correspondingto this flux density is 990 or sufliciently close to the value 980 just used. It was 68. Chap.54 X ^-^^^ _ ^ - " 1. The air gap is reduced to permeabilitycurve He in.29 X 980 471 ^ The value of B = ^ 0.it is error. Determine the flux and the flux density. 151 and 152 have been consulted. be recalculated using the new 18.29 X 800 ^-^^ _ __ - - 0. Such curves in Fig.47r and also the permeability. This is more convem'ent corresponding and avoids using 0. divided by the of the material. lengthof a circuit it is only necessary to know the flux densityand the permeability. Instead of plottingthe permeability is usually againstflux densitythe magnetizationcurve plottedwith ampere-turns per unit length as abscissas and the flux densityas ordinates.MAGNETIC THE 177 CIRCUIT //^ (69) magnetomotive force is equal to the product of the flux densityand the length of the magnetic path. To determine the magnetomotive permeability The y 10 20 30 40 GO 60 TO so 90 100 HO Amper* Fig. a unit solution to be readilyobtained. force for 154. 154 for various commercial steels used in the shown are manufacture of electrical machinery. In problems where flux and the cross-section of the magnetic paths are known. and it is desired to find the requisite ampereenable referred the turns to produce this flux. " -tarns 120 130 140 160 100 ITO ISO 190200 Inch per Typical magnetization curves.the curves just to. . density in the is (approximately)16 in.. 16 in.178 DIRECT ^To illustrate the Magnetization Curves. The length of flux path IiNi is 368 ampere-tums or lower yoke. 140.from a every = length will be 16 X way per inch 118 = = 118. shorter. " flux density in the lower The yoke: ". Typical electromagnet. 155. except that the This small difference will not make the amperes-turns for the two IiNi = poles piecesare: 368 any appreciable . pole piecesare in is 0.^.000 As there curve are two (castiron)the ampere-tums cores.25 in. so a flux of 750. are iron and the yoke and pole pieces are cast steel.. 1. 16 X = 23 - required to produce cores 750.000 lines in the electromagnet of Fig.890 identical with the yoke. mean The density of 62. " ^^^ CMt Fig.900 = 4X4 the 368 is B2 From Fig.000 lines in the 46. Use use CURRENTS of the " to produce an air-gap Example."" ampere-turns per inch for The is steel). Neglect fringingand leakage. Detennine the ampere-turns necessary The cores cast flux of 750..500. the total I2N2 The path error. steel 155. 154 (cast 23. of the magnetizationcurves the followingproblem is given. . 15 8.000 lines per sq.235 Arm. steel).8 = = 64 X 19. sider Conshown in the figure. (See equation 71) (O. each pole into a flux of 7.includingthe leakage flux.000.154). the about 39.000 0.870 (air). For 54.313 = X 39. = =^= /e (approximately) in.870 (air). equal to the armature 8. As simple example a of such It is desired to send Fig.6 in. circumference mean 5" - 10. The paths of the fluxes from the various poles.after corThe the annature. in consider the dynamo shown calculations.800 39. H.000 " as pole flux divides.and utilizingthe magnetization curves Fig. rection has been made for armature The etc. . it is a comparatively simple matter to determine the total ampereturns per pole.) = .000lines from air gap has an effective length of 0.6 (caststeel). ~ ia\ to allow for the 25 per cent. ture another poles introduces flux between of amount factor which leakage be must considered.7 = 6c I2N2 cd hNz de UNi hNi = = 0.000 J T:n Flux cores J if^ m density 54.448 ampere-turns. Therefore ^Core ah IiNi Yoke ' Core ^Gap = 19 X 10. density in the armature: 39.000 as the flux plus the leakage flux.fringing. (caststeel).630.180 CURRENTS DIRECT The teeth. 2.7 in. The lengths of path are easilydetermined.235 in.500.630. air ducts. leakage coefficient (ratioof core flux to armature flux)is equal to 1. air duct space laminations. way between the .25 = ^'^^'^ = = 48.. 154. 7. are the flux path ahcdef.000. ^^ Flux the 19.8 = air-gap density X 1.15. sheet steel).000 The core in the yoke. 1.7" = ^A flux densities The are of in cores = " Flux - = density in yoke one-half going each Flux This and density in must This makes o'/ifi v '\) = armature = ^' J is ^^ 90.000 of Knowing the above factors. 156.235 = the (approximatelyone-eighth in.500. 12. * The 5c 5 length ob 0. teeth. flux in the = be increased the spaces less follows: as = x yoke.^^^ - 5" 24.. 38 7.260 cast 205 X = = = Total 205 = -' 2. fringing.19 ampere-turns per inch are necessary for for ah: cast steel (Fig.etc. in.000 X 1. - efl^i Gap fa ItNi = 3 X = IaNa 12. 157). = = = . is zero duction but the magnetic in- has not reached zero. magnetomotive force If the decreases. This is called curve saturation normal magnetization has already been or and curve the discussed. and the flux (orflux density) As this machine is " will be similar to that shown by Oa curve (Fig. The design of the excitingcoils themselves is not a diflScult matter. 157. flux densityd'd is The negativemaximum d'd negative maximum equal to a'a. A posiforce is again zero and the negativeremanence tive Oc is necessary to bringthe flux density coercive force Of Oa' the magnetizing force again becomes When again to zero. If the magnetomotive force actingon an iron the relation between mmf.THE MAGNETIC polesin series supply the excitation As two 181 CIRCUIT for this flux the ampere-turns pole are per IN = 7. sample begins at zero and increases. density Ob is called The flux the remanence. 142. symmetrical. magnetizing force Oc to reduce the flux density to zero.724. The magnetizing force Oc is called the coercive force. Before the density can be reduced zero.it requiresa negative Fig. the magnetizingforce be increased in the negativedirection If now the flux densitywill be carried to a to df where Odf 0"x'. If the magnetizing force is now increased toward will pass through point e when the magnetizing zero. the mmf. the magnetizingforce flux to must be reversed in direction. Hysteresis. point b is reached.each complete magnetic circiiit requiresthis same number of ampiere-turnsper pole. " Hysteresis loop. Am. the curve Oe Ob.448/2 = 3. the flux will now decrease not but aOy along the line will decrease less When rapidly along ab. That is. 168. on the ordinate scale represents4 kilogausses. The maximum in Fig. let the area of the smallest loop. in. " Oa2..The ergs loss per cycleis: 10 A T^. This givesthe loss in ergs per cycle.and the curve called a hysteresis tion loop. ai. a^ all lie along the norThis is one saturation FiQ. The hysteresisloss is proportional the area of the hysteresis loop. flux densities. ^'^ X 10 X ^ 4. Such a loop shows that the magnetizaforce behind the iron in lags magnetomotive per centimeter is the magnetizing force. is complete cycleof magnetization. to Hysteresis Loss. " The scale is such that 1 in.167 and 158. and 1 in. . on the abscissa scale presents re- gilbertsper cm.Figs. In fact the loss may be obtained by findingthe area of the loop hysteresis to scale. closingthe loop. flux If several loopsare taken. be A sq.000 ergs. mal pointsa.each having different maximum of the three loopsshown they will have the appearance densities.and that an expenditureof energy or requiredto carry the iron through a cycle of magnetization.182 DIRECT the flux densitywill return CURRENTS to its originalvalue at a.Fig. and dividingby 4jr. 168. curve 158. For example. Hysteresis loops for three maximum 143. 000 6.028 ergs per cu. Linkages.028 X 40 = = 7. INDUCTANCE 144.THE To by MAGNETIC this energy convert 183 CIRCUIT loss into joulesor watt-seconds divide 107. are given a few typicalvalues of cast steel Forged steel Cast iron ".004 8. cm.a magnetic This magnetic flux completely flux is set up about the conductor. in ergs per cycle.where a conductor carryinga particularly^ current is linked with an anchor ring.9031 = 6.159." X = 3. As a current and the resultingflux always completely encircle This is shown each other they are said to link with each other. " Some a in the conductor familiar pletely com- examples of this are given in Fig. per cycle. 281.004 0.: 0.004 X Total loss W = 1. the hysteresisloss per cycledepends upon two factors.0009 steel Example. encircles the conductor and the current encircles the flux.6 X 3.025 Sheet iron 0.000i.17 is a flux depending on the material.and B is the maximum is the Wh constant density in Below Hard gausses. Ava. The loss magnetic material and the maximum within certain limits may be expressedby the Steinmetz Law as The follows: Wk (72) nB^'^ = hysteresisloss per cu..013 SiUcon 0.757. cm. cm.2449 log 8.9031 = Wh = 0. .000 1. where the currents and related fluxes are shown. What will be the ergs loss per cycle in a core of sheet iron flux density is 8.0010 0.767. 159 (c).QP0 ergs per cycle.2449 log 1. flux density.020 Silicon sheet steel 0.000 7.000 having a volume of 40 cu. in which the maximum " Wh = 0. of lines The product of the turns of conductor and the number of flux linkingthese turns is called the linkagesof the circuit. If " a current flows in conductor. well in Fig. " henrys. Example.* inductance and / is the current (73) = I X where linkages.thrusting the galvanomother means.000 X 800 What 5 are amp. 160 (a).Fig.500.0 145. amperes. A 20 = of current flux of 2. bar magnet into the coil or by some eter be to deflect observed will momentarily and then to return . Inductance 159.am- etc. A certain solenoid flowing in the winding produces linkages? has " 800 The number of these turns.500. a magnetic field be set up through this coil. Induced Electromotive circuit? Force. a 2. practicalsystem of volts. Oarrent Fig. the 10" linkages. from " definition : N"t" L is the Note. If the terminals of an sulated in- and a coil. Illustrations of flux-current L lines Gurren (5) in to divide line in the by 10* because 10* magnetic peres.184 DIRECT CURRENTS Example.be connected to a galvanometer. " What of the above is the inductance .either by . "t"is the flux in maxwells.000 lines. X unit current linkagesper in a circuit is called the inductance bol " ''L. " are in It is necessary equal to one 10" henrys. of the circuit and is representedby the sjonimplying linkages.^. The unit of inductance is the henry. ^=-5OO0i.=4. 20 X 10" . the galvanometer will be observed to deflect again. case. Induced " electromotive direction of the induced pole withdrawn force. this current will tend to prevent the magnet from being withdrawn from the coil. will be found emf an .will oppose its enteringthe coil. the coil. be allowed to produce a ciurent. it this electromotive force also ceases. If careful measurements be made. the value of this electromotive force will be foimd to depend upon : (1)the number of turns in the coil. When If investigation be made. electromotive force is now such that if the emf. momentarily as before.but the deflection is oppositeto its direction in the first force is that shown (a)North in the Fig. has been that the direction of this induced electromotive figureand that this direction is such that if the emf. from the coil. produces a current. (6)North pole inserted in coil The 160. The average force in volts is given by electromotive N"t"10-8 e (74) = t where N is the number of turns flux in lines linked with the in the coil.this current will is the same tend to push the bar magnet ovi of the coil. be withdrawn If the magnet Fig.(2) the rate at which the flux linked with the coil flux changes. The electromotive force in each chmge of case is transient and ceases when the through the coil ceases.THE 185 CIRCUIT MAGNETIC temporarilyinduced in the flux through the coil has ceased to change. or what thing. that This shows to rest.and is the total change of coil. "t" t is the time in seconds re- . 160("). 10~* reduces the flux 0 to practical units so that e becomes volts. The minus sign indicates that the induced emf is in oppositionto the force which produces it.000 flux through the coil is decreased " is the induced What lines links at electromotive a coil having 360 turns. the the number to a batteryand a switch S closed begin to flow in the coil.186 DIRECT CURRENTS quiredto insert or withdraw this fliixfrom the coil. As this flux increases it must (Fig.161).the electromotive such a direction linkingthe coil and Therefore of turns flux increases. 26. the expense of the mechanical energy produced required to push the magnet in the coil against their opposition. must have in the By Lenz's Law. of electromagnetic cases have such a says: currents direction that their reaction tethds to stop the motion producesthem. This principle firstformulated by Lenz. Fig.the induced currents. in the coil.2 second.'^ law This is also based That energy. which Electromotive 146. volts. uniform a force to rate during the This in 0. of consideration force thus induced increase the on hence this current as to oppose must cannot oppose reach the any its . . rate of is the average J change of flux.so that the induced electromotive force may be said to be proportional to the number of turns and the rate of change offlux. A flux of 1. " If a coil be nected con- coil. for this principle is manifest in practically all types of electric machinery. the law of the conservation upon is. 160(a).current will produces a flux linkingthe induce an emf. fact that the currents The produced by induction oppose the motion producing them should be carefully noted. This magnitude of which depends coil and and current the rate at which also from a increase in the flux of current. which of representenergy. Example. the magnet Force against the opposition try to prevent this withdrawal of Self-induction. in a form known was as LfCnz's Law ^^ In all which which the induced indiLction. zero of withdrawal? time e=350i^^l0-.600.25 = Ans. the or at are requiredto withdraw energy of the induced currents. . tripcoils.resistance 20 ohms and inductance 0. inductive and an inductance Example. The time constant of this circuit is 0. When etc.i The current increases at a Napierian logarithmicbase. Rise of current.as curve in the initialcurrent- be the short-circuited. 162.14 .03 0.06 .4 time? 04 The time constant i = = jj^n ~ ^-^^ second.6/20 should be seconds and is shown the diagram.6 henry. 0. ^A relay having a resistance of 400 ohms is the time con110-volt is circuit.632^ = 0.02 . " .16 .01 aO . " in an circuit.188 DIRECT CURRENTS rapiditywith which the current in a circuit rises to its ultimate value. Fig.18 Second FiQ. connected What stant across a henry of the relay? To what value does the current in the relayrise in this " of 0. T . == and e the E/L amp. t seconds after closing impressed voltage.06 .12 . since it accounts for some the time lag observed in relays. pressedvoltageand the same = J^ "~6. This curve on inr^ compared with Fig. it does in showing the riseof current a non-inductive is*="D(l"~*ir) current at time. 163. The effect of inductance This is also short-circuit. a shortcircuit takes place there may the be considerable delay between time the short-circuit occurs at which and the opening of the breaker or switch controlled by the relay.1738 amp. 163^ shows the rise of current in a circuit whose impressed voltageis 10 volts. delayed rise of current in a circuit due to selfinductance of should be carefullykept in mind. per second at the instant when the switch is closed. in which the circuit has the same resistance but has no inductance. an inductive circuit carryingcurrent current ^ does not cease The equation of the E is the where switch rate factors controlling on rush If of the one of immediately. In the electromotive an due current electromotive induced the to prevent the flux being withdrawn in Fig.but continues to conditions. " Decay in of ctirrent showing the decrease an inductive of the current circuit. 164. If the current tends to inany inductance opposes it. A ^ curve 164.if it tends to decrease. It thus appears that the effect of inductance is always to oppose crease.and ing.16 Second FiQ.12 . The circuit has the same It is usuallyadvisable to fuse the batteryso that it in Fig. Rt - i where the i is the value of the switch. decreases. when the body is at rest. Inductance correspondsto inertia A body having inertia opposes any force tending in mechanics. the closingof . 0 . 163. ^ The equation of this curve.and current = he at a /o is the initial value of ^ time.inductance tends to oppose this decrease.as is shown in Fig. the current when force tended so to to the electromotive of force of self- force in the coil. with time is givenin constants as the circuit shown Fig. 164. will not be injured.160(6).08 40 . since short-circuiting the inductive circuitalso short-circuits the battery.06 . In decreasthis flux also decreases. until an appreciabletime after become zero This the short-circuit. that the way is due does flux the flux induces same flow and similar circuit under not 189 CIRCUIT MAGNETIC THE the decrease of the current. inertia opposes any rest.04 . change in circuit conditions.02 . force of self-induction tends to prevent the electromotive now the instant linkingthe coilis due to the current. The induction. t seconds after current.and if the body is in to set it in motion force tending to bring the body to motion.14 . after having established the current in the circuitof Fig. Field Fig. The energy of the field is dissipatedpartly in this resistance rather than at the switch contacts. should be carefully even avoided. the electromotive force induced in a coil due to a change in the flux hnking the coil is " e =-Ar|lO-" . 165.163. al*cing voltage has been known alternator fields as to in to some reach such puncture their insulation when values in the field ft . in the case of very low voltages. Not only is there the danger of being burned by the arc. To with connections. at the switch the switch S be opened. 165 is often used. At the instant of opening the switch the field (and the hne temporarily)is paralleled by the field dischargeresistance. This arc will be much greater in magnitude than that formed at the contacts of the switch in the circuit of Fig. From equation (74)page 185. Calculation of the Electromotive Force of Self-induction. voltage are the same electromotive have such In a force of self-induction and value fact this as to cause severe circuits may at the switch contacts. a field dischargeswitch shown in Fig.FieldDiM:harge AWVWVVV OQQQQQQQOQQQQOOQ. cuit with resistance only in the circuit. 162.' protect the field from puncture. but of being injuredfrom the high induced voltagesas well. although the current and cirThis arc is due to the in each case.190 DIRECT CURRENTS If. circuit is " Field-discharge switch opened. Contact with switches opening inductive circuits.a noticeable arc will appear blades. THE where N of turns. must maintain field To constant a does require an expending in electromagnets. If the inductance varies as well as the flux.equation (75)maybe written: --i.7(equation73. The energy of the magnetic for energy FiQ. Ans. g^ = To Field.06 of 12 second. generator amp. any Example. potentialenergy and is similar to the energy of raised weight. is " field circuit of a inductance of 6 field current interrupted in 0..L\"l\'.440 volts. of the Magnetic establish a magnetic Energy " 1. field energy be expended. 166. as field is stored a 166. Fig. Work is performed in raisingthe or . induced electromotive average force in the field winding? is the 12 e 6 = 147.-Energy heat in the copper and is not concerned with the of the magnetic field itself. page = 184). the additional term (76) accountingfor the electromotive force due to change in the inductance. and also that the electromotive force of self-induction opposes change in current. and is the number 191 CIRCUIT MAGNETIC the "t"/t the at which rate changes. The to the self induction isproportional ol and the rate of product of the inductance the minus change of current with motive sign indicates that this electro- force opposes the change of current. Remembering that flux L -^ 10-" = N"l"10-8 or jr. of energy even lost in the exciting The energy coils of electromagnets is accounted not of a suspended weight. its value may be writtenic^ electromotive The force respect to time. what The has an If the henrys. energy of the at the switch contacts arc fourth of its initialvalue. 10 ^In a circuit having " What amp. The energy of the weight due to its positionis Wh foot-pounds. what in 0.000watts = henrys. This coil is connected between the bellringing battery B and the grounded gas pipe.is W where is the circuit inductance L (77) 1/2LP = henrys and in / the current flowing. Arts. for In an alternating current contacts. This occurs coil consists of laminated shown a iron considerable number core. When meet. 200 P = ^ = 1 kilowatt. of the magnetic field Equation (77) shows that the energy if is proportional to the square of the current. or watt-seconds. may The energy of the fieldin joules.and a contact on the laminated core the two contacts on the burner magnetic field is established in of the spark coil. The other terminal of the battery is connected directlyto the insulated the gas burner. Example. A very common of the electromotive force of self-induction use in the so-called spark coil used for gas lighting. to maintain the weight in this position. is the iatemipted by the magnetic field during W 1/2 = inductance is the average this time? 4 X = 1. X 102 of 4 magnetic field. many This is available and energy be can utilized in ways. the is current If this circuit is value of the power 200 watt-seconds. The core is of turns of wire wound usuallymade on of iron wires a as in Fig.where W is the weight in pounds and h the height in feet through which the weight has weight been to its raised. 167. the circuit is closed.' the of energy second. In the same the way available and example. as. opening the field circuit of can be reduced to This fact should be remembered a one- when dynamo. the make may itself manifest at the switch arc stored in the energy magnetic field is in many ways. Therefore be reduced by a suitable resistance to one-half the current can the its initial value before opening a highly inductive circuit. circuit this energy all be returned to the circuit.192 DIRECT CURRENTS but no expenditureof energy is required position. As the two contacts of the .2 an expended Ans. A and B. Energy is thus stored in the magnetic field. a change of flux This emf. Coil B is not connected to any source of voltage. the gas beingturned on simultaneously with the closing of the contact pointsand by the same mechanism. Electric " gas ignition.a high electromotive force of self-induction is produced in the spark coil. When the switch S is closed. buildingup a field which links the coil. This causes at the cona hot arc tacts. Mutual In Fig. Gas Cock '^Ground Connection FiQ. Inductance. in B inducing an emf. in a hot spark at the considerable power is developed resulting contact points. simuUaneovsly occurs the terminals is detected by the galvanometer connected across of B. The positionof B with regard to A results in a considerable part of the magnetic flux produced by A linking B. in S. two 148.but to a galvanomete Coil B is placedso that its axis is nearly coincident with that of A and the two coils are close together. Coil A is connected to a batterythrough a switch "S. magnetic field at the gas jetwipe by each which is built up as the two contacts other.THE burner MAGNETIC separatCjthey snap 193 CIRCUIT apart and the circuit is broken denly^ sud- Consequently. 168 are shown coils. When this energy is released suddenly by the contacts snapping open. Therefore. which ignitesthe gas. or if it be altered in magnitude. and upon opening the switch S its deflection will reverse.current flows in coil A. 167. Upon closingthe switch S the galvanometer will deflect momentarily. showing that the induced voltage on opening the circuit is opposite in direction to the induced voltage on closingthe The spark coil may be considered " 13 as having a .if the current in A be interruptedby opening the switch S. of "t"ilinks B. that emf . 02 the change in magnetic links coil B. its magnitude. produced by coil A does not link coilB. is an coils. is induced are CURRENTS DIRECT Because in B coil 5 is in such to the due said to possess Fio. That is: 62 = ^ iV^2 10-8 volts (78) . K being less than unity. " Mutual of flux in inductance between two and an these two induced The induction A. is N2 is the number flux from relation to A mulvxiL inductance. Even though coils A and B be brought close together. coils emf. and t the time in seconds of turns coil A which required to change the flux by 02 lines.all the flux. 62 where change force of mutual equation-(73).194 circuit. Only a certain proportion. electromotive 168.if. page a =^ N^ ^ 10-8 volts in coil B. 184.01. . current which wire and few turns. When the core C Spark"^ FiQ. FiQ.and the cycle C is continually core The . the armature from D. 170.is wound iron on a laminated This winding is connected to a batteryB. That is.P. A 169.Ky may be made all the flux linkingcoilA nearlyunity.169) the coefficient of coupling. zero. in the example of mutual inductance occurs induction coil (Fig. against A is held by a spring. " Effect of iron core upon mutual inductance.practically iron core very also links coil B. By this process the flux in being established and then destroyed. A primary winding. " Induction coil. D the spring then again. The primary coarse is interrupted by the iron armature passingthrough the contact D. A is drawn is magnetized by the primary current.170).196 CURRENTS DIRECT (Fig. opening the circuit and causingthe toward it and away flux in the core to to drop practically pullsthe armature A against the contact is repeated. of comparatively very common core C. 000 ifB is in lines per Example. in. in. 200. It has been shown be accurately between magnetized surfaces.. -^-^^^lb 72. calculated if the surfaces are parallel beinggiven by On the same core " where / is the force in dynes.000lines passes from What is the equalarea. a high alternatingemf.14 per sq./S. solenoid is 2 in. is placeda of secondarywinding. This force can and quite close together. in diameter a the pull on end of the into core the armature in - 63.Its wide use in automobile and gas enpractical ignitionsystems is important.000/3. Because of the change of flux in the core. a total flux of iron armature pounds? 3. F = cm. The induction coil has many gine applications.800 lines an and of . in. and of core 200. A the of each of the two area in square centimeters.8002 X 3. A = B = " ^ (2)2 = A in square inches. due to the interruptions of the primary current.and B the flux This becomes : densityin faces sur- gausses. " " The sq.130.THE MAGNETIC 197 CIRCUIT . This winding is thoroughly insulated many the same from the primary winding. is induced in the secondary. that a force exists 149.but as it is wound core on as P. This induced electromotive force may be considered the due to the mutual inductance existingbetween as primary and the secondary coils.14 63.consisting turns of fine wire. B^A P = 24:64 kilograms if B is expressedin kilolines per sq. the two coils have a high value of mutual inductance. Magnetic Pull.14 sq. elec- quantity.IX CHAPTER CAPACITANCE ELECTROSTATICS: in motion. the electricity is called static electricity. which of static and in the nature difference no electricityand that are connected to the negative terminal will of negative electricity. insulated. " to the charges on tricity. the ellipsoid the positiveterminal will be charged with positive conducting and are connected 171. two insulated of ellipsoids. away 198 each other.electric currents. electricity.Fig. these conditions Under So is There static The of its electricityusually Charges. be stationary or at rest. The charged with an equal amount the entire surface of the over charges will distribute themselves the but the density of the charges will be greatest on ellipsoids. Electricitymay. has only been far. 171. dynamic Electricity when however. Electrostatic machine induction FiQ. through the insulatingsupports. be disconnected In time they . terminals connected Electrostatic to an static electro- equal ellipsoids. This is due to the be fact that the If the two the two will leak positiveand negative charges wires from attract the electrostatic machine charges will not be sensibly affected. ends of the ellipsoidswhich are adjacent. be " If dynamic different because appears small extremely high potential and 160. or electricity is called in motion considered. a minus charge will be Bj which initially As B did not hold any charge found on the end of B nearest A. Charge V will seek a positionas far away from a as possible. If the two " can have out gone from and B none have reached it from c" c::^) c3 can B (h) ia) Fig.and charge V is a free charge. and it is assumed to be perfectly no insulated. that current flows for an instant from one ellipsoid Both of the above effects are due to the fact that the positive and negativechargesattract each other.199 CAPACITANCE ELECTROSTATICS: gether. whereas the two charges a and h remain. This is due to the fact that the unlike charges attract each other and that like chargesrepeleach other. Charges of unlike sign attract repeleach other. at the equal to.h would The above experiments are all illustrative of the following outer must be laws of electrostatics. lipsoid If a 161. The charge V will be found to have escaped to ground. induction. whereas the positive as charge 6' is as far away possiblefrom the positivecharge a. It will be noted that the minus charge 6 is as near as possibleto the positiveinducingcharge a. electricity initially. tofree to move were they would come ellipsoids comiected together with a wire a spark If they were would be observed at the instant that contact was made. 172(6)). " Electrostatic that the net Therefore. of opposite sign the net charge on B is the two and are as still zero.172(a)) be brought near had no charge. If a were be a positivecharge. Also charges a and h are called bound charges. Electrostatic Induction. external sources. a positivecharge 6' end farthest from A. so 172. This may be proved by connectingB to ground (Fig. 6. each other and chargesof like sign . positivelycharged ellipsoid another insulated elA (Fig. showing to the other. charge on must B must also appear This charge stillbe on B zero. a negativecharge. The intensityof this field at any point is equal to the force which is exerted on a unit positivecharge at that point.) Unit electrostatic charge is defined 162. (See Par. it will be found to move along certain well defined paths. two oppositely at various pointsin the field near charged bodies. 16. 173. " Electrostatic field between charged conductors. which can move freely.will be repelledwith a force of 1 dyne. be placed If a unit positivecharge. Electrostatic Lines. similar to the behavior of a unit north pole when placed in a difference of potentialis produced a magnetic field.P. . tively-c charge startingfrom the posialong a definite path until body will always move the it reaches negatively-chargedbody.200 A CURRENTS DIRECT chargewill positive indiice a negativechargeon a body near it. The conductors unit an electrostatic^^ld also results. if placed 1 cm. When unit charge between two starts. Such a field be representedby lines just as with the magnetic field. the lines of force being representedby the paths which the unit charge would follow if allowed to move freely. may The density of the Unes represents the fieldintensity. 173. or it. distant from an equal that charge which.etc. charge on a body near negativechargewill induce a positive north pole a This is similar to magnetic induction. where induces a south pole. 173.The field between two irregularbodies is sketched in Fig. as charge in air. The several paths This is which such a charge may follow are shown in Fig. the path in each case being determined by the point at which the A " Fig. The electrostaticline of force is not like a magnetic line of induction which is always a closed curve. 174. 11. and magnetic lines and electriccurrent lines on one No how matter much current conductor. the point occur Complete rupture cannot and the plate. Let a needle point in air. between electrostaticlines. But there is matter limit to the number which may lines become cannot exist of electrostatic lines in a medium.'' be followed Fig. II. XII. hand. and to disrupted region will advance 1 See Chap. may Vol. In a gaseous medium break-down it is possiblefor a partial to occur.the conductor injured mechanically. This breakdown be detected by the blue glow or corona^ which appears can is around the needle point.and at the same time an odor of ozone between evident. As the potentialis raised. which increases the injuryto and a plate. " static Electrotween lines be- by a a needle-point dynamic arc. The electrostatic lines will be concentrated the plate.or the magnetic magnetic field. no many magnetic hnes exist in it.provided it kept is not a cool.) a Electrostatic lines of force distribute themselves the flow lines or stream lines in the is one the other. In this negatively-charged a at a magnetic line of force which begins at a north pole and ends at a south pole. Neither is a magnetic PfT^^^ be can ductor con- how injured. the medium by burning. the air will obviouslybreak down at this pointfirst. stress . because the air beyond a certain region aa is stillnot stressed to the break-down point.however. too concentrated withstand the stresses and it This break-down is a ruptured or If the the medium which "breaks result down.Fig. flows in an exactlyas do electric current. however. (See Par.at least at first. be raised to a high potentialabove a plate. at the needle pointbut will be spread out over As the stress is most highly concentrated at the needle point. a There on lines of difference. the boundary of the will continue to 66.ELECTROSTATICS: An electrostaticline conductor and of force begins ends at respect it resembles CAPACITANCE 201 positively-charged conductor. 174. Condenser 175. This is medium.000 volts per in. and then come back to zero. and varnished cambric have a much greater dielectric strength than air.a quantity of electricity .that of rubber being in the neighborhood of 16. Two is called " a conductors separatedby a dielectric condenser.. the dielectric strength having rounded corners.-T. the gradientis 24. no stress. " Charging and discharging a condenser. For impressed across a dielectric is pressed example. The abilityof a substance to resist electrostatic break-down is called its dielectric strength.) the circuit.000 volts or 400. about twice as great as the value for rubber. the platesbeing separatedby a dielectric. if 24. the galvanometer vvilldeflect momentarily. air its dielectric strengthbeing particularly good dielectric. same relates to electricalconduction. dielectric. There is also a singleswitch S and a galvanometer G in pole.000 volts are immils of insulation.double-throw (S.but it is one of the best in- is not a known.000 volts to the inch. Capacitance.000/30 or The 30 across 800 volts per mil. as an sulator in- For example. Rubber of air is approximately 3.This unit thickness when the substance is expressed in volts is placedbetween per flatelectrodes For example. 163. volts per unit thickness called the voUagegradient.000 volts per mm. -y^ -" Battery Fio. 175 shows two conducting platesconnected to a battery. If the switch S be closed to the left.-P.. sulators only about 75.202 DIRECT with advance CURRENTS increasingpotentialuntil the longer support takes place. when Dielectrics.D. If electrostatic " between the medimn in distinction to the which remaining air can complete break-down phenomena conductors two the propertiesof are is called the a being considered. This indicates that when the switch is closed.and that of cambric being per mm. Fig. . 177(6)). If a slab of glassor of hard rubber be inserted between the plates so as to fillthe intervening completely (Fig. This constant C is called voltage multipliedby a constant The practical imit of capacithe capacitanceof the condenser.be greater than its value be C2.." A has plate condenser (Fig.1 amp.is the unit of capacitanceordinarilyused.000200 X O. than one The microfarad^equal to one millionth of a farad. The previous value. be increased.U 1.with air as a dielectric. is Q ampere-second. when 0.176). is proportionalto the voltageacross justas the amount of water in the tank will be proportionalto its height H (Fig. .12 coulomb or 200 microfarads is maintained constant and is connected at 0.12 across how = 0.Fig. parallel a measured capacitance C\. The capacitanceof the earth as an isolated sphere is less thousandth of a farad.the galdeflection on charge and on dischargewill increase also. Let this new increase in 154. Arw. The relation between the voltage. : A condenser 600-volt C the condenser in the 0. it will be found to. " = = long is condenser. This is due to the fact that the charge given to the condenser its terminals.and the capacitanceof the condenser space again be measured.the quantity of electricity C. The farad is too largea unit for practical denser purposes. fullycharged? fullycharged. as a conhaving a capacitance of 1 farad would be prohibitively large. 175. If C is in farads and E in volts. = Q/E (82) E = QIC (83) of the use quantity a capacitanceof If the current it flow before must = above the following consider relations.Q is in coulor ampere-seconds. equation (81) may be written as follows: That As example of the an problem The 600 has mains.2 seconds. SpecificInductive Capacity or Dielectric Constant.204 CURRENTS DIRECT vanomet voltage of the battery.177(a)). By transposition. tance ombs is the farad.and the charge in a condenser may be expressedby the equation: If the Q (81) CE =^ in a condenser is equal to the is. of the material between permittivity j or the denser con- capacityof air is assumed inductive plates. 178. " Capacitances in "1^ parallel. the condensers be E and 178.C. densers in Q = CE = C^y and Qi "For 238. of a number of con- 166.5 to 2. O2 complete data see "Standard Qb = CzE Handbook.8 . .7 1.4 Mica 2.just as the magnetic permeabilityof air is likewise assumed to be unity.5 to 3.. specific to be unity. Let it requiredto determine the capacitance.6 oils to 2.5 Paper 1. 177.9 compounds rubber Transformer to 5. the condensers having respective parallel.-Plate In the table of the common * Bakelite a dielectric.3 to 2. Par. The ^ Z (6) (a) Fio.ELECTROSTATICS: 205 CAPACITANCE capacitanceobviously must be due the presence to of the glass rubber. = CiE. be " I JcT FiQ.5 to Rubber 10 Hard 86.3 3 to 6 1. This arrangement of condensers is shown in Fig." Section 4.6 EquivalentCapacitanceof Condensers in Parallel. or The ratio C2/C1 dielectric constant = ic is called the spedjicinductive capacity or . Let the common voltage across the total resulting charge Q.5 2. more et seq. capacitances of Ciy Ciy C3. some dielectrics: 4 1 to Paraflan 8. Obviously. Glass Ice glassas inductive capacitiesof given the specific are more then having air and condenser 5. E is appliedto the system.200 microcoulombs. that the condensers have perfectinsulation. This is analagous to the groupingof conductances in parallel in the electric circuit. 600 (check). r\ " Q umts-x must x i_ be j mduced " j on its negativeplate. and by the law of electrostatic induction Fig.000 microcoulombs 7.c.respectively. connected in series across the voltageE. 3.206 DIRECT The total CURRENTS charge Q C^ = Qi + Q2 + Q3 CE = CiE CE = i?(Ci+ C2 + Ca) = Ci + Ca + Ca C . m.' 179. CONDENSERS SERIES. replace the combination? would condenser each " C (a) (6) = Oi Qj Q" 5 + 10 + 12 charge on 5 X = 10 X 600 = = 12 600 = X EQUIVALENT 27 microfarads = Ana.200 m. ^ i. f3 Cs is desired to determine the capacitance of an' equivalent singlecondenser." IN Fig. 10. there will be + Q units of charge on the positive plate of Ci. capacitanceis the sum of the individual capacitances.and Ez be the potentialdifferences the condensers Cu C2. is the (") What condenser? = 6. if condensers are connected in parallel. Let Si. This since it is assumed system is insulated from all external potentials. and the connectinglead. "^^ C- E% i.000 microcoulombs 600 = Total charge 166. Now consider the regiona which consists of the negativeplate of Ci. and 12 microfarads. C2. Ej ^1= Z9.having capacitancesof Ci. the positiveplate of C2.-. Three of 5. are In It . and Cz respectively.c. Before the voltage was appliedto the system of condensers. -|-C%E = -|-Cs"f (84) TJiat the restdting is.E2. Example. 179. three condensers. having capacitances condensers. connected What mains. 27 X 16. = = CAPACITANCE OF Ana.and across After the voltage C3.no charge ex- . 600-volt across are (a) single respectively. " Capacitances in series. C2 ^3 from ^ ^-3 = of the three condenser sum equation(83). Therefore.however. each of the three condensers in series has the each same charge Q. This charge of + Q units zero. isJ the assuming for condensers connected in series that with direct each condenser is inverselyproporcurrent the potentisdacross tional to its capacitance.Fig. That .the factor of leakage is absolutely neglected. slightly In . (This is analagous to resistances in series.+ Q units must come existence in order that the net charge in the region a may main re0. 172 (a). reasoning holds for the region 6.) carry Consider the voltagesJ?i. equal the line voltage: Ei -\-E2 ")~Ez E have a = y^. Et d = The = ^.page voltagesmust 204. between C2 and C3.a E =-^+^+^ Ci Also E = by definition C2 the C3 equivalentcondenser C must charge Q. (+Q +(" Q)) will go the plateof C2 since it is repelledby the + charge on Ci just as the charge 6'.took a positionon the end of far as possiblefrom the positiveinducingcharge the ellipsoid as The same a. isted in the region a. Substitutingthis value for E. a. 207 CAPACITANCE After the applicationof the voltage. If the condensers are even leaky. Therefore. = El ^-.the stillbe zero. C C 1 C2 (^3 of the equivalent reciprocal of a number capacitance of condensers in series is equal to the sum of the of the reciprocals capacitances of the individual condensers.ELECTROSTATICS'. as no charge can flow net charge in this region must into through the insulation. of which must current the same if no leakageexists.E^y E3. Par. " stored in the be is existence of this energy the condenser the spark resulting from short-circuiting by plates. 157 volts ^ r ^'y2^X^10-^' =130 ^"^ volts. (h) the charge on each condenser. = 600 1566 microcoulombs. having capacitances in series across dOOare respectively. a flows current El where I is the ohmic IRiy Ez = 7/22. 10. Determine (a)the equivalentcapacitance each condenser. of the combination. and fii. each condenser.566 " ^^ X 10-' --^ 10 X 10-^ . 1.^ volts 5X10-' 1. 10-" X ". 147. of 155. is stored in a condenser and a difference of potential electricity exists J^etween the positiveand negative plates.61 I. volt mains. on " 1.^ -313 = .566 Ana. (Seeequation (77) stored in the electrostatic field page 192.. (c)the potentialacross 6. and 12 microfarads connected assuming no leakage. resistances in series: connected Example of condensers Consider that the three condensers of Par.energy must 157. . = also be written wattnseconds is 1/2 QE (86) 1/2 CE^ 1/2 QyC (87) (88) : W = W = similarityin form of (87) to the equation for the energy stored in the magnetic fieldshould be noted.and Rs the respective are of the three condensers.383 2.and E3 = IRz = leakagecurrent. The shown energy in joulesor W This may The condenser.61 microfarads. Ana. As a certain quantity of Energy Stored in Condensers.208 DIRECT CURRENTS through the series and eventuallythe potential distributes itselfaccordingto Ohm's Law.) The energy of the voltage^ is proportional to the square whereas the energy field is proportional stored in the electro-magnetic to the square The of the current.383 2. .=!+-^+^ (a) (h) (c) ^^ C = Q = 1/0. ^1 X =0./?2. 1020 joule Ans. 181 (a).566X 10-" X 1 ^'^' = 0.Fig. As the charge on both outer platesis of the same In this 14 . (89) equationitis assumed that the electrostatic lines between the two platesare parallel. 181 (6).566X 10-")" TT no"iw " 5 X W. A plate in square centimeters. or the mutual capacitance of conductingbodies. The capacitanceis of the medium distance between constant ^ = MxtxW "^i"rof*^ads. The total capacitanceof a simple platecondenser of this type be accuratelycalculated for the followingreason.180. the dielectric between the plates.ELECTROSTATICS: Example. 156 and TF. ^As a rule it is impossibleto calculate the capacitanceof a condenser. series of Par. The plate condenser.4698 joule. All cannot the platesas certain the electrostatic lines do not lie between lines pass from the back of the positiveplateto the back of the negative as shown in Fig. where accurate calculations are possible.1225 joule Ans.-H total energy of the condensers in ' -/ ^ The in each energy the total stored energy. In this case the area A. includes both sides of all the plateswith the exception of the two outside ones. There are curately ac- some simple cases. Calctilation of " the dielectric constants media of the intervening always not are known. Capacitance. Wi^}i (1. " jt_ " Let side of each one C= Capacitance pute of a condenser. 600) = 0. This be avoided by using one more error platein one group than may in the other. however. " Determine Using equation (88).d platesin centimeters and k.because of their complex geometry and also because 168. stored the 209 CAPACITANCE ^ 10-^ ^^fg^^^y' y ^^^^"f = H = K (1.is the mi_ 1 J X simplestform be the the area of "!-!" ^o^ of condenser. = 0. Ana. This results in the actual capacitancebeing greaterthan the value as justcalculated.Fig. equation(89). ^ -"Q* ^rdtdxio* 180. Paper = 495 X 0.01616 mf 10" .002 = 0. " 6 in. means that 496 .486 in.00508 X 9 X 0.496 in. X having and of tin-foilare The 1 mil thick. Fig. Fig.990 in.54 = 0. between pass An due to the error plates. It is desired to construct a platecondenser The plates are of tin-foil having a total capacitance of 8 microfarads. ^d (a) Electrostatic leakage lines ot plate a (h) Multi-plate condensers. and 2 sheets of paper many will be the dimensions of the condenser? What plate is: 6 X The The dielectricconstant " (2. and mils thick and necessary? of each area a distance between d The is of paper dielectric 7 in. plates: 0.002 = capacitancebetween X 2. Therefore: 8 = sections 495 are 0.00508 X cm. Example of Condenser Design. 1. 9 in. two plates(from equation 89) : 3 X 309.54) 8 X 309. (6).01616 These sections platesand Thickness 495 are indicated sheets of paper at are d. : Tin-foil = 496 X 0. 8 in.6 = 4t cm.001 = 0. This necessary. X How of 3. 181 needed.210 CURRENTS DIRECT the plateshave the sign and electrostatic potential. 0. 181.no same bulging or "fringing"of the lines near the edges of the platesmay occur unless the platearea is largecompared with the distance between lines can them.6 = sq. condenser. . \CiE If KD. shunt is used.and E the Then the condenser. the standard now unknown C2E or = KD. If it The galvanometer should return immediately to zero. Googk . A telephoneis used as a detector except in (6). the ballistic throw of the galvanometer correspondingmanner be read on dischargeby closingswitch S to the rightafter may charging. 183 (6). by equation (90) voltageacross Also where Ci is the unknown Qi = Qi = capacitance. CiE KDy = (a) capacitance C^ be substituted for the condenser and another set of readingstaken. In a shows a steady deflection it indicates a leaky condenser.212 DIRECT CURRENTS throw of the chargedthrough the galvanometer and the maximum galvanometer is read. CtE KD2 n j^ is the galvanometer constant. An alternating-current supplyis preferable. . 183 (a). be the unknown capacitanceand C2 are a standard two known which may or may one resistances.Ri and R2 which should be adjustable unless Ci is so. Let C. It is often desirable to use an Ayrton shunt in such ments measure- such a When gives the apparatus greater range. ^ ^ Dividing (o)by (b). The of power secondaryof an induction coil may be used as the source be made to charge and discharge or a battery with a key may the system as shown in Fig. Fig. not be of adjustable. Several check readingsshould be taken.Qi the quantitygoing into the condenser. Let Di be the deflection of the galvanometer when Ci is connected.proper correction must be made for its multiplying as it power. In the of bridgemethod two capacitancesform adjacentarms a Wheatstone Bridge and two resistances form the other two arms. Cable 184.until there is sound in the telephone.showing that the bridgeis in balance. Equation (91) is not deflect on then applicable. such as If a cable be totallydisconnected the Murray and Varley loop tests. Testing Chap. The bridge is balanced when the galvanometer does either charge or discharge. Either C2 no 213 CAPACITANCE ELECTROSTATICS: Under or of the resistances is one these conditions: Cx -K2 C2 -Ki Cx FiQ. Disconnection. and its broken ends remain insulated these loop tests are could be located impossibl^rThe distance to the fault may now be determined . Galv. 183. leakagethrough that there is little it is assumed the condensers. and until the bridge is balanced. it " was " ^Locating an Location shown that open of a a in a Total cable. a double contact key K is necessary. grounded fault in a " In cable by suitable resistance measurements. " Bridge methods " (91) ^ip~ of capacitance. measuring battery is used. K is pressed and released.the galvanometerwill deflect both upon the chargeof the system. When a In the above if any measurements.when released. Ayrton H p Shont Perfect Cable " ""i""=r -i-xFaialt FiQ. 160. VII.adjusted. when the key is the key is pressed.and upon the discharge. The lengthsare proportionalto the galvanomete corrected for the settingof the Ayr- . The capacitanceCi of the length. to the fault is If a similar perfectcable firstmeasured by the ballisticmethod.214 DIRECT CURRENTS The connections are shown in by capacitancemeasurements.x. Fig. 184. Let c be the capacitanceper ft. C2 Dividingone (2Z = - x)c = JRlDs equation by the other. Likewise. Di X ^ 21- The not X D2 capacitanceper unit length and the total capacitancedo enter into the standard condenser capacitancesof the equation. so that it is for the calibration of the various deflections when ton shunt. of each cable. the faultycable. not necessary to use a galvanometer.the two are looped at the far end and parallels the capacitanceC2 of a lengthI of the perfectcable plusthe length I 21 X X oi the faultycable is measured. assxmied to " " be the " for each same : Ci where K is the xc = galvanometer = KDi constant and Di the deflection correspondingto Ci. of means GENERATOR A generator is " acting in conjunction with the and the current applied power 162. south coil. of the turns this on coils is varied shown lines ^. conductors armature the field is driven oo!l generator and flux links the If " armature armature Electrical types is or linking throngh force the most armature Electromotive paasins Fig. a north by the 185 and magnetic the a Simple coil usually stationary of alternatingfield the by mechanical ^^ ) in is based the varied in any passing magnetic a through in Chap.CHAPTER THE Definition. coll field. re- (6). As the plane of 215 ( \ . a relative generated by the This carrying conductors armatm'e an which machine a electrical energy. armature rotates. counter-clockwise position shown a in quarter of a volution. VIII (a) to lines 185. electromotive of linking the the In Fig. magnetic In the direct-current and is magnetic field. if the flux Maximum In the armature Generated that action the generators Either chanical me- accomplished by upon the field is generator rotates.^ in was It " coil is a is induced The coil. an way. into energy X Let a imiform In in this (a) the coil is perpendicular position the this flux be rotated it will lie in the magnetic field produced to possible maximum 0. coil rotating coil revolves a surface. field and be is power stationary and Force. of the motion converts field. in pole. The by the relative motion of field. 161. its its shaft. flux principle. The average voltageinduced in the coil during this periodis. VIII. equation 74) = second. may also be the analyzedby considering is similar to a total electromotive to the being due the force forces generated in each the coil. are connected by the end individual electromotive being generated in the electromotive with no way same nections con- forces conductor are rather conflicts with the fact force is also due the coil. 186. The side of motive electro- force of is the of sum electromotive as turn one of the electromotive sum forces in each ductor con- forming the sides of the FiQ. parallel Therefore. cutting Conductor " in series of the turn. The rails are connected at one end ce by a A magnetic field having a densityof B lines per sq. The to the change total emf. as The in the coil. e where for 10-" N is the number of turns quarter revolution. But Therefore.216 DIRECT CURRENTS the coil is to the flux no lines link the coilin this position. the conductor a6. a per iVr| (Chap.free to slide along the two ef. since .in a quarter revolution the flux which links the coil has been decreased by 0 lines. passes conductor. the in the coil and t the time t = j^ where R = the revoliUions voltage during average required a quarter revolution is e The = 4iVr/j0lO-8 generationof electromotive type.therefore. which volts force in moving coil of this those used in dynamos. Fig. considered that the induced of flux linked either Consider cm. is obtained assumption. perpendicularlythrough the plane of the rails and metal railscd and voltmeter. magnetic then uniform a turn. 186. This in than induced under conductors these field. 1 second.page This e = C6? linkingthe coil is: 30 X = by 1^^10-" = 0.1 second. B is the flux density of the field in gausses. 186. 185 may conductors on oppositesides of the coil through their cutting of magnetic lines. which in themselves generate The which to moves electromotive no developed forces emf. the conducting loop formed by ce. The conductor Fig. are electromotive force in volts cuts a conductor generatedby a single magnetic field is e = BlvlO-^ (93) mutually perpendicular.'s ab conductor 1. ah moves at a uniform velocityto positiona'b' in 0. An electromotive force is generated in the conductor ab since it cuts the magnetic field.000 lines. I and in. These connected conductors in series are by the end conductors. Let the flux have a density of 100 lines per sq.THE Let the conductor ab 217 GENERATOR velocityto the position aV. While this movement is taking place.the voltmeter will indicate a certain voltage. cm. in 0.'s generatied in Fig. in the direction of the electromotive coil sides are such that these additive.or connectors.'s generatedby the cuttingof magnetic lines by the conductor be illustrated by a concrete which make up the coil may example. This voltage may be attributed to either of two at move a uniform causes.006 volt. because of the increasing area 2. . of this loop. Similarly. positiona'V the flux linking is increased. As The force. The is the electromotive What flux change of 0 force a across 20 X 100 = 60. and aa' is 20 cm. change occurs 185 Then by equation (74).centimeters That v are second. I the length of in centimeters^ and v the velocityof the conductor conductor where B. per the electromotive force induced change of the flux linked with a coil is the same that obtained by considering as the emf.the electromotive force developed by the coil in in the be attributed to the emf. The distance ab is 30 cm.. the rails and oft. " electromotive A it finger Fleming's right-hand rule.the direction of motion of the conductor Right-hand Fore Rule. direction a A of the 187. whether being generated by the as itself cutting the field or 163. 187. gives direction of induced emf. FiQ. and the middle fingerof the fore-finger.the middle fingerwill point in the direction of the induced electromotive force. Fleming's definite relation exists among the direction and the of the flux.187). determining this relation is the Fleming right-handrule. force in the definite relation exists between of the flux which Middle conductor the direction just as of current and produces. . Direction = result ia obtained same force is considered electromotive conductor 100 = = flux whether the con- it is considered as linkingthe coil./sec.218 CURRENTS DIRECT Applying equation (93) . Electromotive Force. If the tion fore-finger pointsalong the lines offlux and the thumb in the direcof motion of the conductor. This rule is illustrated by Fig. 20 V e It will be X 30 X cm. " Thumb in direction of motion. finger along lines of force. In this rule the fingersof the rigM hand are very convenient utilized Set the as method for follows: the thumb.006 volt. 200 = ^ that the seen 200 lO"* X being induced by the change in of Induced 0. right hand at rightangles to one another (Fig. . coil current. 190 will show that.one always the same. rectification can be 0 (6) Fig. II. one ring only is used. by saw The or two cuts 190. Each ring is continuous and insulated from the other ring and from the shaft.220 DIRECT CURRENTS Fig. I.as in Fig. A metal or a carbon brush rests on each ring and conducts the current from the coil to the external circuit. to the Therefore. As the emf.-Current from taken External Circuit rotating coil by means of slip-rings. 190.as the direccoil reverses. must which this current be rectified before it is allowed must to enter the accomphshed by using a splitring such as is shown in Fig. 189. its connections simultaneously reversed. since the necessarilybe alternating. produces it is alternatingas has just been shown. such rings cannot be used.Chap.that is. ends of the coil are segments a circuit are in the tion Fig. at Rectifying effect of " two so or commutater. connected one to each of the sections produced. Instead of using two rings. 189. the . This is split external This circuit.. (See Vol. must always flow into the external circuit in the same To Fig.) whose direction is If a direct current is desired. A direct current direction. 189. A careful consideration of of the current external splitring points diametricallyopposite each other. This givesan open circuit type of winding.as shown in Fig. of Fig. 191. Fig. 188 (6)with Fig. In this particulararrangement the full electromotive force generated in each coil is not utilized. By comparing Fig.THE 221 GENERATOR direction of flow of the current in the external circuit is not changed. since it is impossibleto start at any one commutator segment and return to this segment again by followingthrough the entire winding. . could not be used commercially for direct current would have a small output machine service. Fig. The electromotive force wave be improved upon by the use of two coils and four com190 may mutator segments. The brushes pass over the cuts in the ring when the coil is perpendicularto the magnetic field or when it is in the socalled neutral plane and is generating no voltage. a.and the voltageshown by the dotted lines is not utiUzed. Also a single-coil Reaultant Electromotivefoi Fig. weight. 190 (6). value twice in each cycle. 190 (6)it will be seen that the negative half of the wave has been reversed and so made positive. one as coil passes out of contact with the brushes at pointsa. " Effect of two coils and four motive for its size and commutator force segments upon the electro^ wave. a. These neutral pointsare marked 0-0-0 in Fig. 188. 191. 190.as shown A voltage with a zero in Fig. 191 (6). it sine wave. 192. force between that the electromotive electromotive time moves electromotive core. " 192. 193 shows to for each forces one to take its place. In small of copper amount 165. These forces do not they a force between brushes. This type of winding has a high inductance. " Gramme"ring machines. Gramme-ring Fig.222 DIRECT CURRENTS Winding. This winding is simple. these inactive to carry room In gramme-ring winding formed coils cannot be used and this makes the winding expensive.and has the advanthat a singlewinding is adapted to any number of poles. consists of insulated wire wound spirallyaround a ring (or hollow cylinder of iron) with taps taken from the wire at regularintervals and connected to commutator tage segments. force of each coil is plottedseparately. The portionsof the conductors which lie inside the ring cut no flux and act merely for the active portionsof the conductors. there is not conductors through the back sufficient winding. This type of winding in its elementary form. reach all have their their maximum zero value at the value at the same same time . It will be noted in a armature that the electromotive gramme-ringwinding is the of all the coils that lie between a brush another the being assumed The nor do forward brushes of the electromotive sum When brushes due coil passes Fig. voltage curve is four a coils. Fig.which renders good commutation difficult. Because as connectors of the small proportion of active conductors a relatively large is required in such a winding. if the voltage limitations do not prevent. . but under different poles. Winding.191. 166. conductors one adjacent poles)apart.since it is start at any one point in the winding and return to point again by passing continuouslythrough the a winding.THE to the owing GENERATOR of the positions 223 individual coils.in which the resultant electromo- in force does not be of the individual electromotive siun of the successive tops of the individual It will be noted that a fairly motive smooth resultant electro- waves.. With the exception of these end connections. are coil ends). all the armature copper is "active. the electromotive forces additive. centers a be about connected in the individual coils are Due at their to conductors the manner will be in posite opin which these ends. up force is obtained coils. 193.it cuts flux and so is active in generatingelectromotive overcome force. If one conductor north pole the other is then under a south pole." that is. The electromotive force at any point is the sum individual electromotive forces. The sides of each distance between is under and as both coil should move the electromotive are pole pitch (the of forces of these two directions. Fig. The conductors by the use of the of this winding all lie upon the surface of the armature and are back connected to one another by front and connections or coil ends {ad and 6c. Drum " The to the ring windingare objections drum winding.the "ripples"being noticeable but comparativelysmall in magnitude. in the same direction. called dosed winding. 194.-Resultant with electromotive force between A gramme-ring winding is possibleto the same four due four to series-connected coils brushes.Fig. This these at this resultant point of voltageshould compared with the electromotive force obtained with the coil windingshown forces equal the but is made open- tive Fig. 194. Fig. coils in place the other a 4-pole. coil. 224). as the coils are embedded This high inductance. armatures with into proper shape by another machine. equal to the polepitch. 195.they more teeth difficult give pole-face and tooth losses. " On gap.224 DIRECT CURRENTS gramme-ring windings. should be equal or nearly called the coil pitch.and In most in the earlierdrum-wound smooth. the surface of the armature conductors were held in positionpartlyby projectingpins. The slots are lined with insulation and the conductors are held in firmlyby wooden or non-conductingwedges in the largermachines (seeKg. Fig. 194. due to and the flux pulsations have on they also permit type and armature core Two a makes commutation the armature shorter airin iron.so that when one side of a coil is under a north polethe other is under a south pole. This span may be as low as nine-tenths of the pole pitch. and the necessary number with cotton or mica tape.and were preventedby bindingwires from flyingout under the action construction has been of centrifugal force. Fig. The two ends bare so that later they may be soldered to the commutator are left bars. " Direct-current with former-made on These are coils are usually usually of turns. and by bindingwires in the smaller types (seeFig. drum-wound a armature. The core was machines. Lap wound wound are Winding. The smooth core superseded by the "iron-clad" type where the conductors are embedded in slots as indicated in Fig. The span of the .214). They are then bent machines then wound coils. 197. much hand. 167.in which case a fractional pitchwinding results. These constructions much are better mechanicallythan the smooth Commutator. one side. of a coil will be termed a winding element. That is. of the armature denoted Fig.THE Usuallytwo coil sides 225 GENERATOR slot.one coilside lyingat the top and the other at the bottom of the slot. means "ID Fig. 195. 194. passingfrom the bottom to the top layerby of the peculiartwist in the ends of the coils. Even consist of one or when there are several conductors. 16 by 2/5. as indicated in Fig. Formed " armature coils. of one its oppositeside liesin the top of occupy other slot. elements spanned on the commutator .they will be shown as a single ously Obviconductor in the wiringdiagram. The as many of elements is the hack This back number of of these elements that the coiladvances as on there are the back of the winding and will be 'pitch pitchis obtained by the connection 6c. some one This allows the end connections to be easilymade as the coil ends can be bent around one another in a systematicmanner.194 and constituting This may 196).if the side coil is in the bottom of a slot. bundle The there of wires will be twice The number coils.196.ob (Figs. of several conductors taped together. in Fig. As most windings are now made in two windings will be considered.the return connection cannot be made back to the original slot but it must always lead back to is next to the original a slot which slot. This may be greater or less than the back pitch bid not and if it equalto it.197 end of the armature Conductor 198.^X winding winding/ Elements y Elements '^y^ :^'^ -r-TT FiQ. on the at commutator segment. 197.if they were both even. layers. Thus.the two connection back and elements In per is from the top conductor 1 to conductor 10. thence to 3. connected 10 is then 1 is connected = Conductor 9. the winding is progressive.226 mRECT CURRENTS is called the frontpitchand will be designated by y/.This isillustrated in Figs. the front of the armature. be less. is. obviouslyyh and y/ must both be odd. Therefore. If it be greater. even having of a simplexlapwinding slot. .the winding is retrogressive.. i. and to conductor back 3 to being made connection the the back of the armature on Therefore.e. " EZE Single coil representing Therefore.197. armature winding is therefore progressive. to the top of the next slot.only two-layer The conductors or elements lying in the top of the slots will be given odd numbers and those in tlie bottom side of a of the slots even As one numbers. 196. Further.the front pitch yf a coil of 3-turn == This 7.the front back That pitchescan only differ from each other by 2. 2/^ = 2// " 2 (94) . an winding. Fig. all the conductors could lie only in either the odd or the a slots but could not liein t)oth. coil liesin the bottom slot and the other side in the top of a slot.the back pitchyh 10. . per The three fundamental conditions be fulfilledby to a lap winding are: (1) The pitch must be such that the oppositesides of the coil lie under unlike poles. The winding is shown in Fig. and only (2) The winding must include each element once once. per slot. It will be noted that the brushes rest on segments to . Z is the total number where the counter-clockwise a the commutator from ot is in CURRENTS vances winding ad- that the seen segment for each complete turn. 197 and segments the surface on of coils. designinga winding it is necessary that the oppositesides of each coil lie under different polesso that the two electromotive In forces generated in the coil sides may Hence the be additive. ing winding table. Assume that the armature Design a two-layerlap winding having of " There ^ " 9. It is very useful in checkthe winding. By proper checkingit may be seen that each conductor is included once and only once and that the winding closes at the same conductor.1 in this case. 198 it will be commutator one viewed segment is seen armature From direction when end. at which it began. 198 as if it were splitaxiallyand rolled The above is called a out flat. (3) The winding must be re-entrant Example. of elements pitch should be nearlyequal to the number average pole.the number of commutator of winding elements and N is the number Figs. 36 are The elements. has 18 slots.228 DIRECT advance whose It will be necessary. 7 progress as follows: 1-20-13-22-15-24^17-26^19 28-21-30-23-32-25-34^27-36^29-2-31-4-33-6-35-8-1. pitch should y/ on 4-pole machine a elements two average be made pitch can or be nearly equal to 9. back The 2/6 = 9 Startingat 1. that for every coil one commutator Therefore. the winding will l-10-3-12-5-14r-7-16^9-18-l close must equal to = itself. Lap Windings Several Cofl Sides per Slot " it is often necessary sizesof machines elements or in slot sides per coil sides in used. By placingseveral elements in each slot the number of slots is reduced and largerslots result. More than eightcoil for placingseveral rarelyused. Coils made up from several individual coils are shown in Fig. The two and are placed three coils are taped as one or in the slots of as a commutator. cross-section to the slot cross-section) would be so that the teeth would narrow (ratioof the copper Also the tooth roots be mechanicallyweak. or 8. page to the A unit. The selection of the are used. size of the slots and make the space factor low. careful examination of the armature running from indicatinga quadruple coil. 6. Then must reach from the next conductor 1 coil will obviously reach from conductor 3 to conductor 74* fore. and accordingly span different distances on the armature .usually4.199). 195.214. more that The a has 72 slots and 6-polemachine of elements total number Z The pitch. 168.is Assume per slot. This also reduces the cost of winding.* as poles.THE which elements connected are 229 GENERATOR lie which 11 and 19. 246 shows Fig.one number to " between the In the larger place several coil sides slot. four wires each coilside numbering and connections of the conductors are in no different from those alreadydescribed in the case of but two The way coilsides per slot.where = 72 X 6 on six elements the armature surface: 432 = pitchshould be approximately Let If this back to conductor Vh = 71 Vf = 69 pitchis used a coil 72 (Fig. several coil sides per slot restricted than it is with two elements per slot. thereThese two coils. The reason one are slot is a midway follows: If two as elements per slot were in the bottom layer. for example.a large in the top layerand one This would reduce the of slots would be necessary. practiceit is desirable that the coils be all the same posand further it should be possibleto tape all three coils together must have and placethem If in the above in the slots as a imit.230 DIRECT CURRENTS different spans.that is. have their adjacentsides in the top of one slot. the coil containing conductor 1 will reach from the upper side of slot A to left-hand the lower kft-handside of slot JS. = 73 and y/ = 3 will reach from and bottom of slot B. 72 being a multipleof 6. on the armature. Therefore. one greater than 72. For example. 71.from conductor 1 to conductor 74. yt is equal to 73.there will be four paths for the current to follow in goingthroughthe batteries. case Conductor of slot A to the center reach from FiG. Fig. 200 (a). electromotive force of 2 volts and a current capacity of an in parallel. This condition should lie togetherin the bottom is obtained by making the back pitch one greater than a multipleof the number of coil sides or elements per slot. be connected 10 amp.etc. 169. and right-handside of slot A of the center connecting the conductors As all three coils now and conductor to the lower of a span top 5 wiU right- triple coil. " The voltageof the combination will be 2 and the ampere " Digitized by VjOOQIC capac- . In when sible. " yb Method side of slot B. the same tance dis- over. each having If foiu*batteries. 199 will show. Morethe three singlecoils can be taped togetherto form a triple if three coils coil and placedin the two slots as a unit. as a study of Fig. hand the upper 199.form. Paths through an Armature.their other sides of some other slot. in the illustration just given. they will be equalin size. These are two of such " Parallel and more parallel paths. 200. possibleto follow in order to reach the positive in the grammeThe simplestarrangement of conductors occurs ring winding.To determine the number in series. Startingat the (" ) terminal. A third path is obtained by going to brush (c). making a 231 GENERATOR total power capacityof 80 watts. and the power capacityis 4 X 20 be so connected Similarlythe conductors in an armature may same == that certain groups of conductors are then be so connected that there may parallel.THE ity 40. its previousvalue. through path (4)to brush {d)and then to the (+) terminal. path is obtained by going to brush (a).start (a) Fio. but the voltageis now 4 volts. the negative. Pig.Fig.one path may be followed by going to brush (a). If now these batteries be arranged in two groups of two in series. and see how different paths through the armature it is many terminal. there result but two paths for the current to follow. 200 (6). 201 (a) shows a winding for a 4-pole at one of the machine niachine.then through (6)and then to the (+) terminal.as for example. 80 watts. then through brush (6)to the (+) terminal. terminals. through path (3). The current capacityis now 20 amp. A fourth path is obtained by going to brush (c).through the winding at (1)to brush {d)and then to the (+) A second terminal. or groups paths in (6) series-parallel arrangement of batteries. path (2)to brush .. that there 10 amperes path are per " ) and (+) and be considered nals. Fig. connected in parallel minals because their four positiveterminals and their four negativeterconnected together. with heavy lines. The total current are respectively seen are at 20 volts. making 20 amperes The potential per brush or 40 amperes per terminal. battery2 to path2. 198 developed in circular form.one two sake of simplicity paths are shown The . 202 shows For the drum winding of Fig.232 DIRECT This makes these Assume CURRENTS four separate the ( paths being in paths between parallel.each at 20 volts. The armature may as in Fig. It will be 201. Battery 1 corresponds 10 amperes batterydelivering to path 1. paths through a drum winding are not as easy to follow as the 18-slot those through a ring winding. " Four paths in parallelthrough that the four batteries an armature. difference between brushes will be 20 volts. etc. In a similar manner delivered will be 40 amperes each path in the ring winding will deliver 10 amperes. bushes. termi- tween 20 volts be- beingequivalent shown to four batteries connected as Fig. 201 (6). as from Fig.THE 233 GENERATOR to brush b.and conductor 2/". brush 202. There are two conductors per slot. 170. and the other from brush c to brush d. By tracing through the lighter lines.making four paths in all. Furthermore. 17. In all simplex lap windings there are as many pathsthroughthe armature there are poles. not connected only alternate commutator segments are utilized. " a Heavy lines show two of the four parallelpaths of a lap winding. S and 4 are to. this winding. It will be' = . These constitute two paths." Fig.in which every alternate slot is filled. 203 shows a 36-slot. of the armature. The back pitch.the return is made to differing tors Conduca conductor differing by 4 from the initial conductor. ductor Con- making Instead of returningto the conductor 13.two more paths may be found.4pole winding.is 1 connects to conductor 18 then connects the front 18 to 5 on the back on the front of the armature. pitch y/ by ^ from the initial conductor. one between brushes c and b and the other between brushes a and d. Multiplex Windings. These two windings are separate and are insulated from each other on the armature. that is. This winding will also and is.) seen Fia. segments.this winding is re-entrant and is in itself complete in the same manner as any simplex 18-slot winding.the dupUcate of this one.and being connected to the commutator segments not utilized by the other. close on itself. (See Fig. re-entrant. As this winding uses and alternate commutator only alternate slots. and back pitchas the other. that this 203.therefore.202. but are connected togetherelectrically by . another winding. " Duplex doubly-re-entrant lap winding " one winding only being shown. can be this new front winding having the same placedin the vacant slots.234 DIRECT CURRENTS winding closes on itselfafter goingonce around the armature. . ciu'rents circulate when the batteries. dotted. The two Their difference is best windings are the same electrically. this winding does not close or become around the armature. Fig.or two conductors. but will return one slot. shown a. one conremoved from The second winding. This is ilpass After in Fig. close after (a) Duplex doubly Fig. " This batteries. it only closes once. " around winding.236 If the number 35 CURRENTS DIRECT or of coils and 37 coils. the parallel connections may If several batteries are conbeing made nected through the brushes. closes at a.after having passed once but lustrat around must once again before closing.if there commutator segments. Duplex (b) Duplex singlyre-entrant windings in diagrammatic the ring armature winding. in parallel and their emf . re-entrant. form. EqualizingConnections in Lap Windings. that is. so is said to be singlyre-entrant. 205. 203. 171. Although this winding passes around the armature twice. starts at h and after passing once around the armature.'gare not equal. means a constant loss of energy which heats the .to the rightor to the left of the one at which than four elements it started. Therefore.) Therefore. 204 (a). be odd.204 (6). illustrated by the two simple diagrams of Fig. passing once re-entrant 205. the winding will axe not having gone once around the armature. ^Lapwindings consist of several paths in parallel.but removed by two conductors from the conductor at which it started. external load is being supeven no among plied. (If there are more slot at which to the same it return per slot the winding may started. it does not close at a as does the ductor winding in Fig. The initialwinding starts at a.but terminates at 6. this constitutes a singly re-entrant duplex winding. small number some As an example. connected simultaneously at equal potentialsare together by heavy copper bars.lack of mechanical alignment. The number of coil sides per pole will be 24. will cause These through the armature. This allows these circulating to another withcurrents to flow from one out point in the armature these equalizer passing through the brushes. To make of coils should be a multiple of the connections.etc. The to coils that are connected the same the same tive equalizingconnection occupy positionsrelato the poles. several points in the armature of very ' I ri rii 1 I I I im ^ FiG.THE This exists in condition same 237 GENERATOR Because generator armatures. per pole and = two = It will be noted that every fourth coil is connected Fig.the number number of poles. There will be 96 slots and 192 coil sides.. due to the wearing slightinequalities be of the bearings. between currents to flow when flow through the brushes even and these currents must no current is being delivered by the generator. different points in the armature. to an equalizingconnection. Let t/b A portionof this winding is shown in 25 and t// 23. an 8-pole generator having 12 slots coil sides per slot.there may slightdifferences of electromotive force in the different paths differences of emf. as 2 assume or 3. " I i f r [ ] 11 r fVi I ] ivi II I) I i^:i f r'-rrrrri Simplex lap winding with equalizingconnections. (Seethe two half -coils drawn with heavy lines.and the coils per pole should be divisible by which are .206. in the air gap. 206.) This is necessary such coils should be generating the same as . To relieve the brushes of this extra current. 0. connections. This next again two to or a a second conductors """" conductor the imder conductor more shown that in the of the Up winding a COnductor under one nected pole is Conto a conductor directly nearly corresponding positionimder the Electric Co. F. shown in Fig.but as this would of require an undue number such ficient.-General Winding. every the under segments CURRENTS It will be noted in Fig. or coil. third every This number of coilsper 2. 3 a poleshould small number Fig. coil should be connected to an equalizing Theoretically. but removed the initialconductor. south . from hack connected This is N Vf (a) Lap Fig. conductor having a north pole correspondingpositicm ab under a cd is then connected pole. Conductor adjacent to ab under the originalnorth pole. 172.207 shows 4. " Lap and (a). is connected under to the cf which (b) Winding: 208 to next is 208. it is sufto practically. Wave has been rent which armature occupies pole. with equalizer rings.where conductor cd wave Wave "\ Winding windings. 207. every connection. 206 that the positivebrushes two connected are togetherby an equalizingconnection.238 DIRECT voltageat two instant. that the reason be divisible by as fourth or is the connect ture large direct-current armawith the equalizerconnections a at the back of the armature. direct-cur." It is then original pole. after passing once is retrogressive. the average average y-'-^ y may be either even or (98) odd. which connections the end on span the commutator end of the frontpitch and is denoted by i//.instead of returningback to the same to the next north pole.as shown at a'V in Fig. This should also be compared with Figi 208 (a). The number . both as lie coil may of a slot. pitch event.208 (6). 208 (6).THE 239 GENERATOR Obviously it would make no difference as far as the direction and magnitude of the induced emf in the winding is concerned if the north pole.as shown in Fig. follows: have may back pitch of 23 and a pitch average the front and a the back pitch may each be 21 pitch21.it is progressive. 209 (6). it fallsto the rightof its startingpoint. yf may equal yh in the wave The above certain A front making the any winding wave pitch of Likewise In is illustrated The 19. As in the lap winding. When a winding advances it is called a wave from poleto polein this manner. end falls winding viewed from the commutator in a slot to the left of its startingpoint as a'6'. the winding passes successively north and south pole before it returns again to the original every pole.on the other hand. y/ is the armatiu*e and yh must in order that both be odd one side of a in the top of a slot and the other side in the bottom Unlike the lap winding. connection. the winding (a).as shown in Fig. advanced /ort/.208 (6).208(6)and 209 around the armature. Figs. winding. The winding after passing reaches conductor a'h' lyingunder the around the armature once same poleas the initialconductor ah.ard When' the connection is so made. The of units*spanned by the end connections on the back of number is called the hack pitch and is denoted by yh in the armature Fig. This is similar to the correspondingterm in the of elements lap winding shown in Fig. The wave restricted in itsrelation to the winding is much more When the .If. winding. 208 (a). after passingonce around the armature. Let y be the average .if there are two conductors per slot and ab liesin the bottom conductor of one slot. (a) RetrogreBsive commutator wave winding. + a progressive winding and the signa retro- .240 CURRENTS DIRECT lapwinding. That is: py cannot ot py = Z "2 Z "2 or y (99) = p The signindicates gressive winding.conductor a'6'must number of slots and coilsthan isthe lie in the bottom of the slot next slot.of course. close until every slot is filled. itshould short-circuit. after having passed once around the armature. winding. the product equal Z but must be Z " 2.it must not around. Then: a Z = polesand Z the number of coil sides or elements.pitch. But the winding must not close after passing once In fact.this means from each other by 2. that the winding closes which. not As there that conductors sides in each differ to ab. 209 (a). Fig. Therefore. the winding must falltwo conductors either to the rightor to the left of the conductor at which it started.-34 as this would constitute py where p is the number oft and conmiutator coil two a^V will winding " 32 segments. Thus in Fig.for the following In a simplex wave reason.Assume after passingonce aroimd the armature. 209. do are (6) Progressivewave segments. 210.) Therefore. which is also of commutator Let N-c be the number = = Z = 2Nc p = 2pi 2Nc " 2 ^= Nc 2v. Nc Z/2. even. as indicated in Fig. the front and back pitch both being 63.10. Startingat conductor 1.the winding willadvance as follows : As an l-64-127-190-(253or 1) That the is. v^y = 1 " (100) If Pi is odd and y is odd. 210. windingimpossible. ' 16 . and four conductors per slot. Elements jjjT i 1 1 I I 1 1 iTrr Fig. the number of coils.the winding will close on itselfafter going once which armature. Let the average pitch be 63. two odd numbers Adding or substracting unity Ne makes even. the product piy is odd.241 GENERATOR THE that a 4-polearmature has 63 slots assume illustration. makes may wave " Single-turn coil representing coil 3-turn a for winding diagram. If the average segments and coils . (The method by which a winding be placed in these slots will be shown later.a winding is impossiblein a 4-pole machine if 252 winding the elements are to be included. winding whose average pitchis odd and mutator or^ 5^^ pairsof poles. 14 segments pitch is must even the a wave and coils must number each be of commutator each be odd. as the product of is always odd. = pairsof poles p/2 Substitutingin equation (99) Let j"i segments. a single-turn coil will be used to representa coil having several turns. As in thie lap winding diagrams. Therefore. making 252 winding elements.the number of comgoles. condition constitutes around short-circuit and a Windiog.with having^. which condition makes the winding possible. This is another limitation of the wave winding and shows possible. reduces the number of commutator segaround passage Commutajtor Fig.Fig. If. iNTc 3 X 11 + 1 The 34 seg34. The number omitted. winding justconsidered is imwhy the 252-conductor (12"-coil) of coils must be odd in a 4-polewinding.which givesa progressive winding.having 126 slots.209. That is. is 11. the However. 211.the winding would advance by conductors after each two the armature. or 12 poles. 1 32.and the 32 are shown in (6). making 250 elements. the armature standard. etc. if one coil were winding would progress as follows: = = = = - - _ or 3) l--64-127-190-(253 -"6^129-192-5. if j"i is even. so that A^c must be odd.This. 3 X 11 ments shown in (a).in this case.the stampings were coil. There are 6 polesand the average pitch.an except that its ends would segments but would be not odd number.y. be connected to the commutator taped and thus insulated from the main . as ments and coilsfrom 126 to 125. " Dummy coil and "creeping" in a forced wave winding. 208.the product piy is even. 8. which gives a retrogressive are winding. This coil winding would be possibleby omitting one would be inserted in the slots just the same the otftercoils. The appUcationof equation(100)is illustrated in Fig.242 DIRECT On CURRENTS the other hand. Nc is even in either case. Applying equation(100).ofcourse. correspondingto 4. AT. . (The coils heavy.213 shows a 4-pole. By means of a small hand hole in the motor is a comparatively casing. and c are all connected togetherdirecUyby the winding. It should be noted that the three + brushes. In like manner. and also three number that would be used in a negativebrush sets.etc. 6.244 DIRECT CURRENTS startingpoint for each complete passage around the armature. without serious disturbance. It is interesting the current and voltage of an to compare for the various ways armature of connection. the current could easilypass through the armature to brush a and thence to the external circuit. Fig.regardlessof the number of poles.where they are not cutting magnetic lines and are for the instant. Paths Winding. A simplex wave multiplicity winding always has two paths.a duplex winding four paths.17-slot. 174.a.althoiigh number of brushes as poles. the other half constituting short-circuited by the brushes are not included. have any degree of multiplicity or may justas the lap winding may.therefore. if brushes 6 and c were removed. In a simplex wave through a Wave winding there are always two parallelpaths.) A wave ing windbe duplex. Hence. two of the negativebrushes It is desirable could be removed. where it is desirable to use only two brushes. Consider a 6-i)ole " . The paths through the armature depend only on the degree of and not on the number of poles. a wave winding only two brushes are necessary y regardless of the number it is usvAdlydesirable to use the same of poles. showing that the correct pitchhas been chosen. Approximately half the winding is shown the other path. as as two brush long in order sets would mean a to obtain the necessary area.dead conductors. 6. and c. simplexwave winding.a. the conductors which connect these three brushes all he between the polesin the neutral plane. There are cases. There are three positivebrush sets. The best example is in railwaymotors where it would be difficult to obtain access to foiu* or six brushes. One of the paths isshown by the heavy lines.it brushes located on the top of the to reach two simple matter commutator. however.triplex. any to utilize all six brush commutator brush In three times sets. Moreover.having two coilsides per slot.the same lap winding. . that in this particularmachine the triplex result as the simplexlap winding. . Amperes amp.36 . . = able obtain- 300- . Simplex wavp Duplex wave Triplexwave .THE When machine. connected as be 300 volts and the armature Fig.simplex wave winding. The above relations should be kept in mind when it is desired It will be noted of armature 12(^ . 36 12 150 240 36 18 100 360 36 2 900 40 36 4 450 80 36 6 300 120 . 9. one of two parallelpaths shown heavy. . 213. back pitch 7. . Kw. "f . front pitch emf. The Volts Paths Simplex lap Dupjex lap Triplexlap. winding givesthe same wave The kilowatt capacity is not affected by the connection used. the total number conductors remaining fixed.4-pole. . = followingtable givesthe values of current and when the winding is changed. " 245 GENERATOR a simplexlap winding let its emf current per terminal be 120 17-slot. 246 to DIRECT change machine a This another. may CURRENTS from one often be and voltage rating to by merely changing the current done connections. conmiutator Types of Winding. A wave winding has an advantage in that it givesa highervoltage with a given conductors. number of polesand armature It is used,therefore, those designedfor 600-volt circuits. in small machines,especially 176. Uses Two of the " Cam mutator Armature Core Shaft Armature On Is Armattire (6) End view of an Westinghouse wave-wound (a) 25 H.P. armature showing open construction tating-pole D. C. motor. Fig. In this case a lap winding would small conductors. generator This in turn " armature. Westinghouse commu- 214. large number of higherwinding cost and result in means a a very less efficientutilization of the space in the slots. tromotive The wave winding has the additional advantage that the elecforce in each conductors,which produced by series-connected successive north and south poles. path lie under is THE 247 GENERATOR due to such causes as airAny magnetic unbalancing,therefore, and difference does not variation in pole strength, produce gap cross currents,because the correspondingconductors of each and Fio. 215. " Low- voltage, high-speed G. (Note double E. commutator armature and shrink for electrolytic work. rings.) path are moving by the same polesand the effect of such in each path. Hence no equalizer unbalancing will be the same every connections are necessary. Treatedduck stripsprotect coilsfrom rubbing. Leeos ro be aitached bars. to zoft\miAtor Ffshpaper cellsprorpct coils in core slots. Ventitsrion holes. End-plate fitcompaciiy Willi Coi'is "et sideslo^ether rivetedto core. "Armaturekeyed to shaftwhich may be windings. removed withoutdislurbinj Fig. 216. " Partly wound armature showing method house). of assembling coils (Westing- of using only two brushes with a wave winding, possibility and the correspondingadvantage in railwaymotors, have already The been mentioned. large currents are required,the lap winding is more of paths. As 200 since it gives a large number satisfactory, When 248 CURRENTS DIRECT Fig. Fig 218." 217. " Frame rings " Westinghouse type S. K. motor. Westinghouse 230-volt, 35 H.P., 850 R.P.M., shunt motor. THE 249 GENERATOR of paths the limit,a largenumber path is practically be used where heavy current must output is desired. This is true of largeengine-drivenmultipolargenerators. particularly and Figs. 214 and 215 show two different types of armature in the process of being wound. Fig.216 shows an armature amp. per CONSTRUCTION DYNAMO 176. Frame and functions. two It is a " The frame yoke of a dynamo has portionof the magnetic circuit (see Figs. Cores. or nnnnml^if-^ Single SUmplngt ^sssmmnj Bhant FMd Pole Fig. 219. " Construction of a 38,39 and 40) and it acts as a whole. In small 12-pole,direct-connected, engine-driven generator. as a mechanical support for the machine weight is of Uttle ance, importiron. The feet almost always machines, where yoke is often made of cast form a part of the casting. In another type of construction a steelplateis rolled around a cyUndricalmandrel and then welded, Fig.217. The feet in this case are made of steel stampings and In largermachines the yoke is made are riveted on, Fig. 218. of cast steel and is usually more less oval in cross-section. or Figs.219 and 220. The feet are a part of the yoke casting. The yoke for the largermachine is usually cast in two pieces the 250 which are bolted large machines 177. Field and Cores together. This and Shoes. " The to field shipment of be removed easily. cores steel laminations. are When made of made of usuallycircular in cross-section, as section allows the minimum length of turn for a given a Fig. 220. facilitates the allows the armature forged steel,cast steel and cast or forged steel they are such CURRENTS DIRECT " Westinghouse engine-driven, 300 K.W., 500- volt,150 R.P.M. held to the generator. yoke by bolts,Figs.219 built of sheet steel stampings, and 220. The laminated cores are nately alterFig. 221. They are stacked so that the pole tip comes This results in there being side and the other. on one but half the iron in a pole tip cross-section and so producing a When stacked saturated pole tip,which assists commutation. to the proper thickness, they are riveted togetherand dove-tailed is not necessary. to the yoke. In this case a separate pole shoe be bolted to the solid A laminated or a solid steel pole shoe may core section. These cores are 252 DIRECT shaft,Fig. 223. at the CURRENTS This reduces time the amount permits a free of sheet steel sary neces- of air through This air is then thrown out through the center of the armature. the ventilating ducts by centrifugal action,as indicated by the The stampings in Fig. 223 are clamped togetherby arrows. and Fig. 223. " same Cross-section of a passage size generator; moderate end armature plates held by bolts. These end platesmay coils. supports for the overhang of the armature When it is not the armature economical becomes stamping. also serve as greater than 30 in. in diameter, tures completering. Such armamade up of segments similar to those shown in Fig.219. are These are dove-tailed to the armature ping spider,each segment lapthe jointin the next layer. The slots may be straightsided.Fig. 223, in which case the to stamp out a THE 253 GENERATOR binding wires. In the larger machines the conductors are held in the slots by wooden wedges, some Fig.224. The slots must be well insulated,as grounds are troubleand are expensiveto repair. A layer of a hard substance such as fish paper, fiber or press board should be placed next to conductors are held in the slots by the laminations. should This in turn be lined with varnished ally empire cloth. The conductors themselves are usuings. covered with cotton insulation, except in the heavy bar windThe of conductors are bound togetherin one coil groups by cotton tape. (See Fig. 216.) cambric or " ^Wooawi Wedge board Ptpm or paper EiDpIn Cloth -Tape D.c.a -" slot I})Open slot Semi-closed ^a)Open containing triplecoil coil sides, two si 12 turns containing containing slot and "mush" winding. Fig. 224." a Types per coil. of slot, To reduce the flux irregularities in the air gap, due to the teeth, is used occasionally.In this case semi-closed slot. Fig.224 (c), the individual conductors so (O (6) (a) the coil ends must slots. Such must be be placedin by one, placed in the the slot one taped after the coils are pense winding is called a ''mush'' winding. The exof winding prevents the generaluse of this type of slot in a direct-current machines. 179* The Commutator. " The commutator is made of wedge- shaped segments of hard-drawn or drop-forgedcopper, insulated from one another by thin layersof mica. The segments are held together by clamping flanges {DD, Fig. 225), which pull the drawn togetherby throughare segments inward when the flanges bolts. These the flanges are prevented from short-circuiting of built-upmica {F, Fig. 225). This segments by two cones construction is illustrated by the commutator of the machine shown in Fig. 223. 254 The CURRENTS DIRECT leads from the armature slits in longitudinal (il) Assembled the coils may be soldered into small of the segments ends commutator. {B) Commutator bar. insulatingstrip. (C) Mica commutator (DD) Clamping flanges. steel tube. {E) Drawn clamping flanges and (F) Insulation used between Fig. may have 225. risers 180. Field Crocker- Wheeler " (Fig.223) (6).) (Alsosee Fig.214 FiQ. 226. " Shunt Coils. " double-cotton-covered vacuum and the segments or then to field coil and The and commutator which bars. commutator these details. leads soldered. are edgewise series winding. field coils wire. (d.c.c.) impregnated with are The an usually wound coils are dried with in a insulatingcompound. THE The outer wound set some insulation is often protected by tape or cord on In the largermachines air space is often left an cotton the outside. between The coils are also layers for ventilatingpurposes. metal spools,Fig. 226. An edgewise series winding, on distance from the shunt winding, also is shown here. Fig. 181. The the current are 255 GENERATOR Brushes. from usuallymade 227. " " Rocker The ring and brush holder. is to carry to the external circuit. They function the commutator of the of carbon,although in very brushes machines low-voltage or patentedmetal compounds.227. isfastened to the brush stud and holds the brush in its proper positionon the commutator.256 DIRECT they may The be made of copper CURRENTS gauze.227. A rocker ring with cross sure pres- the electrical plated pig-tail connections .Fig. The brush is made to irregularities should any bear down on the commutator should be from and made by 1 to 2 lb.Fig. The brush be free to shde in its holder in order that it may follow in the commutator. sq. is also shown in Pig. brush holder. in. To The decrease resistance the upper portionof the brush is copper this platingis connected to the brush holder by a of copper ribbon. per a spring.227. C. I the active in the speed of the armature pole in cm. 228.. generator. N N 8 ^/ffliiini[iftw\^TO^" ^\ ^/ff/M/iiiiiiiiiii\\\^ "^ /77f/tMniiiinn\\ im FiQ. Similarly.The positive ordinates of the distribution north pole flux entering the armature and the negative curve are ordinates are flux leaving the armature and entering a south pole. as shown The dotted line. leaving a north pole is given by the area under one of the positive parts of the distribution curve. 228. an The " path of the magnetic flux from the poles of a generator into the armature. Electromotive XI CHARACTERISTICS Force in Armature. The maximum the ordinate -Bmax. and The a curve showing the flux distribution are given in Fig.the and entering a south pole is given total flux leaving the armature by the area of one of the negative parts of the distribution curve.CHAPTER GENERATOR 182. which is equal to the average per square value of the flux density under an entire pole pitch. height of this rectangle will be B maxwells centimeter. Let it be required to determine electromotive the average in a singleconductor it passes through the flux force induced as of successive poles.Fig. ordinate at each point is proportional to the flux densityin the flux density is given by air-gap at that point. . Each be positivepart and each negative part of the curve may replaced by a rectanglehaving the same by the area. s area second.-^Flux distribution at load no of a D. cm. Let A length of the conductor revolutions per 17 be the in sq. 228.. Let the total flux leaving a north pole or entering a south pole The be total flux "l"maxwells. and P the number 257 of poles. e since Bl b cut as (ab) gives the total flux between the points a and by the conductor and is therefore equal to "l". and v the velocityof the conductor in cm. Am.) Z such conductors are be Z/p the total voltagegeneratedbetween there must Hence -^^fll0-=|l0- = - Example.m.I the active length of the is the average conductor in cm. 169. on flux density is 60. or one induced voltage. (seePar.s.page the conductor When pole pitch.m. The where f^ - 6-pole generator r. There The per are A " is (""" has a simplex lap winding. (SeePar. Equation (101) may be written . 8 P p . 169) X 15 X 5. per B where second. 300 " .000 -' "Q-^^iQ-s follows: S 10 X = " 183. If there and p paths through the armature. is e Blv 10-8 = flux density.p.000.. such conductors in series. "_ = -- Saturation = 15 r.p. ab where i is the requiredfor the conductor time to traverse the distance ab.000 lines and the average 10 in. in.000 r. conductors 300 0 as 900 brushes ..^ 225 volts. = E 10 X 900/60 = 6 = 6 = = = 50.p.000.by equation (93). square is the voltage induced between brushes? What poles are sq. 5.the passes average 217.000Unes 6 X Curve. the armature.258 CURRENTS DIRECT through the distance ab. . Two curves shown in Fig. Current Saturation " curves 1.260 r \f RECTI ^ ^cENTS similar to that of Fig. ab 900 ^ " 1. Fig. the upper at ordinate ac.230 and differsfrom the curve of Fig. the correspondinginduced will not retrace greater than it by the page curve its was bed. curve.200 ing correspond- curve of the of the value of the ordinate of Thus. The 184. one plotted are a curve for 1. " determined saturation oab. 142.p. " Hysteresis loops.230. This is shown in Fig. generator for speed has one been for other curves be speeds may determined. Par. Hysteresis. This is due to hysteresisin the iron. field current be decreased.200 ac Also at ordinate a'"/ a^ 900 aV Field Fig. 231 (b) shows the effects obtained when the curve is . saturation readilyfound by the method justindicated. 231 (a).m.any ordinate lower being 900/1. the path along the curve field current.200 r.is curve for increasingvalues of the field current. the 231. 230.229 onlyby a constant quantity{KS). and the other for 900 The r.229 is obtained. (See 181. If when E (a)- point 6 is reached Fig. curves are similar. For any voltage will curve given now be This is shown for increasingfield currents.m.200 If the saturation for of curve two a different speeds.) Fig. bao.p. O O r^' D. 232. These conshown in Fig. connect experimentally.which are plottedas ordinafes.the saturation Saturation of the Curve. there is no singlevalue of flux. corrections can be easily made for any variation. armature volts and the induced volts under these conditions are identical. series Am.values of which measures Obviously the ammeter the voltmeter reads the values of induced are plottedas abscissas. Determmation . the armature direct current be connected across curve. As the voltagedrop within the are the terminal due to the voltmeter current is negligible. should " Connections across a for obtaining saturation A of power. described in Par. armature nections voltage. curve To " the determine in field. by the method When the saturation curve of a shunt generator is determined . During the experiment the speed should be determined each time that the other readingsare taken.C.carried 261 CHARACTERISTICS GENERATOR aloDg the path oah. source the fieldcurrent. Supply Field F:g. It is evident that for any given value of field current. and at c the field current is again increased. The value of flux for any given field whether the field current was current depends upon increased until it reached the value in questionor whether it was decreased. the curve ultimatelycoming back to oab at the point a. 183. for the operating characteristics of both generators affected and motors to a considerable degree by are hysteresisin the magnetic circuit. This characteristic of the magnetic circuit should be carefully borne in mind. 202. back to c. tei^minals. with an voltmeter ammeter. up 185. If the speed cannot be mamtained constant. 233. 231 (a). obtain difficult to the field current to a Fig.shown as low as Such of excessive resistance.although the not error then from ing be readthis cause sUght. This relation is and 1 ampere Curve I shows the resistance line shown in Curve II. the voltageis 100 volts.will be introduced. as shown in Fig.ifthe resistance when of a field circuit be 50 ohms. the current will be 2 amperes when the voltageis 75 volts. is 1.such as shown in Fig.Fig. By Ohm's Law the current in a resistance. oEieU Fig. For example. allows field currents without the is use with easily made in rheostat. Drop. Field Resistance for 80 ohms current shows same " It will be noted that at 80 volts the fieldresistance.wire connections " determining the saturation for obtaining field current.5 ampere. the Line.0 ampere. circuit is proportional to the voltage.Fig.5 amperes when the voltage is 50 volts. would be inter-dependentand it would be difficult to adjust justment the field current without the voltage in turn changing this addue Also a voltagedrop would exist in the armature current to the should be varied field current.for a constant If the current be plottedagainst volts. relation for a etc. well-known the tained to be ob- zero a connection ''3-point"type of field Fig.234. at 40 volts it is 0. Otherwise minor hysteresis loops. continuouslyin one direction. The field current in this experiment should be obtained from H for two reasons: a supply other than the generator itself. nection.262 CURRENTS DIRECT it may reduce be high resistance to sufficiently A drop wire conits loT^er values. In 233. 233. III . the true induced would be The voltmeter would voltage.either up or down. curve the field experimentally. 186. Curve fieldresistance of 40 ohms.1. a straightline passingthrough the originresults. 234. 231 (6). the generator excited its own the voltageand field current field. 5 2.Fig. In fact the slopeof the line is equal It will be noted that the 120 110 100 00 80 70 w 300 " 50 40 SO 20 10 1. Types " Shunt use. connections. " There are three type the field circuit is connected terminals.5 Amperes FiQ. 187.usuallyin series with a across the rheostat. " Field resistance lines.263 CHARACTERISTICS GENERATOR higher the resistance the greater the slope of the resistance line. Load Fig.0 0. generator in common In the shunt 235. of Generators.the compound and the series. ture arma- The . generator generaltypes of the shunt. of the anglewhich since the E the line makes with the axis of abscissas is -i. 235. to the fieldresistance in ohms tangent.0 2. 234.5 1. same resistance of 24 At of shunt generator and shunt a on 236.264 DIRECT shunt must field. The has CURRENTS have a comparativelyhigh resistance take too great a proportion of the generator compound generator issimilar to the shunt.5 amp.therefore.) or Field Current FiQ. manner: As Fig.. . in order that it may current.Fig.but not additional field winding connected an in series wth the ture arma- load. page 296. a at startinga generator the induced voltage is come generator may up to voltage in the following the generator is brought up to speed there will be a the instant of The " generator it will be observed. ohms. etc. The curve drawn of " Shunt the Method Generator. 236 its shunt building shows up. 60 volts 2. . (See page 301. This field. the saturation field resistance line so that at 120 volts it takes 5 amp. 188.270.has plot. The series generator is excited entirelyby a winding of comparatively few turns connected in series with the armature and load. zero. If 128 volts are requiredto produce the of 5. where saturation a This field current that each seen current until by drawing voltage. Fig. Critical Field Resistance.GENERATOR small voltage cho. the flows in virtue of this 4 volts hne from 265 CHARACTERISTICS build up cannot is.3 amperes. it is obvious build up to the It is evident that iron did not become increased to 60 not can- point h. be as ampere may 0.the generator will ance a'.with this not build up beyond value of field resistance. The curve. that will continue to the fieldresistance line machine 8 volts of its previousvalue and this machine point/ is reached. duce this field current requiresa voltageg'h of about 128 volts. In this particularcase . If the fieldresistance be slowly decreased until the fieldresistline "reaches oh.33 which the fieldresistance line at 6. The zontal horiThe The by seen jecting pro- produces a highervalue of field value the field current.is about 8 volts. 237. of 5.6'c. a would machine build up if its indefinitely saturated. the saturation 4 because field. the " If the resistance of the field field resistance line will be represented by oa. 189. corresponding to about crosses the saturation 6 volts. be that the machine ohms. This To propoint represents a fieldcurrent og'of about 5.which action the field is connected is o6'or about 0. It will of course stop building up at the point V. magnetism terminals. The value of the field resistance correspondingto oh is the called the critical fieldresistance. This line point a'.the build up crosses the beyond this point for the followingreasons: Consider a point h on the field resistance line.above /. in the field. of field current. in this instance about due armature to the residual 4 volts also exists across the armature across current in this a current across od' be obtained curve to the field resistance line at d.induced in the of the machine. the generator will be observed to start building up rapidly. curve at Therefore. sulting By conit will be seen that for this field case particular about This value of field current The can imtil it meets the induced produces volts. Thus in turn it will be produces a voltagein excess increased voltage in turn increases is cumulative.2 ampere.3 amperes field current and the machine can only produce 122 volts at this field current. produces a voltaged'e.3 amperes But this field current produces an induced voltage g'g of only 122 volts. (2) The field resistance may resistance. the for reasons be may a generator cannot to Build Up. Fig. There are up. residual magnetism instead of increasingit. upon " Current If opening and closingthe the voltmeter it may be assumed and the field should field produces no effect that the field circuit is open.266 CURRENTS DIRECT resistance is 120/3. Under these condibuild up. the criticalvalue. the be greater than procedure is to the critical field reduce the field resistance until the machine (3) There to jarringor may to too be no builds up. In this case. residual magnetism long a period of idleness. open the fieldcircuit. is bucking the residual magnetism be reversed. in the machine. the current Critical field resistance.25or 36. To test for this. the generator cannot of course it on Field 237. If the voltagerises when the fieldisopened. Generator If the fieldresistance exceeds " generator failingto build in such connected a build up. three (1) The that the current way conunon shunt sent field through startingis in such a direction as to ''buck*' or reduce the tions. FaUs 190. due If the armature cir- . 1 ohms. . 268 and the armature when CURRENTS DIRECT current are which actingsimultaneously. (a)into the upper pole and into the lower pole tip in the south pole. the generator is under load. As the generator armature is shown rotatingin a clockwise . The armature occurs magnetomotive (a) Ourrent in Field Ck"ilonly nn^n^xr. 238. force crowds " Effect of armature in both the and Field reaction upon the field of the symmetrical field flux shown pole tipin the north Axla in a generator. -nugoono "Brash Cc) Current Armature Fig. The be at rightangles to Foy provided the direcneutral plane must tion at of the resultant flux is the same as that of the resultant magnetomotive force. It should be borne firmly in mind that the flux is not pulled around by the mechanical rotation of the armature. As the neutral plane is perpendicularto the resultant field. is to displacethe fieldin the The effect of the armature current direction of rotation of the generator. conductors current out to plane. the flux is weakened pole tipin each case.GENERATOR " 269 CHARACTERISTICS it will be noted that the flux is crowded into the trailing direction. When should be set as axis. that it too has been advanced. of the paper. a of the neutral brushes must right must are advanced plane. cuit they short-cirit is passingthrough the that the brushes should be set X Mmf. Magnetizmg Component of the Armatare Fig.all the stillcarry carry that current the brushes of this neutral littleahead If the brushes so the generator delivers current plane. in Chap. 239.238 (c)the fieldvector The vectors. general direction of the resultant flux in the drawing. The and those to the result is shown . To the rightof Fig.as will be shown correspondto the advance to the left of the two into the paper. " Relation field to brush of armature the coil undergoing commutation neutral later. it will be observed It was shown X"0xnagiieiIziiiff Pomponenti of the Armatare OroM limf. On the other hand. in the two leadingpole tips. reaction is shown armature F and the armature by Fa combine vector tion rightanglesto form the resultant field vector Fo* The direcwhich correspondstd the of Fo is downward and to the right. The direction field. redemagnetizingcomponent of armature Fc acts at right angles to F and produces distortion.as is shown Fa may by the vectors. Fd parallel perpendicularto this axis.it tends to reduce the total flux nnnnnn "ti ) (b) \ "ja-^jL^^-p^ Fio. 240. 240. the in Fig. Demagnetizing " and Demii"7ie tizing Armature Conductors Cr^i^ Armfltnre cross-magnetizing Ma^etizing Conductors components of armature reaction.270 CURRENTS DIRECT with the of the armature fieldmoves brushes. Therefore ward points downdownward. All the conductors within the angle 2/8. and is called the action. main Therefore. now Fa) instead of pointingvertically be and to the left. to the polaraxis and Fc resolved into two components. In (a) the brushes are shown as advanced by an angle /3to correspondto the advance in the neutral plane. Its axis always lies along the brush axis.it is called the cross-magnetizing ture component of armaso reaction. Fig.both at the top and at . It will be noted that Fd acts in direct oppositionto F. 239.238. The shown exact in conductors which produce these two effects are Fig. Therefore. 239. conductors 96 the on conductors.Field is 30**. Demagnetizing ampere-turns 2.880.are armature. This a be checked by the corkscrew rule. 240 (6) shows the flux produced by the conductors not included within twice the angle of brush advance. path 120/4 per 30 X 96 Demagnetizing ampere-conductors 2.239. to netizing demag- The machine brushes grees. or demagnetizing conductors.880/2 1.440. Fig. Brush / Axi8"^^ y / there? lead the angle of brush four brushes. de- demagnetizing cross-magnetizing ampere-tums Twice that cross-magnetizing ampere-turns is equal to one-half of ampere-conductors.GENERATOR the bottom to send as 271 CHARACTERISTICS of the armature. tion The direcand perpendicularto the polar of this flux is downward conductors cross-magnetizethe field. conductors. The the external circuit. four paths through the current 30 amp.880. the number is Fc is F^. There the total number that covered by the of degrees ductors demagnetizing conTherefore ^i the is 120"." is lap wound and effect of armature field mmf's. motive force and F^ is the armature magnetomotive force. may The resultant of Fd and should It be and Example. carry current in such a direction flux through the armature from rightto left. lap A " wound how many many armature delivers 120 15 How and 4-poledynamo and advanced are remembered mechanical has the of both sum are surface ^8S the amp. Their magnetomotive force is representedby the component Fd. These producing this flux is representedby the component Fc. Ans. The mmf. of on Therefore. Fig. Ans. acting axis the brush after brushes the been have advanced. As the there are Fio machine Resultant 241. axis. Fo is along F less than the due the to resultant of the two. being demagnetiz- . 241 shows the method of findingthe resultant magnetomotive F is the field magnetoforce acting on the armature. Fig. the number cross-magnetizing armature. number of cross-magnetizingconductors The be % of the conmust ductors the armature. . so are / Fd ir. The = = " = " ampere-tums = is 192 X 30 " "= 2 ^"^ 2. Fig. These conductors thus act in direct oppositionto the main fieldand are therefore called the demagnetizingarmature conductors. for convenience. multipolarmachine are shown. the armature being shown as a flat surface. It in the interpolar falls to zero and reverses The neutral spaces.together with the magnetic flux entering the armature. tributio In (6) the flux disflowing in the armature is shown. however. 243 (a) shows the armature the field current These armature conductors being zero. plane is the region where the flux is zero and under no-load conditions is midway between the poles. The pictureto the eye and be a littledifferent. In Fig.due to fringing.Fd the demagnetizing component mmf and Fc the cross-magnetizing of the armature component .238 (b). the field poles of 242.Fa can be resolved into two components at right angles to each other. uniform.272 CURRENTS DIRECT ing component of F^. of the armature 192. produce The a flux in a a manner magnetomotive varies uniformly from similar to that shown force of the armature zero at the pole axis in is not to a Fig. There is no current conductors. mmf. " Reactions as in the bipolar manner multipolarmachines in the same machines that have justbeen described. In (a)are shown the alternate north and south poles. It will be observed that it is symmetrical about the polar axis. Armature Reaction in MultipolarMaclunes. It is substantially constant under the pole shoe and drops off graduallyat the edges. but maximum in the . Fig. conductors carryingcurrent.242 the armature may in occur FiQ. " Field flux of a multipolar generator. I Fig. " Resultant flux found by combining field flux (Fig. as the magnetomotive forces of all the conductors on both sides are actingtogetherat this point. The magnetomotive force directly under the polecenters iszero since for every ampereResultant !/" FJux-. 244. poleaxis there is a symmetricallyrent spaced ampere-conductoron the other side carryingan equal curdirection. Midway between gr and st the magnetomotive force will be a maximum.^ A 1 Bieucrai nane FiadFlu: Fig.^ . pole-centers The magnetomotive force distribution along the air-gapis shown conductor on one side of any . Flux " due to armature reaction in a multipolar generator.GENERATOR of the center 273 CHARACTERISTICS The interpolarspaces. 243).the current flowinginto the paper on the left and out I _ a panconstituting cake in the conductors in the conductors of the paper L^ -j tween be- conductors on the right. armature the lines qr and st may be considered as coil. The net magnetomotive force at the the same on due to all such ampere-conductorsis obviously zero. 243. " I (a) Armature* Magnetomotive force Flax I . 242) and ture arma- flux (Fig. ) It will be noted that the flux peaks permeability the trailing on pole tip. having but one-half the cross-section of iron along their lengths. the^iix curve but droops in the interpolar the magnetomotive force curve spaces as shown in Fig. Compensating Armature effect of the armature of the brushes with Reaction. Owing to the high reluctance has not the same of the interpolar shape as spaces. is to use a stamping having but one These are pole tip. (Thisassumes in the iron. crowding of flux into the trailing pole tipsin a 4-pole generator. of The resultant flux is found by adding the two flux curves constant Figs.it is desirable to minimize armature if this can be done conveniently.Fig. 243 (6). 245. 193. page 251. " As the netizing cross-mag- usuallynecessitates the shifting tion reacload. as is done in Fig. 244.245 they should be advanced as this neutral planeadvances.as shown in Fig. is built up.the pole tip becomes highly saturated and its per- . This leaves alternatelyreversed when the core in the poletips resulting spaces between the poletiplaminations.274 DIRECT CURRENTS by the dotted line.244.Fig. as in the case of the bi-polar generator. Therefore. Fio. when laminated pole cores are used. 221. One practicalmethod.243 (6). In order to keep the brushes in the neutral plane Fig.242 and 243. shows the " Field distortion in a 4-pole generator. Also the neutral plane has advanced in the direction of the rotation. . " 276 DIRECT spending conductor. 247 (6). Commutation. amp. making 40 amp. 281) and in large rolling-mill are in indicated in Fig.(2) and (3) each coil (and. It is assumed that is being realized. 10 amp. saturated for any flux tendingto leak between the main poles. passing position(3) . however. a commutator same coil as it Fig. field copper and a greater field A longer air-gap means more because the armature current at each current. ^re reaction is also reduced by increasingthe lengthof Armature the air gap.247 (6). As is the brush covers four segments and the current distribution uniform. leavingthe machine by this one brush. The current distribution throughout the brush is also assumed to be uniform. is necessary. copper The has principle Thompson-Ryan been applied to many modern machines where commutation difiicultiesare unusually series motors great. whereas the current through this compensating winding is of the currents in the various parallel the sum paths through the The small polesbetween the main poles. 248 shows the changes of current in an armature approaches and recedes from the brushes.the Therefore. must flow into the brush from each segment. They do as the armature that of one armature pointii^ path. from to when (4). armature. II. direction to the external circuit. These windings allow the use of a very short air-gap. as in alternating-current (see Vol. The are conductors to as in series with the armature adjustedthat their ampere-turns so not connected are a the armature rule have the ampere-tmns same number are in almost at each of conductors exact and position op- point. therefore. 194. force induced in any " It has been shown singlecoil of a that the electromotive direct cm*rent generator is and in order that the current may flow always in the alternating. thus oflFering higherreluctance to the armature flux.Fig. the manner installed in the pole faces This type of construction is used in the Ridgeway dynamo. successive positionsof any one particularcoil)carries 20 amp. armature series with CURRENTS the armature so This winding is connected that the magnetomotive forces in are oppositeand equal at all loads. The load is such that 20 ideal commutation flow in each path of the armature. page The conductors motors. When in positions(1). with the accompanying reduction in field and in fieldloss. " Current 80" ao-u. consists of two parts: Therefore. in the it reverses This is perfect commutation.(9)and (10). The is current reached.GENERATOR 277 CHARACTERISTICS coil must lose the 10 amperes which pass from this segment into the brush. (1) is illustrated by Fig. Hence. practice.commutation 1. Reversingthe current in any coil from its full positive value to an equal negative value. The current reaches 20 in position(7) and remains 20 amperes in the further amperes positions(8). 248. The must current be conducted Part a two paths meeting uniform until the brush amperes rate at the brush to the external circuit. brush from' another armature path. 2. Before coil reaching position (5) the givesup another 10 is zero when the coil reaches position so that the current amperes (5). when amperes. There are two causes The in . 248 coil is +20 at suppliedby the to a value of "20 (6). When the coilreaches position(6)the current flows through the coil in the reverse due to current enteringthe direction. + Brush \\ \ \ \N T h-* Fig.io-^ 0 *-io in coil undergoing "-ao ""^ja6-"-y commutation ""-" " ideal conditions. This reversal must take placein the short time interval required for a segment to pass under the brush. in position(4)the coilcarries only 10 amperes. is only approximated -foregoingideal commutation preventingits realization. in coils (4)and due to voltagesinduced in them (5)respectively. " Change through This resistance consists of the coil plusthe contact Fig. while they are being short-circuited by the brush. 248 (a)the current distributes itselfover the upon . currents of 15 and 5 amperes flowing in coil when brushes are too far back of the neutral plane.278 CURRENTS DIRECT the coilis in positions(4). 250. merely of the resistance resistance of the brush. If the local short-circuit currents of Fig.(5)and (6) it is short-circuited by the brush.since the resistance of the short-circuited It will be noted that when 16 Fig. coil is very low. 249. a large current will necessarily flow. If any voltage is being induced in the coil when it is in these positions. 249 be superposed those of Fig. This contact major portion of the total resistance. " Short-circuit currents resistance constitutes the Fio. 249 shows ^ 6 assumed of current brush. and in one the brush has to handle 50 amperes twice that which place there are 20 amperes per segment. Fig. amperes instead of 40. +20 amperes time hj which "20 to makes amperes has been reduced commutation more from difficult. There are now enteringthe brush and 5 amperes leavingit. 2(j-" lOo-*. 20-" 251. 250 occurs going plane. or occurred under the ideal conditions of Fig. it firstrises to 25 amperes before starting It will be noted that the time for reversingfrom formly from 20 amperes to reverse. Voltagesare then induced in the coils as they are undercommutation.GENERATOR in the 279 CHARACTERISTICS in shown 45 Fig. the current Instead of in the coil dropping uni- -I-Brush \\\\\ T-^Hriizrnaancziiz: aa-"- Fig. 250 (a). This will tend to produce heating and undue spaxJdngunder the heel of the brush manner brush. Therefore. 248. -*-6o Commutation " *-fiOa *-f20o -^26o with the brushes too *^20a -*" 80a far ahead.250 (6)shows the varies under these new in which manner conditions. .248 (h)and 250 (h)are called commutation curves. The time t to curve of when the brush is too far back of the neutral Fig. The curves of Fig. If the brushes are placed tod far ahead of the neutral plane. page in the coil. curve e N = being the " N 2"^i --- number 10"^ volts of turns (fromequation74.in the time t seconds required for a segment to pass the brush or commutating zone. conmiutation its as The " (b ) After of flux through Change The zone. Commutation Electromotive in this assist matters does not narrower Fig. The too are with too a brush.where the ideal commutation 2"t"i This change of flux will induce a voltage. both the heel and the toe will in the short-circuit coils in which voltagesare induced. l\g/. current previousvalue. the flux has changed by lines. upward. Force coil just as wide " Fig. wide.resulting of Fig. This is shown in Fig.253 (a) it is enteringthe commutation The slot conductors embedded in iron and. due to zone. of Self-induction. brush. flux is still"^ibut it has been reversed in direction. coil is shown just after it has left the In Fig.251.bi^L V^^i^^"- (a) Before commutation Fig. "'^'^'^^' by 185) (^OOglC . Therefore. 196. 252. considerable flux passes through in this case the coil. 252.254. 253. Let the value of the flux be "^i. are the current flowingin the coil. through the coil flows in the reverse is the same direction.but it now a ^'L commutation coil undergoing commutation. is assumed. resulting of Fig. Moving the brushes either commutation curve If the brushes backward forward or only remedy is a shows " The case. curve of the commutation distribution and in the current the toe brush. 253 (6) the same armature an N N v^wt^k"^.CURRENTS 280 DIRECT short-circuitcurrents flow under This the toe of the sparking under produces undue condition brush. with its This lookingupon be considered and mutual inductance in Fig. mutual to ElectromotiTo To force o( SelMndactioD Fig. about to zone are leavingthe commutation Therefore. duced statingit is that the electromotive force inahead of the in the coil due to its cuttingflux in the zone neutral plane is in exact oppositionto the electromotive force of shown in Fig. But they are acting in a circuit having coil is extremely a very low resistance. Electromotive " force of self-induction in to voltageit is necessary the neutral plane in a generator. commuta- ahead of coil is undergoing polarityas that enter. force of self-induction. even plane and the coils undergoing commutation magnetic Knes. and so neutraUzes self-and mutual induction. that the brushes be kept ahead of It is therefore necessary the neutral plane in a generator in. Another of way it. This inductance with other armature tends to prevent the current reversingin the same manner that inductance tends to prevent change of current in any circuit. " The of the circuit resistance is at the brush contact. there will be a voltage induced cutting neutral are no in the coil due its to self-inductance own and inductance. it may coil has self-inductance.this field induces a voltage which assists the current to which the conductors reverse.voltage. this follows: The as is shown direction. though the brushes are set exactly in the Therefore. When ehminate this it finds itselfin commutation a a coil undergoing set the brushes the field of the same tion. 254. The resistance of one 196.254. armature as a coils. low so Sparking that most at the Commutator. 254. . voltages induced in a coil due to the shifting of the neutral plane and also due self-inductance are its own to comparatively low in value.order to obtain satisfactory y commutation under load conditions. proper It is called the electromotive Instead of 281 CHARACTERISTICS GENERATOR voltagephenomenon. being of the order of magnitude from a few tenths of a volt to perhaps 4 or 5 volts. In a very this case copper is often gauze used. brushes have a much Carbon higher contact resistance than and therefore limit the short-circuit ciu*rents. brush low. The voltagedrop across the positivebrush. course the copper. The from of the current passage to the brush the commutator phenomenon than it is one of pure will show myriads of minute A careful examination is more of an arc conduction.they are less more more or satisfactory graphiticin their composition and so lubricate the commutator to a certain extent." has been in operationfor a considerable time. due to the brush is different from that across and case negative in the other. After a machine Another proof is the so-called "high mica. Therelow voltage. the two grind the copper Even must though the always wear until it conaes in . In addition. instead of drop between tion being proportionalto the current (as it would be with conducand is equal to about 1 only) is substantiallyconstant Bits of copper be found in the positive volt per brush. it often happens that the mica above insulation between was mica is much trudes pro- in so-called resulting long supposed that this was than of the copper is of fallacyof this supposition wearing segments the surface of the commutator. 255. Unusually hard carbon brushes may cut the Different grades of carbon are requiredfor different commutator. a low resistance the standpoint of carrying the current On other out to the external circuit with minimum loss. short-circuit currents are excessive when they are used. may the negative brush due to the arcing. disadvantage of using copper brushes is that they *'cut" the conunutator mechanically. contact low contact but the resistance. existing between the brush surface and the commutator. cannot evident. The voltage the commutator and the brush.high their appUcation is limited to very Copper brushes have current machines. being positivein one copper These facts all substantiate the arcingtheory. It due to the mica being harder the the commutator arcs away harder evenly for the brush than more the copper. fore.282 CURRENTS DIRECT contact currents reach such may sparking at the brushes. these short-circuit resistance is too If the brush is desirable from excessive values the as to produce severe hand. Another machines. which resulted in The readilythan the mica. givingmuch copper results. "high mica." Fig. . deeper the depressions. " Proper method of fittingbrushes. will deteriorate very corrected. these actions are cumulative. Do not use emery. A slightly with an oilycloth.or the higher the mica. Carbon on be removed not use waste. bars. soon The brushes should be fitted very tator carefullyto the commusurface by grinding with sandpaper in the manner shown the surface of the commutator should in Fig. 257. If the conducting and may short-circuit the commutator sparking is rapidlyand not . arcs Fig. the largerand more vigorous these arcs become.or. of the If a commutator is sparkingbadly and the cause commutator. any condition which creases produces sparking and so roughens the commutator only inthe sparkingand roughening. Hence.the commutator become inoperative. 257. Do be partiallysmoothed with fine roughened commutator may of emery the particles are as sandpaper.284 DIRECT CURRENTS of The increasingmagnitude will be formed. as shown in When the because of the steepnessof the flux-distribution curve. commutating plane. 258. It will be noted that this position is in the fringe of the next pole flux.the trailing tip of each brush may weak a be in too strong a field and the leadingtip in too field."^2. in order that an electromotive force be generatedwhich will balance the electromotive force of may self-induction. 258 shows the geometricalneutral or no-load neutral plane and the neutral plane under load. such as loose mica and loose segments.or is otherwise in poor it should be turned down in a lathe. brushes will not Neutral^ advance if advanced to the pole flux is to the load neutral The zero. appreciableflux. be of the very existingin the neutral now remained brushes must cuttingthe ifthe voltage be advanced so flux "t"i of the next Fig.due to armature reaction. " properlyeven tate Brush The zone. condition. in the because sparkingunder load conditions.could be produced in the geometrical obvious that the flux in the neutral plane could be brought to zero If in a flux spiteof having the armature same value reaction. best positionof the brushes is obtained.there would 258. that the short-circuited coils are commu- plane. It will be noted that this is merely Fig.commutator is 285 CHARACTERISTICS GENERATOR grooved by the brushes. This force of self-induction stillexists in the coilsundergoingshort-circuit. opposite to it in neutral.it is direction. more difficultiesby tighteningup the commutator clamp bolts. are Other difficulties. If as a "^2. difficultto obtain good commutation commutation be impossibleto obtain satisfactory fact.Fig.244 " the brushes reproduced. It is often possibleto rectifythese serious in character. Commutating Poles (Interpoles). If plane.it may pole. even due neutral ^^'V^^ to proper to the fact that the electromotive is due no-load severe Load Fig.but flux having a value "^2+ "l"\ . A very slightmovement of the brushes in either direction makes a very marked change in the flux so it is In under these conditions. 197. The pole producingit at be a south pole.258. Fig.261. Fio. Commutating polesconsist of narrow poleslocated between the main poles. with a few turns of comparativelyheavy wire and are connected in Fig.the compensating flux produced also be proportionalto the commutating poles must The commutating polesare wound. as shown by the .-7-Resultant As the armature induction to of main flux and reaction and commutating-pole " the electromotive in the coils undergoing commutation the armature flux are machine loaded.286 DIRECT CURRENTS would be obtained produced. It must also the produce an force electromotive "t"ito balance in the coil undergoing commutation. magnitude to produce satisfactory proper example. the commutating pole must first produce a flux equal to "/"2so as to neutralize. in Fig. 259. therefore. the inwere N "^ " n^ t FiQ. satisfactorycommutation without moving the brushes. flux This of selftating commu- pole flux is shown in Fig. force of self- both proportional current.258 and 259. armature current. " Flux produced of flux due to armature crease additional induction L^" by commutating reaction. It is the function of commutating poles to produce just this flux. The air-gap in series with the armature. 259. in the neutral zone. They send a flux into the armature which is of the For commutation. 260 shows the resultant this point must flux obtained by combining Figs. 26O. pole alone. 262 shows an interpoleseparate from the machine. 261. Fig. 261. on . " Connections in this of shunt field 4-pole machine. of polesin the direction It should be noted that the sequence of rotation in a generator is Ns and Sn. Each pole has twice the fore.GENERATOR 287 CHARACTERISTICS so that the commupolesand the armature is large. This shunt is sometimes made inductive so that the will flow to the commutating poles proper proportionof current sudden changes of load. tatingpole flux is nearlyproportionalto the armature current between these at all loads. strengththat it would have if four such poleswere used. this shunt being adjusteduntil the best condition of comis obtained. In practice. Therethe proper commutating voltage is induced in but one side of the coil undergoing commutation. It will be noted that only two commutating poles are to the main Fig. 263 shows the frame and field coils for a commutating pole motor. where the capitals refer poles and the small lettersrefer to the commutating poles. and commutating poles. commutating polesare so designedthat they produce necessary a flux of greater magnitude than is necessary. Fig. The entire commutating pole circuit is then shunted by a low resistance mutation shunt. The commutating pole shunt is shown in Fig.such as occur in railway generators. the terminal voltage will drop. 262. The Shunt Generator: Characteristics.P. " Frame and pole and winding. voltageunder load conditions determines . to field coil for Westinghouse 30 H. Fiu. crease of load. in terminal voltageis undesirable.288 CURRENTS DIRECT 198. direct-current. This drop in voltage will increase with in- generator. in generators which supply power to drop a especiallywhen it occurs incandescent lamps. Such Commutating " 263. " If a shunt voltage.interpole motor.be loaded.. It is very important to know the generator for each value of current abilityto maintain its voltageat the terminals of a because the that it delivers. after buildingup PiQ. pointof the generator. it is connected as 263. in the a To test of suitability generator. Further applicationof load results in a very rapid decrease of voltage and beyond a certain point any attempt at increase of load results in load may current even will a decrease of current rather than an increase. The In Load Fig.235. in a 289 CHARACTERISTICS order to a generator for certain determine terminal volts to current.GENERATOR large measure specifiedservice. 264. " Shunt load should then be thrown voltmeter. The machine is self excited and page is connected in the Une to measure performingthis test it is often desirable the field circuit so current as shown a as relation of in Fig. The Current"/ generator characteristic. If the readacteristic be plottedas shown in Fig. be carried to short-circuit conditions and actuallydecrease as short-circuit is yet the approached.in a small generator. The speed of the generator ings should be maintained constant throughout.reading the volts and the current for each load. voltmeter its terminals to indicate the terminal across ammeter the is volts. 264. the so-called shunt charresults. If. nected con- An the load current.264. as shown This is called the break-down in Fig. In ammeter in to connect to be able to follow the an change in the field the load is applied. This is due to the fact that the field is short-circuited and 19 The any .rated load should first be applied and the field current adjusted until rated voltageis obtained. a rapid decrease of voltage will occur. startingthe test. off and the no-load volts read on the load should then be graduallyapplied. the load be carried far enough. 265.togetherwith a lesser field current upon for the return curve resultingfrom the lower voltage. 231 (a). to the residual current If the external resistance be which it started.machines are operated only on the portionab (Fig.. the voltageis dropping and the iron is on the part of the cyclerepresentedby c.231 (a). it returns along the path a. set so that the generator terminal voltage is 230 when it is this load of 435 amperes.000/230 435 amperes.230-volt generator. There is less flux for a given field 60 100 150 250 200 800 350 400 460 600 Amperes Fig. " Typical shunt characteristic.When the load is being appUed. and consequentlyless voltageis induced in the machine the return curve. The increased.264) of the characteristic. the terminal voltage E V laRa (103) (1) The terminal = - . Fig. That is. Fig.290 DIRECT CURRENTS flowingat short-circuit is due of the machine only. 265 shows this portion of for a 100-kw. This. Fig.accounts lyingbelow the other.page 260.the voltage will now rise slowlyand will ultimatelyreach magnetism a value not far below that at fact that the voltagefollows a different when the short-circuit is removed is primarily due to curve hysteresis. delivering There are three reasons for the drop in voltageunder load of a current = shunt generator: voltageis less than the induced voltage by the resistance drop in the armature. In practice. When the voltagestarts to increase. The rated current the curve The generator field rheostat is is 100. . 200 r.a generator when operatingat hi^h saturation maintains its voltagebetter than when running at low saturation.m. ardization The definition of regulation accordingto the A. and the other If the no-load 1.m.due to saturation and also hysteresis. 267. Regulation no defined as follows: be more specifically may and fieldiron than " Regulation As an = 100 example.page 260.p. Standrated load and Rules is the rise in voltage between load. This is illustratedby for curves a 230-volt Pig.the generator will mainits voltage better at 900 r.200 r.200 r. I. 267. the Per cent. is illustrated in as Fig.m. E.p. higher saturation at Field Currentt Pig. Googk be . The regulation constant potential the amount the voltagevaries from rated load to no load. tain (a). E.292 DIRECT CURRENTS flux. The abilityof a generator to of its suitability for maintain its voltageunder load is a measiu*e shows quantitatively service. Therefore.)(104) voltagefrom b to a = be -jr.one at 900 saturation two r. Generator Regulation. on As point (6) correspondsto a much curve.p. as shown by the characteristics in Fig. volts " i~d^ regulation = 100 d rise in (percent.p.231 (a). which shows generator.p. of the armature " Load Relation of shunt Current characteristics to speed. than at 1. curve and at point (6) on the 900 r. 267. This is usuallyexpressedas a percentage.266.m.the generator will be operating at point (a) case the 1. voltageof the generator in each is 230 volts.m. 199.in Fig..m.p. 6 per cent. Reference is often made " in to the total characteristic. Fig. be the shunt characteristic. Let qr. which reference has alreadybeen made. voltage is regulation shunt The 100 ^^ 230 = 230 200.GENERATOR In the 100-kw. /a when The induced // // the shunt field current. total characteristic It may follows: E.236 and 237. Draw done in Figs. 268. Total Characteristic. 265. " characteristic of shunt Total generator. to volts. is the relation existing between a load current and terminal volts. Per cent. the load by current the flowingin the field. current . scale. as was of will have the appearance fact that the abscissas are the field The line owing to the being nearly vertical. 252 ^^ 100 = characteristic of characteristic is shown generator whose Fig. is the relation between The armature current armature diflFersfrom current of current amount The generator. the no-load voltageis 230. shunt The totalcharacteristic and indu^ced volts. Total Characterlrtle "^"^ o Fio. The armature 268. The is the curve showing the relation of la and be foimd from graphically the shunt characteristic as resistance. current plotted to armature . 293 CHARACTERISTICS = rated load 9. resistance line Oa. / is the load ciu*rent and volts E where / + = V is the terminal = V + laRa voltageand Ra the (104) armature includingbrush and brush contact resistance. Oe' to = for two reasons: as la^Ra loss iu the armature itself.07) + = 226.Oq to Oa^ give the voltage.294 The CURRENTS DIRECT the OY horizontal distances from for each value of value of fieldcurrent axis. horizontally resistance drop line Oh is then plotted.5 X 93. that the total induced voltage It should be borne in mind givesthe total power developed multipliedby the total cmrent All of this power is not available. in armature = 226.shunt ohm and shunt a power is developed in the armature Rated current an afield resistance of 100 220 T ^^ =100= Armature _ 2-2 ^"^P- current la Induced _ = 2. Example. It is only to the current..1 kw. of " A 0. it delivers its rated output? when Field current Power heating the 21. sistance re- What . rent horizontally is given by the resultingcharacteristic qe.2 90. givingpoint d on the characteristic qe. is then proportional in the armature value of current to determine the drop e'f at some necessary Oe'.1 X 0. the Une Draw {Oe')Ra = axis.9 + = 93. within the armature. For example. however. The armature assuming The voltagedrop that the brush contact resistance is constant. By adding these the total curto the shunt characteristic. output is consumed of the armature (2) Some shunt is lost in the armature of thi^ power (1) Some in field. 0/'. Ans. appearing copper.1 amp.07 generator has 20-kw.1 = armature ohms. drop for each value of current.the voltagedrop distances e'f the OX vertical distances from The Of. as ef e'fisadded at the point e. 220-volt. That is. the total characteristic qf is obtained. at point c on the shunt characteristic the distance cfdf is added at cd.5 volts.give the armature Adding these drops to the characteristic qe. volts ^ developed P = 220 (93. 269. 269. (93. A (short shunt). The 484 = ^The " Ana. drop in voltage with is characteristic of the shunt load. the flux through the series turns also increases and.295 CHARACTERISTICS GENERATOR f The be obtained result may same by adding losses power as follows: Field loss loss Armature developedin Power P = 20.1)*0. therefore. By proper the series ampere-turns. which 21. = generator. increase the induced The effect of this increased flux voltage. this increase in armature made to balance the drop in voltage due adjustment of voltagemay be to armature reaction . turns when These to rise in a few turns the generator delivers current. " Connections of a slightchangeof voltagemakes power of incandescent compound a generator change in the candle- material lamps. or even voltage as the load increases.1 kw. This a very Shunt-field Rheostat Pig. through the is to armature increases. the ciurent As the load increases. be made generator may constant produce a substantially a voltage. type of generator undesirable where constancy of voltageis essen- to lighting where appliesparticularly circuits.07 607 = watts. Compound 201. Fig.000 + Pf = Pa ^ ^^* watts.091 watts = Generator. makes this tial. by placing on the field core which turns are connected are connected' so as in series with to aid the shunt the load. armature + 607 484 21. are neutralized more completelyby the effect of the series ampere-turns. 270.296 DIRECT CURRENTS and that due to the resistance current causes If the terminal drop in the armature. Therefore. be connected (a). the field will not drop as the load increases. flatcom- possibleto maintain a . w Shmit : Field (a) (6) ShoEtShunt Fig. 271. armature reaction. less the armature the machine case or is called the machine across Over ComponndAd _E!lat impounded Under Compounded Current Fio. 271. The (6).270 shunt. voltage is maintained substantially constant.) It is seldom same is said to be voltage pounded.laRa drop.the machine (See Fig. generator drop in fieldcurrent (Fig. namely.Fig. in which 270 directly across If the shimt field be connected short shimt.the machine operatingcharacteristic is about the same is long in either case.the three of voltagedrop. " Compound characteristics. " Compound Long Shunt connections. generator terminals outside the series field.266). and The shunt field may terminals. Fig. If the effect of the series turns at rated load as at no is to produce the load. The size of the conin the distribution system of such plantsis determined almost entirelyby imderwriters' requirementsas to carrying capacity. constant lOO (a) Fig. used where the load is generators are indistance from the generator. If. A certain The load is suppliedover a load is 4. the generator voltage risesjustenough to offsetthis feeder drop. The particular shape of the characteristic is due to the iron becoming saturated.000 ft. the machine is said to be under compounded.so that the added series ampere-turns do not increase the flux at fullload as much as they do at Kght load. As the load creases. Generators are seldom under compounded.such as hotels and office buildings.the voltageat the load remains constant. reaching the same obtained at no load. in isolated Flat-compounded generators are used principally ductors plants.GENERATOR 297 CHARACTERISTICS voltagefor all values of current from no load to rated load.however. distant from the generator. feeder.the machine is said to be over compounded. 272. The no-load voltage of the generator is 500 500. When the rated-load voltageis less than the no-load voltage.000 CM.due to the voltagedrop in the feeder. It is desired to maintain the load voltage at a substantially constant volts. " Over-compounded 200 (b) generator maintaining constant of a voltage the end at feeder. The tendency is for the voltagefirstto rise and then to voltage at rated load as was drop again. value . 272 (o). Wires conformng to these requirements are usually tween of such size that only a very small voltagedrop takes placebe- the generator and the various loads. Example. " Consider the conditions shown in Fig. When the rated-load voltageis greater than the no-load voltage. Over-compounded located at some the voltageat the load tends to decrease. 1^ 80 X = 48 volts. What current would generator? operated at were of 300 demand the be drop would total drop of 80 volts. Compound generators over compounded. and amp.01 volt per 0.and R^ and Ra the seriesfieldand armature the armature respectively. are being delivered to the load. foot.03 ohm . 338. resistance = Example.) equals the combined In a long shunt generator J. 68). where voltage. mil (Par.(jB"is the equivalentparallelresistance of the series field and diverter.making The actual drop is a amp. has current resistance of 150 a terminal The amp./" the series field current. each armature. called a diis used. page 376..Fig. /o. The generator terminal voltage should rise from a no-load value of 500 volts to 548 volts when 300 amp. (See Fig. and the 0. 272 ih).one connected resistance to 273.Fig. Fig.if a diverter is used. /. then current in the diverter and series field. + + laRa (105) . 273. voltage of shunt " A 230 compound volts field current when generator. connected it is is 4 amp.la is the terminal V current. Compound generators which supply 3-wire distribution systems usuallyhave two series field windings.R. deliveringa the armature short shunt. The usuallywound so as to be somewhat degree of compoimding can then be regulated by shunting more are Diverter or /VNAAA less current away from series field. " Series-field diverter. shimt.001 "normal" the density the per cir.) In a compound generator the induced voltagein the armature each pole. To do this the low a verter.298 DIRECT of 500 volts from CURRENTS load to the maximum no be the characteristic of the must If the cables be 500 or amp. 0.one is: S 7 = I. side of There are the two separate series windings on winding being connected to the positiveterminal and the other to the negative terminal of the machine. . which turns value. The Let the necessary responding cor- crease in- of field ampere-tiu'nsis where turns Nah shunt-field turns = Let / be the rated. Corresponding values of field current and armature current noted. 274 (c). and iV. of 203. Therewill have the more the higher speed machine risingcharin Fig. Fig. 1%. Character- Armature of series the number it is necessary to place upon the poles of generator in order to make it either flat-compounded or it any desired degree of compoimding.adjust the no-load voltageto its the make To shunt a the generator to its rated load and bring the terminal volts value to the of field ciurent by of the field rheostat means desired value. (6)than in (a).owing to the lessersaturation of the iron.300 DIRECT The distance owing the in each same be less than now speed. It is preferableto excite the fieldseparately.' Let this value of shunt field current proper give to determination.acteristic. Deteimination " It is often Turns: Series determine desired to istic. (See Fig. 274 the distance will be ah depends of series turns solelyon the load. Load is applied as shown to armatiu'e and the terminal of the voltageis maintained constant by means shunt-field rheostat. 267. the effect of speed upon the compoimd characteristic is just opposite to the effect of speed upon the shunt characteristic. be Load be /i. But increased the to will oa as case.) This is due to the fact that saturation opposes change of the flux in each case.275. The increase of voUage cd is much greater in fore. It will be noted that is shown as . be may (eitherturns by of series turns means the (h-I^N^ for of the armature flat-compoundingmay characteristic. When the two are are plotted (as . the series turns. necessary The per used). in Fig. CURRENTS the increase it was in (a).load current Then NJ^ number obtained appUed pole or total of the machine. The also be load is in the usual way. 275. 204. The 276. the increase of field current the shunt turns and the current character- rapidlythan the armature feeby multiply by divide Oa. .K = Oa '^A where of turns of the shunt field.276) the resultingcurve istic. current It must consist of the generator. " Connections for obtaining armature characteristic. Series-fieldturns for flat compounding 6c N. winding is connected " characteristic. "^ FiQ. N^h is the number "^ FiQ. determine the number of series turns necessary. " Armature Series Generator. N. In the series generator the field in series with the armature and the external of a comparativelyfew turns necessarily of wire havinga sufficiently largecross-section to carry the rated circuit. The owing current To fieldcurrent 301 CHARACTERISTICS increases is the armature more to saturation. u.GENERATOR in shown Fig. " Series generator characteristic. due to the drop through by the amount and the drop due to armathe armature and field. by the saturation 277. 277 shows the saturation maintains rent series generator and also its characteristic. of curve saturation that of the shimt generator. ture reaction. reaction. cur^ The curve a curve external for low voltage at each point is less than that shown The Amperes Fig. provided the external resistance equals or . in distinction to the shunt generator which constant potential. la{Ra + i2"). differsin no from way The characteristicis similar in shape to the saturation saturation.302 DIRECT The series generator in CURRENTS instances is used for constant most work. The reaches a maximum curve beyond which armature curve reaction becomes so great as to cause the curve to droop These machines sharply and the voltagedrops rapidlyto zero. are designedto have a very high value of armature builds up as follows: If the series fieldis connected in such The due machine to the residual a manner that the current magnetism aids this residual magnetism. the generator will build up.Fig. per commutators.in voltage is obtained by connecting several series generators in The current. The Brush Arc machiuQ and the Thomson-Houston Both of these examples of such machines. which correspondsto substanconstant The current is not affected by a concurrent. power tials the as Thury System. correspondingto the line 06 swinging up or down. one at each end as 5. siderable change in external resistance.Par. Thompson. ripples (SeeFig. (For a Electric Machinery. In the Brush Arc three separatecommutators the voltageper commutator in the voltagewave.GENERATOR 303 CHARACTERISTICS is less than that indicated by the external resistance lineOa. 164. commutator.as has alreadybeen discussed for the resistance to The line 06 issuch generator. a line. XI.000 volts. the external swings down shunt As decreases. McGraw- .) As the voltageon the comfrom 2. Handbook." two Fourth Edition.the external resistance line the right. To obtain close regulationthe series field is shimted by a rheostat. I.^ This high high as 50. It would be impossibleto operate with an external resistance corpractically responding to the line Oa^ or to any line cuttingthe curve to the left of d. the commutator mutators ranges generator are common have generator there connected and between wide gaps are as in series so many as or to reduce out the also to smooth two as segments. In be held this way the current delivered by the generator may constant. the series generator has been much used in series lighting. 189.000 volts to 10.000 volts iSee Hill Co. The line Oa is therefore called the criticalexternal resistance line. The resistance of this rheostat is controlled by a solenoid connected in series with the line. series and voltage transmitting at constant increases with the load. substantially arc In the past. P.000 volts. armatures. machine The to is designed dropping operate tially along the portion6c of the curve." 191.as a small increase in external resistance would swing the resistance line away from the curve resultingin the generator's its load. have open-circuit (SeePar. "Standard generators have The of the armature. potentialmay run as high Regulation is obtained by The commutator. Chap.) is transmitted by direct currents at potenIn Europe. Vol.) There are but four segments per more complete descriptionsee "Dynamo S. The power is utiUzed by series motors at the desired pointsin series with the Hne. the curve. If the drivingpower should in any way be removed. The booster is a series straightportionof the magnetization Booster Motor I Fia. feeder is proportionalto the current in the feeder. " The Volts drop te Feedw series booster.than cheaper to install a booster. feeders.as shown in Fig. Therefore.Fig. the terminal voltage being proportionalto the current Likewise the voltagedrop in the flowingthrough the machine. is direct-connected to a shunt motor taking its power from the bus-bars. When a particular a drop on it may be load.and utilize it at the peak to invest in generator operatingon more the copper. nected con- Series generators are often used as boosters on direct current feeder becomes excessive.278 (a). voltageat the load may The booster be maintained constant.its terminal volts may be made always equal to the drop in the feeder.and adjusted properly.304 CURRENTS DIRECT shunting the fields.278 (6). 278. If the generator be connected in series with the feeder. . 1 20 more see the ''Standard Handbook.the voltageas generatedis alternating " and the current must be rectified or generator.the regulationof the creased generator is made to include the voltage drop due to this dethe regulation making out specifications. Par. 228. 19. For a more complete discussion see ''A Solution of an Acceptance Test Problem. at a constant value. Kouwenhoven. 279 (o) would not be practicablebecause disc shown the electromotive force is generated only at one portion. B.so pieces. 1918.an equal electromotive force is generatedalong each radius. When driven by its prime mover should be of the generator when specified. For complete discussion Edition. commutator a commutated. generator is being tested to determine " tective pro- ^When its characteristic or a its it is assumed that the generator speed is maintained regulation. The in Fig. The Unipolar or Homopolar Generator. In practice. Therefore. Wld.Speed correction applied to characteristics of generators because which is somewhat of the factors involved. mover Therefore. Jan. ^^ In the ordinary direct-current generator. '' by W.so that current when the external flow back through the disc even can circuit is open. Any drop in voltageresulting from a drop in speed of the prime mover or drivingmotor is not chargeableto the generator. Effect of Variable Speed upon Characteristics. Elect. Vol. load is practically unlimited. direct current is In the unipolar generated. If a disc be rotated between the poles of a magnet. 279 (6). A current can be taken from the disc by placing a brush at the center and another at the rim.. of the prime a drop in speed with load in the case is often unavoidable.so -that the current has no return path in the disc itself. 71. 205. If an annular pole be used. speed. 206.the rated speed of the generator.such a and tear itselfto be belt-driven and should have some device to prevent its running away. an emf.the series generator will reverse speed of a series motor without that it will run away booster should never 305 CHARACTERISTICS GENERATOR and operate as a The motor." Fourth .and no is necessary. Fig. Section 8. many enter the computation. Fig. The principleof 'the unipolargenerator is that of Faraday's disc dynamo. 279 (a). however. is generated between the center and the rim of the disc. 306 DIRECT Fig. 279 (c) shows brushes The 66 crossnaection of a a unipolar machine. polarityand the brush a is of the to brush oppositepolarity. A hole in the castingallows access Such with a rotatingcylmade a. inder generators are sometimes and are of CURRENTS one said to be of the axial type. The chief disadvantageof the unipolar type of generator is the at high speeds. It is necessary very low voltagegenerated,even to connect are several discs in series in order to obtain Fig. 279. " working unipolar generator. The (c),having an armature diameter of about 20 in.,and running at S,000 r.p.m., would give only about 40 volts. Another disadvantageis the difficulty from of conducting the current the disc at the high speedsat voltages. The which Such generator in Fig. 179 these machines generators are are run. necessarily manufactured by both the General Westinghouse Co. Their field of appUcation is that of a high speed,turbo-driven generator,designedfor high currents at low voltages. 207. The Tirrill Regulator. It has been pointedout that the voltage of a generator varies with the load, speed, etc. By of a Tirrill regulator, the voltage of a generator can be means maintained constant under even rapid fluctuations of load. Electric Co. and the " 308 DIRECT other is connected The relay contacts CURRENTS the line through the main contacts. intermittentlyshort-circuit the generator across field rheostat. The control magnet can open to close. These contacts are main the main contacts or allow normally held closed by a spring. Assmne that the voltagerises. The potentialwinding of the main control magnet strengthensthis magnet and opens This opens one of the windings on the relay the main contacts. action. The relay contacts magnet and so nullifiesthe diflferential and the short circuit removed from then pulled open are the generator field rheostat. This immediately reduces the action takes place when the generator voltage. The reverse voltagedrops. As a matter of fact both relaysare constantlyvibratingso that the changes in the generator voltageare very small. The relay contacts are shunted by a condenser to reduce sparking. Owing to the fact that these contacts can carry to have the only a very small current, it is usuallynecessary and so maintain the bus-bar regulatoract on an exciter field, voltageconstant through the exciter. be A compensating winding on the main control magnet may series shunt to give the system a rising connected a across characteristic and so compensate for line drop. \roltage them CHAPTER XII MOTOR THE Definition. 208, is machine a for It " stated was converting Chap. XI in mechanical that energy a generator into electrical energy. In similar way a into mechanical cal energy be used may 209. the motor either as is The energy. motor a as or for machine a generator. a Principle. Fig. 281(a) shows strength or intensity in which same converting electrimachine however, a " is stant magnetic field of conthat placed a conductor N (a) (J) Fig. 281. carries Force " no acting on w in current (6) the conductor In current. carrying conductor a is shown but the field due to the N into the paper, been A removed. cylindricalmagnetic field about the field,which this due conductor be may to the current determined in it. carrying a and S poles as current has field. magnetic a The exists now of direction by the corkscrew rule, is clockwise. the Fig. 281(c) shows field and the main current above to reduce The in The by combining field due to the conjunction with the main it opposes result is to crowd the flux field obtained to the current. acts conductor, whereas conductor. and that due in the conductor the resultant the main the flux above density in the region below field below field the the conductor the conductor. 309 Digitizedby (^OOgle 310 DIRECT It will be found that push the conductor CURRENTS force acts a the on conductor,trying to by the arrow. think of this phenomenon down, as shown It is convenient to crowding of the lines on as due side of the conductor. one lines of force may be considered as tension. These lines always are to the Magnetic actinglike elasticbands imder endeavoring to contract so as be of minimum length. The tension in these lines on the side of the conductor is tending to pullit down as shown upper in the figure. If the current in the conductor be reversed,the crowding of the lines will occur helow the conductor,which will tend to move it upward, as shown in Fig.281(d). The operationof the electricmotor depends upon the principle that a conductor carryingcurrent in a magnetic field tends to at rightanglesto the field. move 210. Force Developed with Conductor Carrying Current. The force acting on a conductor in a magnetic field is directlythe strengthof the field, the proportionalto three quantities: magnitude of the current, and the length of the conductor lying in the field. The force in dynes is given by to " F where B is the flux active lengthof The amperes. 5ZJ/10 = densityin lines per direction of the force all are sq. cm. or gausses, I the in centimeters and I the current the conductor direction of the (106) dynes. the field, conductor,and to mutually perpendicular id the one another. of 20 turns lies with its plane parallelto a Example, ^A coil consisting flux density in the fieldbeing 3,000 lines the field magnetic (seeFig. 286), The axial length of the coil is 8 in. The current per conductor per sq. cm. the force in pounds which acts on each is 30 amp. Determine side of the coil. (See arrows in Fig,286a.) " B Z = 3,000 = 8 X 2.54 = 20.32 cm. / =30 Fi As there are = 3,000 X 20.32 X 30/10 = 182,900dynes. 20 turns F = 182,900 3,658,000dynes 3,658,000/981 3,730 grams 20 X = = 3.73 kg. = 3.73 X 2.204 = 8.23 lb. Ans. 311 MOTOR THE relation between Rule. The Fleming's Left-hand the direction of motion of a direction of a magnetic field, 211. " in that fieldand force is given by the ductor con- the direction of the induced electromotive Fleming's Right-hand Rule. the direction of a the relation between similar manner, the direction of a cm-rent in that field and the magnetic field, In a Fio. 282. Fleming's left-hand rule. " direction of the resulting motion of the conductor by usingFleming's Left-hand Fleming'sLeft-hand Rule: fingerin the direction of the current in the vnll point in the direction in which is illustrated be determined Rule. Point the forefinger in the direction of the field or This can flux,the middle conductor,and the thumb the conductor tends to move. by Fig. 282. N N "Cotton ib) (a) Mator Fio. Another 283. " Motor method and generator Generator action. determiningthe above relation is to make of the fact that the crowding of the magnetic use lines behind the conductor tends to push it along. It is necessary merely to sketch the main fieldand the Unes about the conductor, shown in Fig. 283(a). It is evident that the Unes will be as convenient for 312 CURRENTS DIRECT crowded motion at right of the conductor the so that the direction of is to the left. Fig. 283(6) is shown a similar condition for a generator. to the right. In this case the conductor,as a generator,moves In Hence in a generator the conductor must against a force move tending to oppose its motion, and so the conductor requiresa This drivingforce is supplied drivingforce to keep it in motion. to which the generator is connected. by the prime mover 212. Torque. When an armature, a fly wheel or any other force is necessary device is revolvingabout its center, a tangential This force may be developed to produce and maintain rotation. itself as in a motor within the machine engine,or it or steam be appliedto a driven device such as a pulley, a shaft,a may " Force Belt Fia. 284. " Torque dae to Tension developed by a belt and by gears. otfa street car, etc. total effect of the force is determined not only by generator,the driving gears on the wheels Fig.284. The its magnitvde but also by its arnty or radial distance from the center of the pulley or gear to the line of action of the force. The product of this force and its perpendiculardistance from the axis is called torque. Torque may also be considered to produce rotation. as a mechanical coupletending It is expressedin units of force and tance. dis- Englishsystem, torque is usuallyexpressedin poundsfeet. (This distinguishes it from foot-pounds which represent work.) In the In the c.g.s. system the unit of torque is the dyne-centimeter (a very small unit),and in the metric system the unit is the kilogram-meter. 313 MOTOR THE The Exam-pie, ^A belt is driving a 36-in. pulley as shown in Fig. 286. side is that the 30 loose and in lb. 90 belt is in side of the the tension tight " Determine lb. to the the torque applied 3^ Lb. pulley. The sides of the two ' ^^"^ in belt are that the O "^ acting opposition pull on the rim of the pulleyis so net 90 This 30 - 60 lb. force is acting 18 the ft. from 1.5 = in. of center or the pulley. Therefore the torque T 60 = 1.5 X 90 = Ib.-ft. Arm, 90 Lb. Fio. 285. 213. a a " Example of torque produced Torque Developed by a pulley by a belt. upon Motor. Fig. 286 (a) shows coil of a singleturn, whose plane liesparallel to a magnetic field. " out flows into the paper in the left-hand side of the coil and of the paper in the right-handside of the coil. Therefore, the left-hand Current Fi and conductor to the right-handconductor Fio. 286. force Fi. These Both to act develop tends a " Torque two turn torque. tends to at diflPerent forces tend to rotate it in a downward move a force upward with positionsof a a coil. the coil about its axis. counter-clockwise As the current with direction and in each of these conductors so is force they liein magnetic fieldsof the same strength, F2. In (a) the coil is in the positionof maximum Fi torque distance from the coil axis to the forces because the perpendicular acting is a maximum. When the coil reaches the position(6) neither conductor can move any farther without the coil itself spreading. This is a the same = and developed move 314 CURRENTS DIRECT distance from torque because the perpendicular positionof zero the coil axis to the forces is zero. If,however, the current in the coil be reversed when the coil reaches position(6) and the coil be carried slightly beyond the EL^iojaafi ^^j^^^" Fio. dead 287. " center, as tends to turn To each Torque through on shown in (c),a torque is in motor continuous the armature the neutral torque in must still direction. motor, the be reversed plane or plane of is therefore necessary. a armatures. developed which the coil in the coimter-clockwise develop a coil developed by belt conductors just as current it is passing tator torque and a commuThis is analogous to using a comzero in 288). = expressedby the above The equationsis the entire torque developed by the armature. of the is certain motor a of its originalvalue new CURRENTS DIRECT 316 60 X 45 Ib. the final value of torque will be ^ ou 45 72 Ib. developed? the constant ening value of torque. by VjOOQ Digitized IC . considers one especiallywhen of such that the rated cmrent of 90 in the is in motor neighborhood When amp. Counter If this armature ohm. operation.05 across 110-volt " The is motor directly connected were the of resistance ordinary 10-horsepower. increases to current 75 per. cent. of the direction voltages in a motor a The and so of conductors in addition to its surface. torque available at the pulley will be slightly to the torque lost in overcoming friction and in supplying the that the torque be remembered It must iron lossesof the armature. due to the weak- new be 0. " develops 60 the and value of the torque If the current remained would field. the line it from amp. = to the increase in the value of the current.75 Due 50 taking If the field strength is reduced lb .05 This value of current is not only excessive but unreasonable. due less than this. to is the what 80 amp. are be of armature a on carrying developing torque. generatingan If the right-handrule be appliedto determine the direction of this induced electromotive force (seeFig.-ft. The every Ifotion Qf Conductor Fig. of currents " Relation and conductor. cutting flux. Therefore..-ft.however.it will be found they must . 110. would mains. electromotive force. current is in motor similar to that way generator.200 amp.volt of the armature Force.-ft. = = 0. the current.^When Example. 288. Electromotive be Law.torque.the the armature is by a is motor a through not determined evidently current its ohmic resistance alone. Ana. by Ohm's 110 / 2. 214. about 0. close closingSi the lamps will bum brightly. /. interestingexperiment for demonstrating the existence of counter electromotive force is shown in Fig.5 = 105. The net voltageactingin actingin the armature circuit is the armature V The follows Ohm's current armature E - TT Law and is r" . transposedand written E =V laRa - (110) compared with equation (104).05 ohm. armature ^ the " '^ = 110 - (90 X 0.it opposes oppositionto the current. As the current it must also force opposes Therefore.289. At the instant of . resistance is 0. being practically speeds up to candle-power. Li a generator the induced emf. force electromotive counter electromotive the counter the line oppose voltage. Ans. motor is taking90 amp. " when The the terminal voltage is back 110 electromotive volts and force of its armature a 10-hp. As the armature and become dimmer will dimmer. Ra is the armature where This be equation may "'V^ =^ (109) resistance. Then motor.the net electromotive force circuit is the difference of the line voltage Let V equal the line voltage and the back electromotive force.317 MOTOR THE That is. which is the similar equation for a generator. flow into the armature This should be Determine Example. showing that up. is equal to the terminal voltage the induced resistance drop.05) = 110 - 4. these lamps Si.page 293.5 volts. Li a motor plvs the armature emf. is equal to the terminal voltage minus the armature sistance realways drop. A lamp bank An is connected in series with First close switch S^ which the armature of a shunt closes the field circuit.. back or electromotive force. This induced emf iscalled the enteringthe armature. and E the back electromotive force. The counter electromotive force must be less than the terminal or impressed voltage if current is to at the positiveterminal. that it is always in the current . s the speed of the armature where poles. and lO""* are all constant for any given motor.Z the number of conductors on the surface of the armature. P. coming up to full candle-power. M. S being given in R.the counter electromotive force E volts -^-TTTT^ 10^ = p from one north 4" is the total flux enteringthe armature in revolutions per second.the field circuit should not be opened under any conditions whatsoever. therethe counter electromotive force will be immediately reduced will be shown which to zero practically.318 CURRENTS DIRECT generatinga counter electromotive force which opposes the Une voltageand so leaves less voltagefor the lamps.however. pole. P. When fore. for the induced electromotive force in a generator will obviously apply to a motor.) Equation (101). If. " (^O Demonstration of counter electromotive force. 7". Solvingfor speed E S ^K (111) where K = 1/Ki . and p the parallel paths through the armature. P the number the counter of electromotive force becomes E which is identical with Ki"t"S = equation (102).page 258. (In practicewhen a motor is in operation. As Z. 289. That is. by the lamps again the armature is 5^ 00 Fig.page 259. the armature is up to speed.the lamps will be very dim. the fieldswitch S2 now be opened.the flux and. THE 319 MOTOR speed of a motor is directly proportionalto the counter electromotive forceand inversely to the field.290 (c). a magnetomotive force Fa is produced in the armature. Ans.10 01 " Therefore: ^^ 216.060r.m. Applying (112) ^110 -'50X0. F. Fo is obtained. By adding these two the resultant mmf.^=l. to the armature ampere-turns. It will be noted that (1) the flux has been crowded into the leadingpole tips.and (2) tlieneutral plane perpendicularto the resultant a motor armature .p. field has moved to move backward. Fa and the field mmf. these same . Therefore the brushes backward in a motor with increase of it is necessary load. When K^^ ^ " with motor a ^A certain connected speed changes of load.whereas in a . Annature Reaction Fig.p. proportional Substitutingfor E in (111) its value given in (110). = ^'200i5|. its speed amp. produced by Fo is distorted as shown in Fig.200 Therefore: ^-I'^iSS But 02 1. Fig.1 ohm. What is its speed when taking 50 the with field increased 10 per cent. 20 taking is 1. " Due carrying current.m. an" armature has motor 110-volt across the law of mains and resistance of 0.the speed The becomes "S This ^-^- (112) a very important equationfor it shows ij3 variation of Example.1 ^ __ 01 "f"i ' 108 4"i 108 4"i Si = 1. 290(a) shows and Brush Position in a Motor.1 Si 105 02 105 0f __ Si 110-20X0. and the direction of flux produced by this mmf is at rightanglesto the polaraxis.200 r. ? mains.290 (6)shows the the magnitudes and directions of the armavectors representing ture mmf. The total flux vectorially. from amp. 195). Due. of the brushes is accompanied by a the field.320 DIRECT CURRENTS motive forward. as indicated demagnetizingaction of the armature upon in Fig. and the generator it is neces290 (c). to the necessityof counteractingthis last electromotive force. That is.as is shown in Fig. Were it not for the electroforce of self-induction (see Par. load neutral planein order to force of self-induction. however. the brushes are set behind this load neutral plane.where F'^ is the demagnetizing component of . 290 (d). sary 290.in both the motor generator they are moved onnoprn Keuiml FiQ. the brush axis would coincide with the neutral plane. " to set the brushes counteract This I'lancv Armature movement Axis reaction in beyond the this electromotive backward Brush \^ a motor. incorrectly magnetomotive 216. F'a must then be opposed by a south pole.is Nn /Ss. This continues until the increased sufficient torque to meet The of a suitabiUty motor the demands for any force is armature current duces pro- of the increased load.as the flux remains substanelectromotive flows into the armature decreased. If the back more current tially force. parallel A field rheostat is usuallyconnected in series with the field. the relation of main polesand commutating poles. It will be reaction Fa in the first inter-polar noted that the armature space is upward. 291 shows the armature and passingunder successive north and south poles.as the load is increased on a motor the armature reaction tends to increase the motor speed.its field is connected the line in with the armature.) The polarityof the interpoles should be carefully investigated with a compass.in the direction of rotation. Relation " of commutating force of the poles to main poles in a motor. In fact instances with short air-gaps(producing where motors have been known reaction)have run away when the load wasappUed. (seeequation 109. particular dutj^is determined . Therefore in a motor.that is. as the sparkingmay connected. 261.or opposite to the corresponding relation for a generator. In the case this decrease of speed of the shunt motor directlyacross lowers the back electromotive constant.) Therefore. (See Fig.321 MOTOR THE Therefore. page 287. high armature conductors carrying current Fig.if a commutating pole is to be used it must be a north pole. If load is appliedto any motor it immediately tends to slow down. 291. if a motor happens to be sparkingbadly from unknown be due to their being some cause. a shunt " armature ^The shunt motor is connected in the generator. (See Fig. by tending to send a flux down into the armature. page 317).in order to oppose this Fa' y N O O O O0O 0O 0 ee"e""""""000000000o $ N O Rotation Fig.243. The same Shtmt manner as Motor. " speed of a series motors. 292. V.the torque will vary For example.la increases and the numerator of changes only a small amount. is 30 amp.torque. stantially all subAs the increases. when the with the armature current. That is. load on the motor motor.322 DIRECT CURRENTS factors.293. almost directly from equation (108). ThereIn the shunt motor the flux is substantially constant. of F. is of this per cent. and when the current is 60 amp. 80 Ib. the percentage drop in speed of the motor the shunt motor is conorder of magnitude. the motor develops torque.when the current doubles the torque almost entirelyby two doubles. The 292. The speedof the motor willthen drop with increase As laRa is ordinarily from 2 to 6 of load. 0 10 40 30 20 60 eo 80 70 Amperes Fio. laRa "t" In the case of the shimt constant. slightly this equationdecreases. Ra. As a rule the denominator Googk . armature the motor current develops 40 Ib. torque-current and Shunt where accordingto equation (112). in Fig. varies motor 7- S K = curves. fore. For this reason sidered a constant speed motor. and "^ are Therefore. K.-ft.the variation of its torque with load and the variation of its 8j"eed with load.the only variable is 7o.as shpwn in Fig.-ft. even though its speed does drop with increase of load. . Therefore the load is removed. 294. should not be started under load. Startingboxes are usuallydesignedto allow 125 per cent.if the startingperiod is too long.-ft. Therefore.. motor could be made to develop 150 per cent. The Series Motor. Therefore. comparativelyfew must nected con- turns of be of sufficient cross-section to carry the rated armature current of the motor. providedthe field intact. the torque is 80 Ib.-ft. Ktl"l" proportionalto /..etc. of full-load current to flow through the armature the first on notch.^^^ ^j^^ ^^^^ armature cur- is ^f ^^ie motor motor. series operated at moderate saturation. motors There will be noted definite no-load a when away circuit remains Shunt has motor chapter.in the expressionfor torque. of torque are the current increases characrapidly."^.de- In the series motor the entirelyon FiG. When the current is 30 amp. in series with the fieldis In the series motor " the armature. field has wire and as shown in this wire The Fig. above It will be noted thai as the torque rises very of the series motor makes its use 60 increases in amp. of full-load the torque at starting.the almost flux will be directly proportionalto the armature current. torque is proportionalto the square of the armature rent. of 294. low 217. pends the flux. the at 60 amp.the motor develops125 per cent. This teristic desirable where large desired with moderate increases in cur- . of full-load torque will overheat boxes however without trouble. current results in the quadrupling the doubling of the armature shown as of the torque. By decreasingthe startingresistance. It erroneous an a startingtorque and therefore.-Connection8 a jf ^. 292. is speed. Ordinary starting under these conditions. the expressionbecomes T when = = K':P (113) constant. impression that shimt motors have a as in machine required. cur- Fig. torque is 20 Ib. T to be if "^ is assumed The K\is a.blowers. That is.324 DIRECT CURRENTS ciency will be discussed in the next that the shunt it does not run used where are constant speed is substantially shop drives.spinningframes. that is. however. correspondingly must and the armature speed up in order to developthe required If the load be removed back emf. It . speeds where as their armatures are action will centrifugal them.the back emf becomes the motor to run more slowly.the voltage drop in the fieldresistance and the armature resistance increases because this voltagedrop is proportionalto the current.resulting a very high speed. to remove almost wreck the load from certain to reach series motors. altogether. the armature speed the series motor. The flux with the load.i2"the series is now pole. Both effects tend to slow down the motor. be of the proper value. /?" the resistance of the series field. As the load increases. of a series motor Fig. 0 becomes extremely in is dangerous small. which is usuallya few per cent. as rapidlyas the square of the prevent the torque increasing In rent. The speed upward for the reasons is practically inverselyas the current.at largevalues of current the speed is low and at small values of current the . 295 shows the characteristic curves concaves plottedwith current as abscissas.THE 325 MOTOR saturation and armature reaction both tend practice. increases almost directly the speed must drop. inversely proportional given percentage change in "l"produces the same percentage change in the speed. less than the terminal The resistance voltage. to current. of the terminal drop is ordinarily voltage V so its effect on the speed is only of this magnitude.which causes effect is only of the magnitude of a few per cent. to the flux "l"and a The speed is. Therefore. The torque curve which have justbeen stated. from 2 to 6 per cent. decreases the flux "t" Wheii the load is decreased. resist- with the load.in order that the back emf. ' When equation(112)is appliedto ^ S where if is a rent. resistance armature field resistance north = "l"the flux entering the armature and from added resistance in order to obtain the total motor la and 0 Both vary cmv includingbrushes.however. Ra the K " + ^'^ ^"^^" (114) /" the motor constant. Therefore 0. the a to ance.although this less.V the terminal voltage. automatically slows down . such dition street cars. maintains Assume the therefore tends series motor. street When car. 296. A hand. The effect of these becomes field and The of the current The (PR). increases. efficiency about half load and with the load. current. 293.cranes. as torque. to the largestartingtorque. so that these losses increase when occurs efficiency maximum largeas pared com- less as the load loss varies armature maximum This is due to the fact lightloads the friction and iron losses are that at load. locomotives. The at reaches increases rapidlyat first. then decreases. These curves should be carefully istic compared with the correspondingcharacterof the shunt motor.326 DIRECT speed is high.. a the as square rapidlywith the the friction and iron Current Fig. practically equalto the copper losses. The characteristics cannot small values of current CURRENTS because the be determined speed becomes for dangerously high.-Typical series motor characteristics. the shunt approximately the a is running an is used on excessive level ground. Fig. curves Series motors used for work which demands are largestarting In adetc. on the the car shunt a ascends speed of the value that it has when motor that other the to car take car at motor to grade. there is another characteristic which makes them especially desirable for of series motors losses are traction drive motor same The a ' purposes. Fio.327 MOTOR THE i I I I I 1 I I I I 1 I I M 40 H. PINION OF TERMlNAl.3I6 i 800 30 12 2b 8 10 4 200 0 0 0 296. RATIO TURNS 8. P. 297. fi $ 40 *^ I I20 I 1000 ** s .8 CAR HELD t9. GEAR IkPUT 12 AMP. lowered for inspection." 67. " " Typical railway Railway motor motor with frame characteristics. B" 100 S 90 86 80 82 TO 28 "24 60 S " 1400 1200 " ^ "- 60. VOLTS OUTPUT AT DIAMETEB ARMATURE S TURN0. AT MOTOR BOO WHEEL 83" SPOOLS n". Fig. . because upon It therefore develops more torque drop in speed allows the a motor to increase of power. The speed. The Compound Motor. may additional series winding in the same manner as a shunt generator. shimt than motor a moderate smaller of the increased at reduced current. As acteristics speed charcompound the load is appliedthe series turns motors. causing the greater than it would be for On the other hand. 295.Gen- curves Electric railwaymotor. The characteristics cumulative are Fig. of the motor armature.the refer to the output at the track and not at the motor shaft. The cumulative develops a high torque with compound motor the . eral Fig.. the characteristic curves Fig. flux causes the speed to decrease more rapidlythan it does in in Fig. develop a largetorque with but Hence. 298.328 CURRENTS DIRECT reaching such a grade.m. This be winding may " connected shunt so that it aids winding. When the characteristics of railway motors are plotted. curve resemble closely is also the efficiency at the rails. These differ from curves the of torque curves and r. " of Torque and shunt and a compound combination of the motor of the shunt and series characteristics.determined by the gear ratio The efficiency and by the diameter of the drivingwheels. These characteristics are shown the shunt motor. this increase of simple shunt motor.p. in which the case is said to be cumulative the motor the series compound. respectively by a constant quantity. The speed of the car in miles per hour is given rather than the r. These curves of Fig.40-hp.m.p. increase torque for any given current to be the flux. railway motor have an ^A shunt motor 218. could series motor a operating under the be same conditions. 297 shows a typical with half of the casing lowered.298.in which case the motor issaid to be differential compound. It will be noted that tractive effort is plottedrather than torque. or the shunt winding may oppose winding. 296 gives such characteristics for a 500-volt. armature the direction of rotation in any motor. in the shunt field ampere-tums compoxmd motor are speed also shown in 298. permissibleunder commercial starting. 219. Because of the substantially very speed of the shunt motor there is littleoccasion to use the differential motor.increase of load. as current large passingthrough the series field may be suflSciently constant to overbalance start to the and cause the motor Typical torque and direction. unchanged.punches. sudden does not run It also has a definite no-load speed. This the armature electromotive force. Cranes a straightseries motor cannot and elevators are representativeof such loads. In startinga differential compound motor the largestarting the series field should be short-circuited. in Par. Such motors are constant speed is desired. the series field opposes the shxmt field so that the flux is decreased the load is applied. This speed characteristic is obtained with a correspondingdecrease in the rate at which This used where a the torque increases with load. the resulting Hence. back " be gradually speed and developsa . In the differential compound when the motor reaches motor.shears. This type of motor is used also where a largestartingtorque is desirable but where be convenientlyused. 10-hp. Motor Starters. 110-volt volt Such motor It a would current connected were the motor armature cut out as be not resistance when would 214 that if a directlyacross be ^-^ or should be connected comes ditions. immaterial which line is positive. shown was current mains. as results in the constant or speed remaining substantially even increasingwith increase of load. Therein so far as the direction of rotation of the motor is concerned. either the alone or the fieldalone must be reversed. If both are reversed the direction of rotation remains To it is reverse fore.such as in rolling occur mills. In elevators the series tmns are usuallyshort-circuited speed. con- in series with resistance may up to 110- 2. when away 329 MOTOR THE Its field of applicationlies principallyin driving machines which are subjectto sudden applicatipns of heavy load.200 amperes. wrong of the differential curves Fig.. etc.so the load is removed. 299. Fig. 300. This resistance is so low compared with the resistance of the field itself that it has no material effect upon the value of the field current. As this the starting When is moved resistance is graduallycut out. in the slate front of the starting terminal of the motor. g^her. field terminal line One tied to- with the startingbox. the line and at the same the field is put directlyacross time all the startingresistance is in series with the armature. connects in R motor. arm the arm the startingresistance is reaches the running position. is the right-handend of the startingresistance. the line and armature conductors frequehtty are connected directlyby a laminated feeds brush..330 DIRECT Fig.. is connected armature to the other armature connection in the startingbox contact. over These no contacts contacts startingresistance. through the box. the connections directlyto It makes series Uttle ^^ purposes. there would "* starting. which connection does in difficulty set connect The with taps distributed along the terminal of the startingbox. voltageacross no outside K the field were the resistance. startingarm makes connection with the firstcontact. The other line goes to the line terminal of the startingbox The starting which is connected directlyto the startingarm. 299 shows a motor. A spring tends to pull the startingarm back to the startingposition. This field terminal is connected The field from the first starting to the field terminal of the directlyto the other minal ter- of the shunt field.^1^^^^r''^'''' Rtarung from con-' terminals. shown in Fig. to insure good contact.. When the . The field current now copper back through the startingresistance. There ^'''"^!f. all cut out and. the CURRENTS of use It will be noted simpleresistance a for R starting that this resistance is in the armature circuit and that the field is connected the directlyacross the armature across putting the with resistance the whole be littleor torque the field be would developed and startingwould be experienced. nected line and shown and armature an This in a whatever not differ fundamentall Fig. is connected hold-upmagnet. 300 shows a 3-point starter. moves arm box. . hold-up magnet may of field current and " Connections for a ^^JUi^mt 4-point starting box. except that the hold-upcoil is of high resistance and is connected the line. It is similar to a 4-point box difficulty the box shown in Fig. therefore.332 CURRENTS DIRECT springsback to the startingpositionand so prevents the motor running away.300. "J Fig. This results in the field current The having approximately this same range. The 3-pointstartingbox cannot be used to advantage upon variable speed motors quently having field control. be too strong. The across only directly difference in the connection connected is that the ''lineterminal" to the side of the line which runs be must directlyto the com- . Such motors frehave a speed variation of five to one. 301. highervalues To obviate this is used. 301. Fig. at the too weak at the lower values. The starting and speed-adjustingrheostat. " then has two Westinghouse arms. 302. period the field rheostat is short-circuited by the fingerS. is removed . which has no spring.inserts resistance into the field When backward. When the voltage leaves line. as within the shown in arm to starting Fig. the the field resistance is contained Sometimes box.THE and armature mon 333 MOTOR field terminals. the voltage goes off. 302. The by this arm longer arm. arm arm is pushed up resistance in the When is held the starting resistance by the is all cut out.the circuit when moved shorter arm springsback carryingthe longerone with it. shorter 302. Fig.the hold-up coil becomes dead and allows the springback to the startingposition. The box Fig. the shorter sistance magnet and the short circuit of the field re- pushing S to the right. and cuts out the by the longer arm armature During the starting ordinarymanner. the line switch can be opened with no appreciablearc. if the gradually through the armature.303 (a).the startingarm the motor current is released. In CURRENTS the line switch should always be opened With shmit motors. shown in shown in Fig.302. few turns one in series with the motor. no-load Fig. In the latter type. The seriesmotor starter needs no shunt fieldconnection. 303 (6). falls below the desired When value. this results in a hot arc which bums To prevent rather than (") Series starter. Fig. small fingerbreaks the arc. throwing back the startingarm. the hold-up coil consists goes two are of a principaltypes. Fig. There having a no-load voltagerelease.334 DIRECT stoppinga motor. " Series being burned. is thrown startingarm back.and one having a no-load release. since the has a back electromotive force and the field can discharge motor On the other hand. Owing to the inductive nature of the field. motor a release starters. This . the contact. the contact from 303. the field circuit is broken at the last contact button. the hold-up coil is connected the voltage when the line and releases the arm directlyacross off the line. In the former type. They have They cut out advantages over the hand-operated starter. so that the blowing of tion. 304.304 shows an automatic starter . Controllers are be usuallyfitted with a ''reverse. used where the operationof the are the direct control of under and elevator motors." so that the motor may run in either direction. i.as in controller must be is street more tinually con- car. When with remote solenoid S becomes energizedthrough L2. due to too rapidaccelerafuses and the opening of circuit breakers. results. starting. especially starters alone can in rollingmills. " automatic Cutler-Hammer starter " dash-pot type. Fig. since the controller is used for constant while operating. the control switch.MOTOR THE last type is a particularly adapted of possibility motor speed the load dropping to such where there is low value that the a dangerous.stopping and reversing the motor Such controllers usually have an external resistance which is in the controller. crane to series motors become may Controllers 335 The an motor operator. avoided. many the startingresistance at a definite rate. are likelyto shut the motor Employees will be more with is not being used. the control switch is closed. Fig. practice.automatic give satisfactory a snap switch. Automatic starters are often used in is used In many installations where a motor be started and stopped by merely turning it may intermittently. because of the ease down when the power In the largersizes of which startingand stopping are effected when extremelyrapid operationis necessary as motors. A shunt motor cut in and out by fingers field rheostat may also be incorporatedin the controller.the control. of the slidingcontact type. rugged the than startingbox. (C)3 Electric Controller and Mfg. pressure Fig. the control switch. and Li.reducing circuit becomes its current D and therefore its power !-" R\ Bi Ri 1 Fig. B. The againstthe energizingof this solenoid pullsup the startingarm action of a dash pot. Co. in the solenoid to The motor a value is stopped by- By using 3. B. The armature current flows from L2. D. D. As soon as the starts arm noid the line switch sole- to move. or any other automatically-operatedswitch. through the startingresistance to H. H. Instead of a simple be controlled by a float switch. L.C. 6- Arm. B'. B'j Li. L2.Aij through the series field and armature back to Aif to N. This reduces the on starter.O.and 4-way switches. opening the control switch.a switch. The contactors themselves operate as follows: . contact At " LHu ^8 H5 (h the the with same When consumption. to Li. automatic startingresistance is all cut out. -ff. Bt is 2 A.336 CURRENTS DIRECT C.this type of controller may be operated from widely separated points. This inserts the additional resistance DB' into this circuit. 305 shows a simple and ingenioustype of starter of the contactor type. the between makes arm Li and Ai- resistance A-B short-circuiting current sufficient to hold up the startingarm. to Li. making time a brush direct connection the contact opened. This closes the line switch and energizesthe solenoid through the auxiliarycontact Fy to A. 305. the of the motor switch.the motor may snap switch. short-circuiting to feed now passes .on the motor contactor sufficiently strong armature to the CCz is also put negative main. magnetic where lines will stream the air-gap. FF. If a heavy current flows through the coil. the same as in Fig.P. which which short-circuits Rj.but there are stilla few in the air-gaps. already described. small and the pullin the gap. 305 (a) and (5)represent a rectangulariron frame.between the plunger.P. and the top of the frame. is suflScient to raise the plunger. R2.P. and the bottom of the frame.closingthe contact pointsBl. between airthe plimger. and also across DD Fig. in the figure. A coil is placed around the plunger. is that the narrow P. DD. FF. across f/. This causes an increase of current through the coil C2.305 (c). of these lines now Most part of the pass through the narrow DD. The magnetic lines in the air-gap. and R^ . of the coil. gap. when a large are current flows through the coil. contactor CP2 R2 and causing the current operates. the air-gap U.cause an upward pull on the plimger. reason DD. When the line switch is closed. as shown the black circles represent the cross-sections of the wires CC. due to the motor coming up to speed. part of the plunger. and the frame FF. across A shunt the line but it is not to raise the plunger of 3. is now pull. thereeasilycarry any more magnetic lines.P.P.DD. The downward plunger. FFy and than at at the bottom plunger.FF. DDj hold the plunger down.P. with the result that there are not so many Unes existing through the plunger P. These lines. When the current drops again.back through the frame. 305 (a)except that less current flows through the coil CC. and one [/. forced to pass through the air-gaps. is saturated.or. in series and coil.the current flows from the positivemain through the coil Ci of contact 1. The plunger. The operationof the switch is shown in Fig. is narrower the top and the narrow part of it fitslooselyin an opening in the bottom of the frame.305 (6)conditions are gaps. through the plunger. the plungerP. and through the narrow part of the air-gaps. There are two air-gaps.THE 337 MOTOR Fig.305 (a) The that some of the lines go through the air-gaps.She. When the current falls to a suflGiciently low value. f/.but the weight of the plunger and the downward pullof the magnetic lines in the airIn Fig. it cannot fore. DD. the resistances Ri.the plunger CPl as rises. in other words. U. PP. due to the Unes passingthrough the gap. They can carry but they canof the motor safelyfor the short periodof starting. Starting boxes are usuallydesigned the startingcurrent for startingduty only. When in The contacts placedbetween the the contacts open. through Cz. as the largertypes. between which polesof a magnet. cast-iron gridsare used. resulting from opening a circuit. the current as the arc shown tends to per- Arc Fig. 221. so The principle and so bum the arc does not persist the contacts. not carry such a current continuously.Cs operatesand shortcircuits all the resistances and coils so that the plungers of 1 3 is held up by the shunt coil She. in the form be wound In of a helix. asbestos It may be self supporting porcelainforms. 306. 306. In the smaller types In " the wire is wound or shown in it may Fig. Resistance Units. Controllers and circuit breakers 220. sist in the form field so to of across arc. Magnetic Blow-outs. The box resistance units are usuallyof the type shown in Fig. 307. Their function often equipped with magnetic blow-outs. and 2 fallback. Magnetic This arc blow-out. The arc starts the field according to Fleming'sleft-hand rule.338 CURRENTS DIRECT drops again. When the current " of blow-outs is follows: as is to be broken are Fig. on or . are that is to extinguishthe arc. finds itselfin a magnetic immediately follows.307. that motor move an " action doing so it draws itselfout to such an extent that it is broken. . 25) - = 218.25 = 3.? the speed of the motor resistance? in much is lost the (c) What percentage of power terminals? armature a speed regulationis the usual series resistance the " load rises to no the to the armature Example. at its rated load of 30 amp. Without is lost. Googk .p. motor takes 6 amp. The speed regulation equal practically pliedto speed resistance method. 30 resistance. 3 or 4 per cent.200 109.m. shows and (6)there is shown shunt a CURRENTS circuit is delivered at the armature delivered to the armature (d) What speed regulationof is the the armature? Neglect reaction.p. 1.p.3 - 110. In for comparison the speed-loadcurves the with and motor armature. When ohm.69 ohms.m.7 = = 30 3.) 218. speed control speed regulation is very poor. Ana. (a) Fig. has an armature resistance of 0.308 of The that of power of is lost in the armature without speed-loadcurve resistance in series with with series armature half speed is obtained at 308.340 DIRECT The principalobjectionsto this method that are excessive amount an series resistance Fig. running without load at 1. load) El (atno = 220 (6 X 0. the armature ^A be resistance should connected in series with the armature to to 600 r. (a) What reduce (6) How the power (a) value which is about and of the power supn in the series resistance.6 volts.3 volts.44 ohms.200r. BOO E2 (at600 r.5 - 220 Total {R + Subtractingthe Ra) armature R = 3.7-hp. armature " that the is about It will be W) Speed control and regulation " the resistance rated load.25 220-volt. - 0. at speed of the motor when there is no with resistance resistance. observed series armature 60 per cent. 50 per cent.m.69 = 109. 600 53.200 1. with the 4-wire system shown. Owing to the necessity can and due to the large of having a balancer set. this system is little used in this country. 309.600 = 3. Multi-voltage In " available are These voltagesare the at = ages this system several different voltterminals of the motor. In this system. System.600 watts.096 - 3. field of the motor is connected permanently across fixed voltage and. circuit delivered to armature Pi Power 341 MOTOR THE = 6. shown in Fig. 309. " Set Multi-voltage speed control.1 per cent. are be made with a limited fieldcontrol. 310.Af 2. Mi. (d) Speed regulation 600 1. the desired voltage across the supply field is connected motor The is obtained.6. the motor terminals. delivered to armature Pi 6. driven by a motor. Fig.or its equivalent. Ana. e Balancer Fid. generator. .(6) Power lost in the series resistance Pi (c) Power (30)2X = 3 44 220 = 30 X 3 Q9g ^ wQ. 50 per cent. across Ward mains Leonard in " parallelwith the fields of the other two machines. = delivered to armature Percentage power 3.504 ^ = 6. of a separate variable motor voltage is obtained by means By varying the fieldof the generator.200 - System.tiH. Ana. six voltages a Intermediate speed adjustments available for the armature. a balancer set. The shunt of wires number necessary. armature suppliedby often Ans.504 watts. Ward " Leonard system extensivelyfor turning the of speed control.342 CURRENTS DIRECT Fig. The resultant flux is Fo. (? in turn supplies Jlf2 whose speed of motor variable voltageto the armature This system is very flexible and gives close is to be varied. In the foregoing methods Field Control. of speed control. used 310. of turrets but is battleships. any 311. supersededfor now this purpose. F is the field flux at low speed and Fa is the correspondingarmature flux. If it be attempted to double the speed of the motor fieldflux will be F\ the new The brushes by weakening its field. A change of speed may also the armature of a fieldrheostat. Referring to Fig. be obtained by varying the flux. The chief disadvantagesare the necessity of having the two extra machines and the low over-all eflSciency of the system. adjustmentof speed. In Mains Fi^ld Fig."^. " Eiffect of a weak field upon brush position. especially This system has been at lightloads.by means " This method is very efiicientso far as is concerned power and for \ -"\ Field Flti* Fig. The range of no speedobtainable by ordinarymotor is limited by commutation difficulties. this method will now with the have to be moved farther backward so that the armature . volts have been varied. Ml is a motor drivinggenerator G. particularspeed adjustment the speed regulationfrom load to full load is excellent. 310. 311. at F positionshown flux will be at the 343 MOTOR THE The a. to backward the main to eliminate moving of the brushes. A range of 5 to 1 in speed variation with is obtainable properly machines designed having commutating poles. slide in 312. mechanism. In armature The other words. speed range Motor. the Motor. As the and therefore the speed of the motor.313. faster in order to . may reluctance to the armature flux is increased at the higher speeds. the is varied by moving the rotating armature Electric and the armature out cutting flux of the field is reduced. motor.the flux. Stow The this In " type of motor. As the armature conductor the length of armature in Therefore the armature must rotate develop the requisiteelectromotive force. 312. By length of the air-gap. ratio of field ampere-turns does not ampere-turns Lincoln " change. In the Lincoln " motor. resultant field is F\. made out of the field structure. with the increased air-gaps. This gives a finelygraduated speed control over wide ranges. with commuthere is little difficulty tation. It is evident that the neutral to considerable a equal the field flux. the is large. are provided with commutating poles. the field cores and of the out actuated through by yoke and wheel hand a are bevel gear varying the rod and a The Stow Fig. These motors ratios as high as 10 to 1 being obtained. to so flux is about sparking at the severe field may the strong armature commutator. shown in Fig. to in and Fig. as shown is moved liance by the Reflux entering Engineering Company. be varied. to and extent plane has been moved that the armature In addition field that the motor tends to run demagnetizing action due commutating-pole motors only the be should where used the weaken In order away. 344 DIRECT Fig. 313. " CURRENTS ^Lincoln adjustable speed motor. . these two groups are connected of a taking the place of the singlemotor in Fig. Each motor connected in parallel across full-linevoltage. " (c) Starting. " Trolley Trolley Trolley ICall ( }") Running Motors Fig. receives full-linevoltage.both groups are then receives the line. the two with each other and in series with parallel a portion of the resistance J?.THE 345 MOTOR ^In a 2-inotor trolleycar. the full-speed When running positionis reached. the currents become out In the heavier electric cars so . that obtainable with full-linevoltageacross 223. In starting. This startingcondition is shown 2-motor car. car. The motors different si)eedscan are firstconnected in series through a startingresistance 22 as shown in Fig. Railway Motor be efficiently obtained. This resistance is graduallycut the running position is reached. 314 (a). As there is no external resistance in the circuit. 314 (c). with 4 Motors in Parallel control of series motors. This is the firstrunning position. each motor out and when in Fig. the motors of two motors which are always in parallel each group consisting motors with are each thrown in other. This resistance is gradually cut out by the controller receives comes as the car up to speed and then each motor one-half the line voltage. the motors are nearly equal to operating at an efficiency very the terminals of each.as shown In a 4-motor are usuallydivided into two groups.each in group Multiple-unitControl. Series-parallel it is desired to increase the speed of the car. For given value of armature current each motor will run at half any its rated speed. " and locomotives. 314 (6). two Control. series. largethat direct platform control is of the questionfrom the standpointof the size of controller. When 314. being accompUshed by car contactors automatically-operated proper the times. which car too close in sequence at the acceleration and eUminates circuit breakers and the shocks to the rapid acceleration when manual ment equip- operation . a single In the multiple-unit system. is done by solenoid-operated These contactors in turn are operated by an auxiUary circuit which runs the entire lengthof the train (Fig. Train / .346 CURRENTS DIRECT Moreover. can platform Another distinct advantage of this system is that the rate of cuttingout the startingresistance during the acceleration periods is outside the control of the motorman. connectors "^-S^i " J 1 Principle of multiple-unit control. called the train line. " 1 "=?=" Ground " 2 Fig. control and that they shall operate simultaneously. Trolley Wire . . located in the couplers. The wires of this train line receive their power through the master controller operated As this train line current is only of the magby the motorman. nitude of 2. Line Oar 315. 315) The train line is made continuous through plug and socket . itis necessary that the motors on all the cars shall be under trains.5 amperes. all the heavy-currentswitching contactors located beneath the car. when cars are operated in safety. small be controller a used. S^ Coupler Ground Car " . This insures uniform openingof the caused by is used.and expense. . 316. " or a resistance. The solenoid of the mechanbrake becomes de-energized. Such a system is used on the electric locomotives of the Chicago. as the braking action when the armature is stationary. the armature acts as a generator sending current through the braking resistance and so is retarded. at of a motor the efiiciency 226. ceases Dynamic braking for a series motor is shown in Fig.) In (6). page 23. that the power is returned to the line rather than wasted in resistance. Milwaukee and St. which shows the holding or "ofif" position. The armature has a 316. Lowering Dynamic braking. 33. Paul Railroad. Prony Brake. resistance connected across its terminals through the brake solenoid and series field on one side. except Regenerativebraking is based on this same principle. Motor determine Testing " " It is often necessary to certain definite loads and .resultingin the brake being set. In (a). The brake is released.the motor is ical totallydisconnected from the line. across the line in series with (") Braking Fio. (See Fig.the brake solenoid and the series fieldare a connected resistance.348 DIRECT the line in series with CURRENTS Such braking is not effective for completelystoppingthe motor armature. ". the efficiencymay 349 MOTOR operation. pump. One typicalform is various forms. such as a for determining the power blower. generator. power given input delivered to etc. can the most in efficiency This Such brakes shown in length. etc. of making direct measurements about 50 hp.further. The Typical " stops band By and means of a a wooden hand of the proper arm wheel for of this hand sion applyingten- wheel the motor . knowing the motor be computed. 317. A knowledge of of in the as case of acceptance an power-measuring device taken by some machine.THE over frequently its entire range be necessary. the pump. 317. and a voltmeter. canvas to the brake brake.which generator. to in of It consists brake for any output will be the method common motors prony the output efficiency. be used may as a |BHfiWBMi. is to use a prony brake. Knowing the motor input.and also ammeter with an be measured can the motor test. Fig. band.a are up made Fig. Let F be the net force in pounds acting at a perpendiculardistance L feet from the center of the .consider Fig. same amount convert of water As a a the drum is considerable small amount of will keep the drum equation for the horsepower developed by such a brake. can There two are of the brake for brake band The arm. cannot reach in the open much exceed this.to prevent An arm. The are To determine the heat arm. oi this type cooled are into the hollow brake drum. the torque of the motor The balance the measures be determined.. By multiplying the net balance readingby the distance L. so determiningthe dead weight and is loosened the top of the is placed between pencil.318. requiredto into steam. due to the to read too of these two Fig. edge.-Work by developed a will prony brake. If this tating operation be repeated by rothe drum in the opposite the balance reading direction. can vibrations of the brake oil dash pot is advisable. 318. and stop In this read the case the brake the balance. plus the dead weight of the arm. a sort some fricsubstantially the dead weight of that the balance registers carriage. This acts the as a alone. friction of the balance causes high.350 CURRENTS DIRECT load be controlled. will be too low. prevents the drum developed in into steam. a moderate comparatively cool. due to the rotation pullon the arm of the drum. the drum temperature hot. becoming excessively water balance rect nearly the corvalue for the dead weight give of the Brakes The friction. water very from As the maximum can of heat units readings ordinarilyby pouring water This water utilized in converting the water number average temperature which air is 100" C. such of knife drum simplemethods and tionless as the brake fulcrum. arm and Another easier way is to turn the drum toward the balance by hand. 000 ^'^ 0. around arm the drum arm distance The work is the force F(2tL). whether the drum is and voltmeter Example. The speed of the motor " is found 26. horsepower = If /S is the revolutions per minute. the ammeter measuring the input read 34 amp.6 of this type.8 lb. First is pulledaround done in the drum revolution one times the distance The of the force F.480 watts. .= Obviously.4 - arm reads " 23. arm Therefore. In a brake test of a shunt motor.'output (6) Output Input = = X X 746 34 = = 26.p. 319. = -' 100 = 82.the of work amount same TS 0. should be kept approximately simple type of brake is the rope brake shown in Fig. means of this The F acts is 2tL. 220 volts. A rope is given a turn and a half around a drum and the The largerbalfree ends are each held by a springbalance.8 = = Efficiency17 In brakes X 2. 7.317 and 318. = 33. the brake level.-ft. (a) What weight of the arm at this particular (6) What is its efficiency dead is the output load? the balance and r. the 27r(FL)S Hp. 6. = 47.000 Therefore Hp.00019 (115) is done the brake on face sur- rotates or the stationaryand the arm is stationaryand the drum rotates.000 lierefore T. = is S revolutions done work by is stationary and that the through which the force revolution per that the drum assume 351 MOTOR F{2TrL)S. Ana. 910 X = 8. a of the motor? (o) Net reading of balance The on is found to be +2.23 hp.m.equation (115) appliesto brakes of the type shown in Figs.23 220 23. arm Ans.THE drum. Another two 2-ft. therefore 2irTS Hp.2 to lb.6 Ib.00019 8. but FL is the torque = 33..140 watts.4 lb.2 = 2 X 0.00019 = 33. be The 910 torque T Hp. brake 47. power It will be noted that in this particulartype of brake the horseis independent ot the diameter of the drum.1 per cent. 319. brake.400 = 2.352 DIRECT CURRENTS the end of the rope which is being pulleddownward by the rotation of the drum.2 lb. " The torque in Ib.4 - ^ 8. balance As Fi and F2 oppositedirections with respect to the rotation of the is Fi the net pullat the drum periphery Fj. 319. of the type shown in Fig.is (Fi-F2)R r= where R is the radius of the FiQ.2) 24. in diameter.. = (32. Fi 32.08 X 1. rope The brake 320.00019 X 10.p. TTie drum is 1. speed = horsepower does the motor develop? torque T The Fio. . horsepower Hp. what pulleyin fed.2 = X 6/12 = 10. " and Ft = Rope " In a 8.68. Example.m.400 r.-ft. Ana.4 lb. - 0. in pull drum. Let Fi be the reading of the larger is on ance and Fi that of the smaller balance.08 lb. If the motor is 10 in. " Jagabi Tachoscope. common 353 MOTOR counter the on directly zero. The simplerthan conical rubber a of the shaft. Measurement of machines is as The torque. Tachometers indicate the instantaneous There actuated checked tachometers. is a combination and stop watch.THE of 226. start eously. Speed however. where mechanical are by centrifugalaction. must $peed. most having counter a " rule much revolution counter. If this voltage is directlyproportional armature error . 320. The of speed Jagabi tachoscope. instrument are value of speed.the voltage induced in the magneto to the speed.321 (a). the actual speed reading before from that after the measurement. A littlepressiu-e. simultan- They also stop simultaneouslywhen the pressure on the made with this type of Measurements tachoscope is removed.Fig. free from personalerror. causes with magneto measurement the counter and stop watch and to voltmeter. so Therefore. been in service for some occasion having A simpleand convenient type of tachometer isthe combination of and a voltmeter. The spindle may counter be inserted in the counter-sink of the shaft without recording. as it is especially subject to time. a direct-current magneto In the magneto the flux is produced by permanent magnets and is constant. Volts (6) Speed-voltage curve of magneto. at each after This the indicator is type should be carefully of use.as shown in Fig. method Veeder The revolutions be found cannot of the measurement is to use type is are a of simple revolution a convenient sink counter- form of recorded be set to by subtractingthe speed the measurement tip which fitsinto the The As this counter counter. This plotis ordinarily a straight line through the origin.354 be measured DIRECT with CURRENTS voltmeter.The relation of speed by a constant be plottedas shown in Fig. as shown in Fig.the voltmeter readingmultiplied gives the speed directly.which makes termined one point accuratelydea It is convenient of the machine whose to attach the magneto to the shaft speed is being measured. It is usuallynecessary to thread a small stud into the end of the shaft whose speed is to be measured. by a pieceof rubber tubing. 321 (a). .321(6) and the speed to volts may read directlyfrom the plot. . = I. These currents represent an excessive . 323 (a). Series Field. the instrument may be injuredon opening the circuit by the rise of voltage due to the self-inductance of the armature. losses and The IRON a can be either high degree of precision LOSSES iron rotates in the same Eddy Currents. rents largecur" would shown be set up in the armature iron were it a solid mass as in Fig. depending on whether the machine long or short shunt.voltagesare also induced in this iron. Therefore. " as this is ^The series fieldloss is P. is the seriesfieldcurrent.^R. should be made limit the current Par. As the iron is a good conductor of electricity and the current paths are short and of largecross-section. Rt is the series field resistance. foregoinglosses are all copper measured directlyor calculated with from instrument readings.) in three average or flowing through The measurement four different positions value of resistance.the power lost in " the fieldis Pf = (117) Vis lost in the field rheostat This includes the power chargeableto the field circuit. (See with the armature in order to obtain an 118. As the armature magnetic fieldas the copper conductors.the voltmeter should be disconnected when the circuitis beingopened or closed and when the armature is being turned. ^The field takes a current 1/ at the terminal voltage V of the generator or motor.R" is the equivalentparallel diverter and the series field and 7. As the used in making low-readingscale of the voltmeter is ordinarily this measurement.356 DIRECT resistance R the CURRENTS is inserted to stationaryarmature. losses in the The the same way as are commutating polecircuitare determined in those of the series field.which may or may not be equal is to the armature current. Therefore. is the current of the series field plus that of the diverter. Shunt Field. (118) where I. diverter is If a series field shunt or resistance of this used. Laminating does not entirely eliminate these eddy current losses. By laminatingthe armature 323(6). to the direction of since they are parallel the magnetic flux. power OPERATION EFFICIENCY.as shown.500.000. This small section has the small section it happens to be under poleat When the section reaches position(6)its poleshave its ends.143)there results an of the hysteresis loss proportional to the area loop.LOSSES.324. (6) (") Fio. " Eddy currents in armature iron without with laminations. 323.p.^Itwas shown in Chapter VIII that when iron is carried through a cycleof magnetization(Par. " ^" = The "x(IS)'x(S)"-. As the loss varies as the square of the current (PR).the paths of these currents are broken up and their magnitude is reduced to a very low value.m. loss both varies as the square of the eddy current the speed and are the flux. The energy iron in an armature zation undergoesa similar cycUc change of magneti" when of the armature the armature iron at rotates.""'--- Hysteresis. Obviously.nearlyallthe armature a north a north and a south . iron in the manner indicated in Fig.000 lines per pole and the speed is 800 r.Fig. become reversed. These eddy currents proportionalto both the speed and the flux. eddy current loss in a certain machine is 600 watts when the total flux is 2.200r.they do not interpose reluctance in the magnetic circuit. when pole.p.000lines and the speed increased is the loss when the to 1. but it does reduce them It will be noted that although the laminations to a small value. and break up the eddy current paths. What flux isincreased to 2. Consider (a). could not be tolerated in loss which a 357 commercial machine.? Example.m. the pole face. 40. (SeeFig. Fig. A hysteresis function of the flux pulsations.by laminatingthe polefaces.) (^ " FRICTION These LOSSES brush bearing friction. to tufts in Pole-faceLoss. The flux enters and leaves the armature tufts through the teeth as has alreadybeen shown (page 29.These combined losses are some flux and of the speed. " as follows : . loss. 324.326.as shown in Fig. Therefore. losses consist of windage. and all are friction and SUMMARY The foregoinglosses may be summarized Copper losses: Armature Shunt la^Ra field 77/ Series field L^R.there results a hysteresis loss in the armature iron as the armature rotates.being in part due to eddy currents. As these tufts of flux pass across in the pole face. Chap.221.358 DIRECT CURRENTS iron is continuallygoing through similar cycles of magnetic reversals. Laminating the iron does not affectthe hysteresis page 183) Fio." -Reversal in armature of magnetic iron. loss also accompanies these results in a power loss. These pulsations "theyproduce flux pulsations This set up eddy currents in the poleface. flux Fia.6 power. functions of the speed. of the flux density. They are reduced. This loss is directly tional proporto the speed and is proportionalto the 1. II). " Pole-face loss due of flux from teeth. maximum by the Steinmetz formula. 325.(^uation 72. may Example. a mechanical torque is making the torque available at required to supply these losses. Iron losses (armature and poleface): function of flux and speed. " stray " power " The f lated. In distinction to the copper losses the stray power isallsupplied mechanically. Thus: nor so as " Eff. Friction losses (bearings. and not i generator these losses are suppliedby the prime mover by the generator itself.. In a the pulley less than that developed by the armature. the electricallosses are suppliedby the generator itself. followingways = (119) " output + losses Eff. losses can copper measured accurately iron and friction losses The calculated be readilymeasured can or can neither be so be calcu- ' accurately. function of the flux. 359 OPERATION EFFICIENCY. iJ^ILi????? = : (120) mput Therefore. Moreover. in a motor. speed be kept constant. the efficiency be found for any given input or output. For example. Efficiency. the power that they represent being called stray power. brushes.it will be constant in a given machine provided the flux and the Therefore. What Using equation (120) " ^" takes 40 amp.or speed.no matter what the load is. or both) since they are all some these losses are combined and are called stray losses. The efficiency? " -^ ^ . is the motor (220 X 40) - 1. A shunt motor losses are 1.800 at 220 volts.800watts.LOSSES.if the losses in a machine be known. ' does not change unless either the flux or the the stray power speed changes.' separate losses. On the other hand. is the ratio of 229. total motor .The efficiency of a machine output to input. 2HtP^ = input also be written in either of the This may -2Ht2Ht - Eff.windage) function of speed. Eddy current HyBteresis function of flux and speed. As stray power is a function of the speed and the flux only. per of efficiency The determined from a motor simultaneous of its input and as in Par. was Theoretically. In the direct measurement of efficiency the power necessary for the test must be equal to the rating of the machine.75 per cent. where a used. its FiQ. but may Torsion factory unsatisthey are be suspended in a '* shown in Fig. . The ends of the generator as cradle.82 per cent. 326. Efficiencies of Motors of electrical apparatus is high as a rule.equation (119) is ordinarilyused in eflSciency and equation (120) for used for generators (output is electrical) motors (inputis electrical). For instance.is not readilyadaptable to all generators and necesthe generator shafts' protrudingbeyond both generator bearings.the efficiencyof generator similar be determined may by manner a in measurements a of input and output.and of 94 machine may have an efficiency As electrical units rather than " cent.'' shaft are supported in bearings.so that the frame is free to The turn. of about 65 per cent.a 1-hp. The of the dynamometers as a torque have rule. Such cradle is a necessary sitates expensive. The output with an ammeter is readilymeasured The input. a 10-hp. in ment measure- Ues difficulty transmitted been difficult to to devised generator the the. " Cradle dynamometer.generator. The efficiency and Generators. The measure. a 5-hp. howand a voltmeter. In addition to supplying this power there must be means for ab- in the .326.88 or 89 per cent.360 CURRENTS DIRECT mechanical quantities are determinations. shown was brake prony be may urements meas- its output 225. In any direct measurement of efficiency percentage error any measurement of either output or input introduces the same percentage error into the efficiency. 230. a 20-hp.. . motor has an efficiency A 500-kw. torque is determined by measuring the torque to prevent the frame's turning. is Very ever. the speed in of the flux and duplicate. 327.000 94 195.ma =(YIa)- field is is: S. + la^a + S. sorbingit.002 1.360 watts 0.some is the stray power. motor a in of stray dynamo. mainder re- Therefore (121) .800 watts 184. 230 the generator Output = field current at this load? efficiency 230 800 X = Sh. the output f The rheostat.supplying and absorbing if not quiteimpossible. OPERATION EFFICIENCY.LOSSES. field loss = 230 Armature = 820" X 820^ X loss Ser. The generator is connected long shunt.500 watts = power = = = Total loss E"F.340 watts 2. I.000 + 11.000 watts. Via + VI S. is run (without load) as a motor. This is not a serious matter but when large machines are tested.= 11. 230-volt is d. The resistance is is 20 amp. armature 0.600 watts 0. 20 4. " 250-kw.c. this load is 2.005 3. a a connected The This the line in series with across total power power in input to the machine is distributed the field loss. as shown or 327.800 = 184. stray measure order the power. Fig.500 watts. .000 184.P. field loss Stray = X 184. order to duplicate the stray loss. generator 800 delivering amp. whether to value of 0. 361 with small machines. What is at The volts. merely to It is necessary " motor a or a generator in = force E obtain the proper To in machine. per cent.P. Measurement = Stray Power. = VI armature J goes to supply la^Ra loss and the beingzero.002 ohm.005 ohm The stray power at and the series field resistance is 0.. As the speed from power equation (111) is S KE/it"y it is onlynecessary to duplicate the speed's and motive the electro- Ana.P. power may Because of the foregoingreasons. follows: Some as suppliesthe a Fig. the necessary be difficult. it is often desirable and even to obtain the efficiency by determining the losses. necessary A Exam'ple. it be " Determination power Ught generator.800 231. the stray power will When is running the machine in both cases.the induced emf. It is desired to determine the value of its stray power under these 110 conditions.2 = follows as R ture arma- The is first adjusted that Vi = drop at this load beingnegligible.000 these (107 X 0. is stray power minus this CURRENTS DIRECT that the armature = 0. amp. ^ an motor. 116 = 7 " X 5 = - 5 amp. adjustments of E and is IAmi R S. nected con- A rheostat R % Fig.000 r. = Arts.p.p. for stray power rheostat measurement. Therefore. the generator run as -|fc_J-A/VWW shown as 328. from The stray power.75 - 574 watts. in this la^Ra is negligible instance. The fieldrheostat is then adjustedto give a speed of 1.2 the small volts. armature /" current S.000 r.na. and ture is the stray power loss of the machine at What of flux and value particular armature input to the field current The resistance is 0.m. - that the above Assume 100 amperes generator is delivering at The field current volts at 1. armature " Googk .P. If the full-load electromotive the lightas same a When is readilymeasure the stray power d carryingthe above load. The the total to generator when shunt A " equal resistance loss. the armature Example.the stray power as it did under the two cases and is equal to VJa la^Ra^ 113. is 7 amperes. value of speed and flux The machine is now operatingat the same is the same in load.volt mains. (5)*0. motor ^ S To cated speed S be dupli- the generator is running light. and are nected con- i the terminals.03 ohm. : volts 113.362 The 115.03 675 It will be observed takes motor a 12 speed? 12 = running lightas the armais 7 amp.p. a 1 z ammeter Fig. when be force E and make = 110 + = 1.03) r. so a is connected across directly Connections the circuit and voltmeter " in directlyin armature 328.m. . the run 400 600 300 the over field current be may may held at a probableworking then be adjusted repeated. 230-volt of Fig. load.8 + 1.5 amp.8 amp.3 amp. FiQ.p. M. The Determine 1. the maximum Curves value. 329 are manner. the respectivevalues of field current The speed is constant / = 43. 329. At least three values 700 600 800 900 1000 1100 1200 1800 R.) is In a stray-power definite value range The of the machine. value and another to speed varied the and 2D0 100 the field current run.244. P.5/2 = 21.m.6 230 X 1.even page 273.000 r. were its armature a in each same 1. Fig. ''peaks"under load so increased.8 amp.5 and At half 'and the minimum is likely to operate and similar to those shown in an mediate inter- Fig. obtained from a 10-kw. power be used. 329 were justdescribed.3)20.the generator being run as a motor curves obtained. generator by " when these 43. of field current value under should which in this Example. = 76 watts (23.5 at 1. The rated current is generator at half load and at rated load.14 ohm.the case.14 = = = 345 watts . obtained Typical stray " f = = 21. la la^Ra VI of this machine resistance is 0. 23. its efficiency as voltage being the being the machine the method curves and curves.364 CURRENTS DIRECT that the loss for any value of total flux (See though the average flux be the same. ma- in '"^ .356=^'-^P^^^^^*^ It is also possibleto determine the stray power of a machine of a smaller machine whose by drivingit without load by means In using this method is known. 43. ordinate. two-thirds the distance from II (= 1. I curve to curve 230 ^" X 45- ^^' 264 - 368 - 225 9. 1. is found to be 1. 230 j. ^ .3)^0.p. = = 230 21.000 21. suppliesonly the losses of the two connections for making such a test are Shown the line chines. - "^ ^^^- ^^'^^'' ^"^*- = ^ of this machine efficiency the when the at 230 volts from r.m.330.m.8 amp. the stray power is found to be 225 watts.490 = 230-X45 ^.4 amp. 233.m.329.ni." when The foregoingstray-power method of machine the losses are is not under load when the field circuit is objectionto the measuring losses is that the beingmeasured.14 230 X 1.Fig. these conditions the field current at 900 motor /a = la^Ra VI f = = 45 1.8 X ^ ^^ Eff. 329.one-third distance from the stray power 1.6 264 watts = = 368 watts On the 900 r. ^ cent. on 1. be determined their losses may when both machines are loaded." ^^- 230 = III.8 (45.and yet The Fig. LOSSES. The efficiency at this load is: 230 5. Under .3 amp.5 X = 10.000 r. amp.650 At rated load. = is found watts. curve II to to be 330 X 1. ordinate.6 - 43.4)20.6 amp. 5.14 = VI f + as a line. it is possibleto sepaefficiency rate the friction and windage losses from the core loss by measuring the power delivered to the machine closed and again when it is opened. the stray power is found the on II curve ( 365 OPERATION EFFICIENCY. Prom I to curve one-third 1.5 la = 43. so their values may able.6 amp.. = (43.8 X 76 + 345 + 88. Fig.p.5 X 414 +287+ -h 330 that it is desired to determine Assume running 287 watts 414 watts.p.8 the ordinate. OpposdtionTest" Kapp Method.5 la^Ra In Fig. and taking 45 amp.).). == = the 1.000 r.000 UfiSO = 230 43.329. ^^Io. If two similar machines are availbe in error.5 =* the distance from to be 230 watts.corresponding to curve 45.p. / = 43.6 per ^ = 230 + ^ Ans. owing to the losses in the machines. The total input to the two armatures is VI that . Let El induced equal the motor induced volts and volts. are startingbox. Five ammeters used. This power is distributed Motor Ri and R2 are Ii^Ri = loss armature = h^Ri stray power Generator where loss armature Generator Motor follows: as stray power the motor and generator armature ances. because it requiresthe higher internal voltage. The are to the in each one so similar machines two are CURRENTS 330. supplies trical supplieselec- motor generator. as stray power increases with increase of flux. This in turn to the motor. " fields Kapp opposition method operation of the mechanical is less than by the ammeter for determining follows: The as The delivered power supplyingthe directlyto the line Ai.366 DIRECT The and have coupled togethermechanically then connected The motor should line.the power total stray-power loss may in be divided between the two machines proportionto their induced voltages. two Therefore. losses.its stray will be greater than that of the motor.this deficit must be made up by the line which suppliesthe current 7. a circuit and armature The armatures. Ei = E2==V V - + IiRi hR2 E2 the generator .as shown. power is set to the power connected are indicated not are in the line one by the generator requiredby the motor. one in each field. resist- As the generator field is necessarily stronger than that of the motor. two that their currents Fig. As a close approximation. The assumptions made in regard to the stray power distribution may be slightly in error. be determined. That is: Pi + P2 The field losses = V7 WR^ - by directly mea^red are h^Ri - the anuneter in each field circuit. at 120 volts.5-hp. suppliedby power 120-voit. current the and = 390 watts = 243 watt^ = 633 watts.the line need supply only the losses.Care should be taken that the correct polarityis observed. li is 45 under P = amp.the total Tstraypower (Pi + P2) remains. 330. Let Pi and P2 be the values of stray power Then: k-k total The input machines the two to "'^'' goes to supply their because the output of the sysand stray-power losses. just as generators are connected in parallel.12 Total in the is 0. in the two machines.. speedare of .367 OPERATION EFFICIENCY. tem tracting and the field power is suppliedseparately. may similar The principaldisadvantage is that it requirestwo machines.12 46^ X 0. The machines are brought into operationby firststartingthe motor with the startingbox. the line is Find the stray power the line 12 connected resistance of each / of 12 amp. By sub- armature is zero losses from the the armature input. Under 120 X are these conditions = I^^R. = li^Ri = 1.12 ohm. The generator voltage is then made terminal voltage and the generator equal to the motor terminals are then connected directly the motor across terminals.440 watts 57 2^ 0. these conditions of load. adjusted that the motor current machine obtained. is that each machine are advantages of this method the regulationof each machine operatingimder load conditions. The generator field until the is then strengthened and the motor field weakened The desired conditions of load and " manner The in shown fields are so generator current supplying a each The similar Two Example. LOSSES.7. /i is 57 amp. motors The armature Fig. (Commutation may at times limit the output of direct-current machines.Ordinarily. = stray power 1100 ^""" The 125.2 + Knowing the stray readilycalculated. E. watts. 113. Practically it be steam whether engines.2+125.2 volts = 125. easily. Electrical apparatus is usuallyrated at the load which it can safelycarry without overheating. they can carry at least 100 per cent. 0.determines the rating of various power 234. It is interesting can sider safelyor elBiciently what. has definite power ratings. insulatingvarnishes. Both a the load steam engine and for which types of prime a steam turbine their efficiency is mover can carry a a are usuallyrated maximum. E. These high overload at two without load difficulty.368 CURRENTS DIRECT Total stray power El E2 The motor = 1. and the fieldconductors.4 807 =424 " and power. the the armature efficiency all power apparatus. Ratings and Heating.12) 0.gas engines or dynamos.which is near the point to operate. Owing to their excessive weights and costs. The A.12) 113.) If the temperature of electrical apparatus becomes the cotton insulation upon the armature high.4 volts. I. overbut at reduced efficiency.become This may result ultimatelyin grounds and shOTt-circuits within Rules specify the machine. " devices. Their thermal at which efficiencyis they cease so much ordinarily greater than that of the steam engineor tiu-bine that the questionof weight is more important than the question of efficiency.4 generator stray power ^'' is ""^"^^'^^^113. and fieldlosses. largegas engines are usually rated as high as possible. in general. Standardization and the safe temperature limits as follows: .440 = 120 = 120 633 - (57 - X X (45] + = 807 watts. These ratingsare determined by the manufacturer and are supposed to givethe power which the apparatus to condeliver. too carbonized and brittle. 48. imtreated 95" C. 125" C. prin- idea of the average a winding may temperature be obtained.to be able to test a machine in order to determine whether it is operatingwithin safe temperature limits. this By utilizing ductors con- ciple. desirable to plot a curve of temperature . therefore.00378 an generators should accurate test of their be run = a 0. No etc important. The be measured temperature at the surface of the winding may bulb againstthe surface and by placinga thermometer It has been found that coveringit with a small pad of cotton. be made.at points that the highest temperatures are which are not easilyaccessible. The difficulty in making such tests lies in the fact within the coils. For example.silk. the increase of degree rise is 1/264. asbestos (C) Pure mica. constant from temperature Ans.00378. paper.4 C. (A) Cotton. added to this reading will give an approximate value of It is very the hot spot temperature. (B) Mica. page 43. temperature of 30" C. To get an idea as to how close a machine is to its ultimate temit is often 1 See Par. The increase of resistance per degree rise of temperature be obtained from the formula 1/(234. EFFICIENCY.5 With " or an ambient = temperature 0. ture. accelerated by running overload for an hour or so and then dropping back to rated load.077 = " r^rj long time requiredto reach and is its What ^ fractional change in resistance is The ohms.LOSSES.5 + 0/ where may within an t is the at surrounding ambient an resistance per Example.077/0. quartz. the heating is often long time is usuallyprohibitive. of 30" C. the resistance of the a generator increases lProm 104 temi)erature rise? shimt field of Temperature Owing to the motors in order that such rise = 0. By this procedurea very good idea of the As a ultimate temperature may often be obtained in a run of 2 or 3 hours. 112 to 20". or room ambient temperature. perature. allimpregnated. 15" C. tempera- 6 to 18 may hours. It has already been shown changes with that the resistance of copper the temperature. limits specified.enameled Above 369 OPERATION wire 105" C. The highesttemperature within the machine is called the "hot spot" temperature. measurement. 331.the voltmeter leads must be held on the commutator in Fig. Thus in Fig.332 (6). the field coils sUght differenise of temperature between of heat is given and the room. but to determine the change of resistance in the armature due to change of temperature. . This insures the same same conducting path for each measurement. Hour* 331 the Fig. At the beginning of the test.370 CURRENTS DIRECT of this type for a shunt typicalcurve in Fig. as shown in should be marked and 332 (a). the division of multi-polararmature in the various paths is determined in part by the brush resistance. When current contact a to The is so measured. the current from brush a brush h is 7i and total current that from brush entering the brush a a to brush is their sum. Moreover. meapath through the copper be the same To exclude all resistance except that of the copper. for a dynamo. less rapidly. but a the difference between As the coil temperature temperature conitant Tempcratare^^ and the room and increases.there is during the rise field is shown A test. the coils is heat developed m the heat dissipatedby the coils and the coils have to reached of curve rise ^ "^ i equal This the time increases. c / is Jj. it is essential coppery be taken in Care must the that and that of the copper alone be measured in every surement. becomes curve the total practicallyhorizontal. Therefore.but a small amount out by the coils and as a result the temperature rises rapidly. as is illustrated by the FiQ. amp. -Curve with When 331. rate constant a temperature. for other resistance when measuring the armature determining temperature rise. segments inside the brushes. resistance the current the brush and contact resistances be included not must in the Therefore. The object of this meaaurement is not to determine the resistance with the idea of calculating the loss. Therefore.the rises morc givcn out " ^ y^ increase becomes of temperature / less of temperature time. Similar curves " i """ would " hold parts of the machine. these segments the under subsequent measurement they should be directly every brushes.more hcat is by thc and the temperature coils. Therefore. . 333. 1 deUvers/i amperes and generator No. generator No. Amperes Fig. 236. are added. 334. volts above are volts terminal 6000 pressure. their be the same. This keeps of service to load on the units loaded up to their rated ciency capacitywhich increases the effi- operation. are in parallel.for a common terminal voltage. because of their drooping characteristic. coil sides between CURRENTS If the between or located thermo-couplesare coil sides and core in a i2-layer added. The station load may stalled inthe (e) exceed singleavailable unit. 333 are the capacity of shown any shunt generators which will be 2 respectively. for if a unit is disabled the entire power supply is not cut be conoflf. reUable than a single large (a) Several small unitfe are more unit.It wiU be noted the characteristics of two designated as No.372 DIRECT temperatures at any time. Shunt generators. That is. Therefore. generator No. The hottest spot is the highestvalue by either method after corrections have been applied. for every winding 5" C. In Fig.Fig. be . that some Assume condition arises which temporarily causes that . 2 delivers h amperes. terminal voltagesmust neglectingany very small voltagedrop in the connecting leads. " Characteristics generators shunt of -several in the station. and 1" C. drooping characteristic. Parallel Rmming In most of Shunt Generators. (6) The units may nected " in service and taken out correspondwith the the station. are well suited for parallel particularly operation. Fig.the machine with the more drooping characteristic carries the smaller load. (c) Units be repairedmore readily if of may there 333. 1 has the more .Vi.(d) Additional units may to correspond with growth of station load. If the two generators are connected in parallel. xx"wer plantsit is necessary and desirable that the power be supplied by several small units rather than by a singlelargeunit. 1 and No. if the thermo-couples are tween placed becoil sides and core coil sides and wedge in a between or 1000 single-layer winding 10" C. Therefore. is sufficient for all the machines. its share of the load. 1 is supplying 2 in service. system if any carry are The shown such the system occurs. each of the increase or decrease of load. . 2 or tial poten- selective switches. or it might be occasioned by change of load on No. that No.334. generator No. Generator ate its characteristic. This results at some in a point a on drop in its terminal voltage. Therefore. 1 to take than more 373 OPERATION EFFICIENCY.LOSSES.Moreover. 1 would immediately tend to operthe system.which tends to make it take less load. machine are operatingshunt generators in parallel Each individual machines bus on for Fig. 2 is started and No. This might arise from a temporary increase in the speed of its prime mover. any tendency of one machine to take more than its share of the load results in a change of voltagewhich this tendency. must ammeter. in stable change of load some for the paralleloperation of shunt Connections be said to be may A " connectors of service and It is desired to put No. to as generators. mover generator should have its own of No. can 2 is out to the voltmeter be connected through suitable plug that No. 3^.shunt generators in parallel opposes condition Bw-bMB Double Trip C C Pole ^^'^^^^ Breaker BbeoBtat Fia. is or The brought up The to prime speed. The reactions of the hold the generators in parallel. common Assume equilibrium. connections in voltmeter all the load. . clearingthe to the prime mover will be delivered one to Compound and then in parallel.that voltage drop from no load to fullload. is strengthened until the load of the first machine a voltage It may be necessary to 1 simultaneouslyin order to maintain the the field of No.their characteristics should be similar.which condition may be determined by Its field is then the voltmeter. No. shows two over-compounded generators connected to the buspositiveand negative terminals being properly connected as regards polarity. Each generator is taking its proper share " of the load. generator be weakened this generator. service in this from and 335. that if shunt generators are to divide the load properly at all points. its induced voltage is just however.as equal to the bus-bar voltage and no current potential. too will much.374 DIRECT CURRENTS adjusted so that its voltage is just equal to that of the bus-bars. are Under that of the bus-bars takes generator bus-bar voltageconstant. run as current a motor mover. Parallel Running of Compound Fig. it is not taking any load. breaker The is connected 2 to switch and the system. these conditions.the field of No. 335 bars. must that it may be deUver strengthenedxmtil the out of its fieldis weakened and that service.each should have the same Generators. take 2 is will flow between its share of the load. current. machine is The zero. 236. Its induced points at the same greater than closed and now of the other machine -^^Bng FiQ. which tend to drive its prime It is evident generators breaker manner or If the field of " Connecting in and removing machine. weaken To in order Therefore. machine disturbance system. is. the switch shocks prevent any to the are or a opened. Assume that for increased load. driving No. 1 will be a motor. On the other hand. which shows the machines. reason in its series current strengthensits field and force thus causingit to take still load. 2 as and ultimately the breaker of at least one of the Amperes ^"' ^^^' " Characteristics of compound in .Assume a slightly increased load.336. LOSSES.l " the system load is assumed to be fixed. 2 will at as of its drop some load. 1 takes then tend to rise to that the machine . generator No. more which a winding slightly must crease. In a a quent conse- dropping of its short very time No. in- raises its electromotive No. which for two compound parallel. " to the are operatingat Typical connections a Fig. 337. This condition is again illustrated by machines individual characteristics of the two the machines Fig. respectivecurrents /i and Iz. This increased voltage means generators that corresponds operating in that No. Its voltage will some point a. some The 375 OPERATION EFFICIENCY. Assume voltage Fi. 1 takes generator No.resultingin a weakening the time same of its series field and further load. generators will open.parallel. This connection. It is not always possible teristics to adjustcompound generator characof series field diverters so that they divide the by means load properly. . stable compound generators may be considered to be in unequilibrium. + 1 but more than its proper will pass also.337. by connectingthe two series fields in parallel.any action tending to throw the machines out of equilibrium is accentuated by the resulting These reactions. 337.376 CURRENTS DIRECT takes stillmore and current the efifectwill continue until ultimately the breaker opens. 337 ties the two negative brushes together. equalizer. " Compound generators requiring two equalizers. 338. of it will pass through the fieldof generator No. Its operationis as follows: The machines Assmne share may be made stable that generator No. some and Therefore.by only not of the means BaB -^Jqaa^i"^^ Series Field Fia.is a conductor of low resistance and is called the equalizer.the followingconditions must be satisfied: must (a) The percentage regulationof each armature maintain the no load be the same. That is. To to 1 is unable to take the entire load.that the seriesfieldof generator . 1 starts to take of the load. This increased current through the field of generator No. Suppose Fig. (b) The series field resistances must be inverselyproportional to the machine ratings. 2. Fig. proportionatedivision of load from full load.which in Fig.both machines are afifectedin a similar manner No. If the equalizer this diverter shunts the series fieldof genenegUgibleresistance. compound generator with a singleseries field usuallyhas a as shown 3-poleswitch. and electric circuits motors in generalrequireprotectionfrom short-circuits and overloads. fore. due to the fact that may some If it is connected indicate the generator not of the generator current be passingthrough the equalizer. Two the short-circuit current. 338.LOSSES. cost and . Compound generators are put in service and may in service in the same is adjustedand manner as shunt taken out of generators. If a 3-wire generator (see page 394) having two series fields is to be connected. after being blown siderable (unlessit is of the refillable type) and coninconvenience often results from not having spare fuses at hand.a 4-poleswitch is necessary as there are two equaUzers. 337. 377 OPERATION EFFICIENCY.one blade of which connects the equalizer. The fuse has a much lower first On the other hand. The sudden load imposed by a short-circuit may injure the generator or its prime mover. However.) The load ammeter in a compound generator should always be connected between A the armature terminal the series field and the circuit. the bus-bars. Therefore. it is worthless occupiesless space. it is constant at all loads. 1 is shunted of the series fields. The proper load adjustments of a very low resistance in series with be made by means may * No.the fuse and the shifted circuit breaker. by means 237. The circuit breaker has a higherfirstcost and requires On the other hand. in Fig. rator No. it operates an indefinitely more great space. ammeter current. Thereespecially it is desirable that generators operating in parallelhave similar characteristics. 2 as well as that of No. and bus-bar have by a diverter. one It should either shunt obtained that the desired division of load among be compound generators at any one load may be noted or by adjusting their field rheostats. usuallydesirable that this division remain if an operator is not in continuous attendance.--"jrenerators.resulting common devices are used for opening short-circuits and overloads. 1.the load of the shunt field rheostat. Wires may overheat under in fire hazard. (See Fig.that is.the diverter merely drops the characteristic of the entire system but does not afifectthe division of load. Circtiit Breakers. " " ^Two CURRENTS pole. . 340.2000-ampere circuit breaker (Condi t). Fig. 339. circuit breaker 6000-ampere.378 DIRECT Fia. electrically-operated (Gondii). . XIV CHAPTER TRANSMISSION 238. stations generate power and current DISTRIBUTION AND used in this country. economically transmitted voltages. direct congested districts effects. FiQ. 204). large scale a ing alternat- as as alternatingcurrent. power ordinarily utilized at volts).but it cannot only advantages under and Typical " 600 distributed Its 341.which are with current is that 341 and large cities. of the absence present Fig. and Another distance for commercial most be reserve can method of power be of direct of are eddy current readily utilized. is Power (110. In fact. Power 380 voltages economically transmitted these conditions also the absence advantage be can low comparatively these at system. 220. The modern raised and lowered efficiently be may of transformers. a storage shows is generated battery the at the general power . but is power is required to transmit less copper high voltages. in transmitting the Thmy The by transmit does system means power as power is not high voltage (see Par. of inductive alternating losses in the cables. to any current considerable use in the capacitive current. distribution. at on POWER OF Under " using alternatingcurrent for reason Systems. Power Distribution central most that the transmit voltage this power Much direct current at conditions. Assume The that the current to V^.the voltagebeing transformed to power These systems are discussed 550 volts. the loss . more fullyin Chap. the transmission voltage is seldom less than 6. 3-phase.) The sub-station receives the in large amounts and distributes it to the various consumers power in smaller quantities. the distance and the loss are fixed. alternating-current power being transformed near the consumer's premises to a 230-115volt 3-wire system.300-voltalternating-current Une suppliesa factory. transmitted. Vol. the power. a 2. II. XII.by transformers. a 3-phase 2. supplying a trolleywith 600 volts direct current. Voltage and Weight of Conductor.600 volts)." rA6 weightof conwhen the power ductor varies inversely as the square of the voUage.300-volt the voltage circuit supplies for lighting. The current "-k The power loss Pi = Ii^Ri voltageis raised and the distance remaining fixed. and current /i over 239. Let it be requiredto transmit the power P at the voltage Vi wires having a resistance Ri.TRANSMISSION AND DISTRIBUTION OF 381 POWER current at high voltageto station.000volts is shown. At the sub-station it is either to 2. the sub-station (Fig.It bears the same relation to the power system as the middleman or retailer does to an industrial system.is transmitted as alternating the sub-station (66.300 volts alternating current transformed by transformers to 600 volts or 230 volts direct current or by motor-generator shows 341 sets or synchronous converters. at 110 volts (") Repeat for 220 volts. 50 kw. (o) What is the power loss? over a 400.000 " 10-8 X X 400.. are delivered at a distance of 500 feeder. able (b) The voltagedrop to the load must be kept within reasonwhen limits. the loss and the distance are fixed.000 50.when the power. . transmitting by direct current. Tables of the permissible ciurrent-carrying capacity of wires are given in the Appendix.000 = "f^ CM. a 100. feeder. This is particularly important with inside wiring where fire risk exists.with the of Conductors. four factors must or distributing be considered in determining the size of conductor. = The loss is ' ^'^^ (lis) ^ ^'^^^ ^***"' ^'^' loss in (6)is one-fourth that in (a).000CM. (see Par.150 watts.000 CM. Let the weight of copper in the two cases be W\ and 1^2.the conductor resistance varies directly the weight of a conductor of the voltage. 240. This is particularly incandescent important lamps constitute the load. " ft. Exam-pie. power the Size same distance.382 CURRENTS DIRECT as the square is. 69) the loss would be 454. (a) The wires must be able to carry the required current without overheating. (a) The current J /i If the Cable had 454.the weight of the copper is quartered. 5.. the voUa^e. . the the the transmit feeder in one-fourth of would having just weight (a). 454 = amp. If the voltageof a system is doubled.other conditions being the same.000 ^ (454\1. page 410. Therefore. (5)/2-^^227amp. That the square the condudor weightvaries inversely as of Therefore. The same power. But the volume or of givenlengthvaries inverselyas the resistance. " In same loss.000 = 1 X Ans. respectively. the minimum are of copper for a givenvoltage drop is obtained when the amount mains are uniformlytapered. DISTRIBUTION Voltage. 1. Distributed used at the Loads.200. these highervoltagesbeing for trunk line electrification. This occurs short and the voltagedrop is small. POTENTIAL (a).) The conductors may be of uniform cross-section throughout where the mains their entire length. but in view of the considerations stated in CONSTANT 241. Inthe size of conductor means higher investment costs less energy loss in transmission. not for municipal traction. even 3. Thereby an increase in the requiredweight of copper. because itis not trolley distribution.as is generallythe case with be distributed uniformly or non-uniform ly feeders. be concentrated at one or two . " The load on a feeder or main may points. 342(a). 110-115 volts has been standardized for Ughting and for domestic use as being the most desirable when all factors are taken for Distribution " Six hundred into consideration.(6)and (c).and trolleyin railwayelectrification.2.342.G. to use wires smaller than No. or may along the conductors. (SeeFig.An lower voltagethan this would be desirable from the standpoint even of the filament. That size of conductor should be chosen which makes the cost of the energy loss plusthe be modified This* may interest on the investment a minimum.W.342(6).000 volts volts is are 242.Fig.TRANSMISSION DISTRIBUTION AND POWER OF 383 (c) The wires must be of sufficientmechanical strength. It is not so high as to be dangerous to persons. creasing (d) The economics of the problem must be considered. About 110 volts has been found to be the most convenient voltage for incandescent Ughting.but a lower voltage would be accompanied fore. This is important when the wires are strung on poles. It is not advisable for pole Unes.400. Incandescent of 110 volts become so lamp filaments for voltages in excess long and of so small a cross-section that they are fragile.Fig. difficultiesand it saves systems of lower voltage. so commonly high as to used giveoperating considerable copper as compared with At the present time. 8 A. are Where the mains of considerable length. as when lamp loads are located at various pointsalong mains. " Copper cross-section Copper Conductor Cross-section of distributing system or of mains. the loads in the manner spiralsystem.followed by another uniform conductor of lesser crossmember section. This system allows all the lamps to operate at nearly the same voltageand yet the voltagedrop in the feeding wires be large. cross-section is run for part of the a distance. assume conductor. A good rule to reis that the current densityin each section should be the For example. as in theaters and auditoriums. Systems of " .342(c). the second secCM. carrying200 amperes. ^In order to keep a number lamps at the same voltagewithout excessive copper. to arrange 243.000 same. 342. a Ordinarily4/0 wire would conductor. = 190. This objectionis often overcome by arranging called the open shown in Fig. The two feeding wires are connected to oppositeends of the load. CM.384 DIRECT CURRENTS As it is impracticable to have a conductor of constant a uniformlytaperingconductor.it is often possible the lamps in this way.000 be used for this second section. the firstsection may consist of a 250. the return loop or anti-parallel system shown in Fig. 343(a) is often used. 343 (fe). may The objectionto the return loop system is the extra lengthof wire required.and so on. (a) Uniform Copper Section QOOOOQO^ (6) Tapered (c)Varying Fig. as shown in Fig. of Feeding. 150 tion carries 150 amperes. it should be 000 ^7)^*250. Where large groups of lamps are switched off and on at the same time. open VMdiag {d) Open its Return Loop (c) Spiral System Fig. can EDISON THE 246. " Fig.TRANSMISSION The DISTRIBUTION AND be closed spiralmay closed loop system of Fig. a by running a third wire. Also.343(c). the system be operated at 220 volts. " Systems Series-Parallel the g Anti-Parallel or 385 POWER ends. " be eliminated the two between lamps 26 at 3-WIRE SYSTEM sjrstem objectionsto the series-parallel called neiUral. resultingin 0006660 Point (6 ) at OF System Closed Loop of feeding. both of the lamps in series must be of the same lamps . the lamp to which it is connected ceases rating. This approximately 110 volts. The copper section will then be may one-fourth that requiredfor straight110-volt distribution. " Series-parallelsystem.as shown in Fig. burns out. The that obvious disadvantages of the series-parallel system are 244. The outer wires. 343. may Advantages. Doubling the voltage of a system results in the weight of requiredcopper being reduced to its initial value. 344. neutral The all the maintains advantage of a higher . only be switched in groups of two and if one lamp to operate. System. If 110-volt lamps be arranged so one-fourth that two are always in series. 344. In per cent. is copper greater than 623^ even cent. 345.current tends to positivewith respect to B. y. S A to of the loads Each same. flow from the load a on and h " 6 (o) takes and *.the outer total copper for the Edison system is ^ or 373^ per cent. amperes. amperes taken by load a through to load h and then back through wire B to the source. Ampr" Amp-" 5 10 " Amp. 3-wire system loads. Fig. third negative. Fig. Under these conditions the current in the neutral wire is zero and the loads are said to be balanced. 345 shows the conditions which each being the positive be must 220 between is maintained N volts from 110 and B have " 10 sl 10 Amp. per general plan of the system is shown in Fig. Amp. Therefore the saving in is copper 62)^ the neutral practice. " Edison balanced the B difference of wires.the 220-volt of an equivalent the copper that the neutral of the Edison cross-section same is obtained copper the two as wires. " The Unbalanced 10 3-wire systems. a 110 Amp.10 ^mp. A of potential N Therefore volts maintained them. 346 (a) shows the conditions existingwhen the load the positive side of the system is 10 amperes. If it be assumed system is of the neutral no by the use wire. This is equivalentto a series-parallel system as both loads are equal and are in series. that for a 110-volt system of the same kilowatt capacity. IsAmp. Fig. at of the other two each negative with respect That is. smaller than the be made can wires outer two the that so . 10 wires A Two FlQ. A to Nj and from iV to B. If there were system would require one-fourth of 1 10-volt system. The " Amp. and 345.386 DIRECT CURRENTS voltagein reducing the weight of this system. iio| N saving in 1=0 y ) Amp. (b) 346. and the load a on h on . A wire side of the system is the 10 Amp 5 ^ 110 " exist when Amp. . 2 ohm.2 n amp.1 eo amp. = load 222 across Vi ^"'P- load Ri across Vi ^ ^'^ = = 13. IKOY. " f loads are e = 60 X 0.17 X 88. VoltageUnbalancing. This For that the resistance of the assumes the above the neutral reason of the 3-wire system is rarely sees circuit breakers in the neutral wire of power plants.1 ohm resistance of 0.75 9. 0. The voltageon the two sides of a become 3-wire system may if the considerably unbalanced loads on the two sides of the system become unequal. equal. "90 amp. io"r. In 348.60 X = 132 volts. the two having balanced and the generator voltage is wires.60 = 9.0 volts.resulting in a material decrease of candlepower.1 =6. iy ". that the largerbank of lamps is operatingat a much reduced voltage. 0. 349.the voltagedrop per wire for the outers is As the two wire.which would result in the lamps burning out in a short time.V.0 volts.however. It will be observed.348 (a) a load of system. Each neutral has 220 volts a across a 3-wire 60 amperes wire has outer system a outer exists on The loads. lip V" r i fOT r amp. (b) (a) Fig.388 DIRECT is now There 220 volts CURRENTS loads in these two across so that series. I-O 11 ov. 246. usuallygrounded and one " Q 0. .and that the smaller bank is operatingconsiderablyabove rated voltage. each side of the resistance of 0. " CO 104 v. the current 220 ^J voltage Vi The ^ voltageV2 The 2"2:92 9.there is no current in the neutral Therefore. as shown in Fig.1 I6. = lamp filaments does not change. ^ 0 " ^ 00 lioV. Voltage drop in Fig. The 100 110 V. 100 amperes the other side. is 0.1 2 volts. This Fig. Fio.e_20a (") 349. 349. Under these conditions.2 n. . Ans.1 n . drop in the positivewire The ei 100 = 0.as it carries no current. = negativeload 7.TRANSMISSION DISTRIBUTION AND OF 389 POWER voltageacross each load is 104 volts. on loads. drop in the neutral The 6a Vi The drop in the Voltage across now 16 volts. 348.349(6) shows these conditions graphically. Fig. This rise in voltagefrom power of the drop in the neustation to load is obtained at the expense tral. negativewire 20 X = 0. " Assume Voltage unbalancing that the loads in 3-wire a are as in shown one unbalanced Fig. a _. When they than loads motor are to are usually connected between an outer be connected between wire and the two neutral 3-wire system outer wires rather to so a that they will not panies comvoltage unbalancing In fact some power will not permit motor loads exceedingone horsepower to be produce connected any to neutral. the the load on the voltage across negative side is greaterthan the voltageon the negativeside of the system at the power station. There is no voltage drop along the neutral.1 X = 10 volts. voltageson the sides of the system. m. 0.t"80fl 0. = 26 - 84 = volts.2 X 110 = 62 There 80 = positiveload Voltage across two having system side of the system and 20 amperes total amperes in as represents the same on TW (6) 40 = 110 -r 2 + 16 = 124 volts. volts difference between the Ans. 348(6) shows a plot of the voltagedistribution. Fig. connected each machine suppliesonly the load its own side of the line. that half of the batteryon the more heavily loaded side will dischargeand the other half will be charged. obtaininga 3. When the load is unbalanced. " by the same 86a Storage battery giving neutral in a 3-wire system. The neutral wire is connected to the middle pointof the battery. 248. in this manner. be driven generators may -*" FiQ.351.wire system which Two " to generators is. Fig. the outers. The obvious objectionto this method on is that two separate machines are required. A storage batterymay be floated across the line as shown in Fig.351 shows an " .390 DIRECT METHODS There 247. Storage Battery. 350.350. 351. in series between Both When prime mover.the generators are " shunt Two generators may be Fig. that SYSTEM 8-WIRE : should be connected one A of Two-generator Method. The positiveterminal the negativeterminal of the other in in series as shown Fig. connected of OBTAINIKG various methods follows as are are OF CURRENTS supplying a 3-wire system. Fig. the centrifugal may pump If in act as a water wheel and the water wheel as a pump. Some of . " -* S22a -" Balancer set The action of this set may analogy shown in Fig. In virtue pump of the water of the water passingthrough the water wheel some where it may in the canal B is pumped back to A by the pump. by the hydraulic is suppliedby the canal A.QOp QOpO"* "'^- Fig.TRANSMISSION AND DISTRIBUTION OF 391 POWER In this particularcase the upper unbalancing of 10 amperes. 353 more than can be suppliedby the weir at A. 352.2 a QO. They in series across connected wires and the neutral is broughtto their the outer terminal. The water wheel corresponds to the motor to the generator or machine B. and the centrifugal pump the water wheel shown machine or in the A. best be illustrated Water be made to do weir into canal B and may doing. both halves of the batteryat the same balancer set is a very common method of obtaining the neutral. A " generator mechanicallycoupled together. This water wheel is belted to a centrifugal operating between B and A. useful work canal the in B so and of the water Some in givingneutral a 3-wire system. 52. Balancer Set.as shown common are a in Fig.352.352. All this water is not needed between falls over This water 40a " a the tail race which is not point of utilization D. is requiredbetween canals B and C water Fig. half of the batterysupplies5 amperes. at D passes to C through C at the needed figure. The objections of obtaininga neutral are the high mainto this method tenance of maintaining cost of a storage batteryand the difficulty condition of charge. This set consists of a motor and 249. 353. and the other 5 amperes in the neutral go to chargethe lower half of the battery. be utilized again. current The generator output will 0. 352 there is an excess of the system. as representedby 20 amperes in the neutral.392 CURRENTS DIRECT requiredin B will be suppliedthrough the upper operatingas a water wheel and discharginginto B. Zi 12.64 times the motor input. I2 = = Solving = = The machines if their fields are readilyto unbalanced loads respond more crossed. This current distribution is determined then causes side of the positive in the following manner: Each of the machines A and B isassumed to have 80 percent.that is.8 amperes back to the line.2 flows throughthe motor and in dropping of this 20 amperes amperes condition Waterfall! Fia. pump. 353. This of load on the negative side correspondsto an excess of the system of Fig. 352. be the motor be 0. Let Ji efficiency. In the extra water machine so doing the upper The machine lower machine drives the lower machine then pumps water from C back as a to B.12.actuallythey will be slightlyunbalanced. motor the generator to pump 7.64 20 /i + /2 7. through 110 volts " Water-wheel analogy of balancer givesup its energy.8 amp.2 amp.8 voltagesare = be the generator current in machine A and h in machine B. 110/1 IIOJ2 X 0. The set.if the motor fieldis across the will .8 X 0. Assmning that the equal. of load on the positiveside If in Fig. drop so Connections reverse the motor of what side of the is Une. by compounding the so connected that the actingas a generator is cumulativelycompounded. rents. The machines are started in series. The (excess load on the positiveside of the system (Fig. a to take 3-wire system of unbalanced care using result may be obtained The series fieldsshould be a balancer cur- set. widely differthe currents in the two halves of the differentialrelaybecome unbalanced. and is differentially that actingas a motor compounded. The " same machines.352) tends to reduce the field of machine A and to increase must of machine that voltage is the increased raise the not FiG. Fig. 354 shows standard connections for a balancer set with series fields. In order that a motor may take additional load.TRANSMISSION DISTRIBUTION AND generator side of the line and side of the line. Therefore.resultingin the main generator circuit opening. If the voltageson the two sides of the system become ent.even though its load is not excessive. are up to . motor OF the generator field is In order that 393 POWER supply- generator may a the across additional current. B. When speed the neutral switch S is closed. This relay then closes the tripping coil circuit of the main generator breaker. with the neutral machine switches open the machines and the shunt fieldsin series across the line. across much of the are the generator field and will voltage. 354. its terminal voltagemust drop or its induced voltage must rise. its terminal now generator induced voltage need two effects These If the generator fieldis across desired.either its terminal voltagemust rise or its induced voltage drop. any current flowback through the neutral can readilyflow back into the armature The connections of such a through this reactance. 1 be extended See Vol. on connections (Dobrowolsky method). page 341. generator are shown in Fig. after current iron be obtained can core which from A coil wound the machine.two and even employed. . The Edison 3-wire system may wire systems.) The complications sively of wires prevent these multi-wire systems being exten- used.Chap. ing Moreover. alternating has already been shown. Occasionall This the reactances are placed within the armature.394 Generator. II. ^3-wire generator the a cen- (6) (a) " an high inductance and offers current this alternating is connected across therefore high impedance to the slip rings. arrangement requiresbut one slipring. to obtain better three reactances are balancing. All have their neutrals tied together. this inductance coil offers very little resistance to the flow of direct current. is a three-wire The " very efficient method details of the method The generator of obtaining be understood can or better have alternatingcurrents and the synchronous converter of the method The principle is as follows: Alternating been studied J is generated within a direct-current armature current as If slipringsbe employed. 6. Three-wire method Dobrowolsky a CURRENTS DIRECT neutral. Therefore. Sometimes. 260. the voltageto either brush from the neutral will be the same. ter of gravity of the voltages generated within the armature.355 (6). Further.but increases the weight of the armature. and 7- and (SeeFig. page 375.355 (a).if the three-wire neutral be connected to the center of this coil. XI. has center of such a coil is at 355. number to 4.as shown in Fig.309. The Fia. 5. . as shown in Fig.for example. A junction box thus providesa convenient method of connectingthe singlefeeding wires to the several distribution wires. . 357 shown in t he i ssectionalized as (d) In Fig. it cannot be conveniently increased. Where the best the densityof trafficrequiresseveral feeders. which is suppliedby a separate feeder.357 (c).357 (a). it is not permissibleto take chances of having the due to a ground at one entire system shut down point only. Therefore. Electric railway generators are generallycompounded. the seriesfieldbeing on the negative side. 262.to suitable terminals alinstalled in the junction boxes.at any pointon the trolley.through fuses. As the size of the trolley wire is limited by the trolleywheel.but only disconnectinglinks are used for the feeders. the trolley lines. involves the entire system. The trolley be considered as forming a and feeder togethermay singleconductor.due to a ground. the trolley is of insufficientcross-section to tage time to keep the volsupply the requiredpower and at the same drop within the necessary limits. Except in small installations. Electric Railway Distribution. trolley each of this method the trolley is divided into insulated sections. This is called the ladder system of feeding. objectionsto the precedingmethods of feedingare that trouble. Each feeder is protectedby a circuit On short breaker. Trouble in one section The . the size of the trolley The same effect as increasing be obtained by running a feeder in parallel with the trolley may and connecting the feeder to the trolleyat short intervals. The positive terminal feeds the trolleythrough an ammeter. The mains are always fused. to carry the current to the car.357 (6).396 DIRECT containinga set of insulated mains mains or the CURRENTS tribution bus-bars. alone may suffice with lighttraffic. a switch. The negativeterminal is usuallyconnected directly to ground or to the rail through a switch. as shown in Fig. results are obtained by connecting the feeders in the manner shown in Fig.and a circuit " breaker. In cities where trafficis particularly dense.it being deemed advisable to allow the feeders to burn themselves are clear of any short-circuits. are Distribution ready connected.to which either the dis- feeders connected. Most " . Such currents in spread263. This creased in- the expense of a less efficient the feeders are unable to assist one another.but seek the pathsof least resistance by which they may return to the negative terminal of the station generator.1I I I I I I I I Trolley (b)Ladder System Single Feeder - Feeders (c) Multiple Feeders Trolley (d) Multiple Feeders FiQ. " Methods - Section^lized Trolley of feeding a trolley system. as In the precedingsystems this mutual tise help is obtained. I I I I I I I 1. Trolley (a) Simple Trolley Feeder.TRANSMISSION is not OF DISTRIBUTION AND readily communicated reliabiUtyis obtained other the to 397 POWER sections. 357. currents not only pass through the tracks themselves. trolleysystems use the track as the return The return conductor for the current taken by the car.. Electrolysis. at of the copper. 1. To decrease several expedientshave the effects of electrolysis been devised. Fig. must ultimately Fig. The polarityshows which way to the pipe.etc. to the negative bus from various pointsalong the track. " Electrolysis by earth currents. In so doing solution.gas pipes.398 DIRECT CURRENTS as ing through the earth follow such low resistance conductors water pipes.tiby good bonding and by using insulated return Tfollay ^^ Fig. situation is stillin an unsettled state both. In may some cause the current cities the total to leave the permissible drop in the ground return circuit must not exceed from 10 to 15 volts.358. two as This successful methods most good a is done are following: the path through the track as is pra". the current other. (6) Discourage the current's entering the pipes by occasional insulating jointsin the pipes. ..heavy copper feeders that are run negativefeeders. 358 shows how track and poor enter rail bonds the pipe. back that is. it is obvious that such ciurrents leave these pipesas at (a). 358. they tend to carry the metal of the pipe into electrolytic which ultimatelyresults in the pipe being eaten away. inserting is to measure the In testingfor electrolysis the usual method voltageexistingbetween the track and the water pipes(as at a hydrant). However. if the track is positive must be flowingfrom the track to the pipe.current For example. The fact that the current enters and flows along these conductors in itselfdoes no harm.as shown in Fig. The (a) Provide cable. 358.cable sheaths. as The electrolysis for regards its mitigationand as to the ultimate responsibility the damage resulting. The magnitude of this voltageindicates roughly the magnitude of the current which must be flowingfrom one to the is flowing. and a few all-night " This portionof the load curve is called a The load valley.00 a.00 occurs evening peak.00 p.consistingof street lights conmiercial loads. are ratio of the average is called the load factor. Central load curve Station of DISTRIBUTION BATTERY Batteries.m. The load drops ofiF A. Even although this apparatus is in use only one hour a day. value. a OF 399 POWER SYSTEMS " Fig. after which This peak may and 6.TRANSMISSION AND STORAGE 264.00 a. 6A.m. loads. central station. IS Nt central station load 1.00 to 7. hold up for an hour. Battery smoothing valleybetween commercial 12. due to commercial power and to the beginning of street car service.lights perhaps The morning peak occurs about 8. it drops to the evening load.00 is due to the because curve. 359 Between shows 11. Fig. The load to the maximum load of a station . The of the 359.M ISNt.M.m. which consists mostly of lighting. shuttingdown of the luncheon hour. increases rapidlyfrom 5.00 and loads out 6 P.00 typical a p.m. This load graduallydiminishes to the all-night have must sufficient station Obviously the power company and distributing capacityto carry the peak. " ISNn. the investment charges in eflFect24 hours a day.M.00 the load is comparatively small. " graduallyuntil noon. The between 5. which is usuallythe largest. and 5. the transmission system. For example.therefore. in the generatingsystem or in In case of a shut-down the load. often used. A battery may . could not be foreseen and so cannot be met mediately im- by the generatingstation.) Storage batteries are also useful in taking care of unexpected result in a sudden loads.000 kw. the battery maintenance than offset the economies effected by is usuallyfound to more be of the load off the peak. is the daily load factor? What The average load The load factor " = tlf^ ^ in a day and its peak load g^ooo kw. 94. the battery can help maintain service. As a rule. Such batteries may taking some useful in office buildingsand other isolated plants. For this reason pasted plate batteries are more because of their high overload capacity. This equalizesthe load on the station and increases its load factor. They are placed. in large central Batteries are commonly installed as reserve the center of near station systems. Par. a thunder storm may out demand steam the load which curve. be discharged on the peak of the load curve.000 kw.batteries are not installed for the purpose of smoothing A storage battery operatingunder the of complete best conditions is good for only a limited number charges and discharges. (Seepage 103. station delivers 192. In fact loads that will fill in the companies welcome any power and are usually prepared to offer attractive valleysof the curve rates for such loads in order to improve their load factors and thus to utilize apparatus at times when it would wise other- be idle. a a out by the use station may be smoothed The battery may be charged at night and earlymorning and so fillin the valleyof the load curve and then in Fig. thus eliminatingconsiderable labor on charge. Therefore. load The of of curve storage battery. 8 000 " oQliOO " ^ ^' ^""*' ^^' Obviously a high load factor is very desirable.because very to shut down the entire Ughting plantand run it is often possible the batteries at night.as it takes time to get up be put and put a generator on the lipe. as shown 359.-hr.400 DIRECT Example. is A CURRENTS 20. " If an electric rent cur- in dilute through two plain lead platesimmersed sulphuricacid..1 " drop -=- be must drop adjusted voltage of battery of dischargea storage battery. The disadvantage of this the is the loss of power the voltage and method . adjusting be conliyered by the battery may trolled. J sistance resistance.which depends with Even 360.001 X 0. the load.5 - 0.105 Force ohm. the series resistance be adjusted? To what value must total battery electromotive force cells each of 0. the m ~- 1=1 re. the line it takes battery is already floatingacross automatically..1 volts and an internal resistbus-bars that the into 220 volt delivers 100 battery so ohm. The E The bus-bar X2. 266. = 220 volts. = 10. load increase the sudden carry 401 POWER OF DISTRIBUTION AND the load increase In order to control the load taken " to the bus-bars. FiQ.115 +i2 22 11.it is necessary to change It is not its induced voltage by adjusting the field current.115 ohm.consisting 115 ance having an electromotive force of 2. If the brought into service. battery resistance r Let 115 voltage V The = R = the added = 115 external 0. By battery. Cells.as load this the deresistance.1 = 242 volts.TRANSMISSION immediately and the line on until boilers and turbines so be can Resistance Control. ' 360 Resistance " con- battery discharge.001 amperes. Counter Electromotive = 0. . possibleto adjustthe voltageof a storage batteryin this manner. It is desired " to troi of resistance the for the occasionally to compensate during discharge.a simple storage batteryis formed which immedibe sent ^ Digitized by (^OOgle . upon load constant -r- .L_ by a and generator connected insert resistance in series with to shown in -^- Fig. Example.5 Arts. in the . = resistance 242-220 "" lOOi^ = R 266. the battery of controlling One method ^ load is to have the battery voltage sey-|" eral volts higherthan the bus-bar voltage -. of cellsto A " givean p.a ciu ^. service. The to a not being in continuous cells. a switch similar to that shown is connected contact The main to the auxiliarycontact by a When from one batterycontact to the next resistance R.0 volts. the cells at the end Opening the circuit.) The force of the bat- hence its load. The* resistance R is usuallyso chosen as to allow the normal batterycurrent to flow during the transition period.402 DIRECT CURRENTS atelydevelops a counter electromotive force of about 2.) Neglectingthe small IR drop in such a the counter electromotive force is practically independent of cell. be used. 92. and oont"ct out "=" T 361. 361 is used. delivered by a battery. It is essential tO do this with- csellcontrol of storage battery. To charge such a bat- tery " a booster -^=^\a"tu"y (See page "=- electromotive -=- tery. may -"" " End of the battery. The end cell switches become rather massive in largebatteryinstallations and are often This also permits remote operated by a motor-driven worm.similar to that shown advantage of this method The used. 102. is that the the resistance control over opposing or control electromotive force is independent of the load. contact control. For this purpose in Fig. Par. sliding maintains the circuit connections through the auxiliarycontact the resistance R. is do this an end cell switch. 361. Therefore they require individua attention on charging.are discharged lesser degree than the others. To rate of the battery more in Fig.Bat cient battery usually consists of a suffielectromotive force exceedingthat of the bus-bars by an ample margin. and ^^^ Were there zero resistance between the main its auxiliarycontact the individual cells would be dead short-circuited during the transition period. If it is desired to decrease the disof these cells are cut in. 111. Par. End 267. may be controlled by cutting in or -S- Fio. (See page 97. ^^^i^ end / . This principle is utilized in controlling the current the current. in dilute acid and are connected Plain lead platesare immersed charge in series with the battery. number Cell Control. ""^-fl^ T PT^^ n. . mile extends out 4 miles from The the station. occur " Rather to install a not to install more than it may copper.'' Each electromotive force of average 2.05 ohm when there is no much amp.the Une voltage should drop to such a value as to allow the batteryto dischargeand assist the power station.26 + 0. 363.002 ohm.002 = 0. " voltage (Fig. As the voltageat the end of the line requiringa goes batteryunderfluctuations of considerable magnitude.404 DIRECT CURRENTS In order to reduce the current flowingthrough Ri and Rt and the battery.26 ohm ' per resistance of ground and track At the end of the line a storage battery consistingof per mile. same manner as the booster of Fig. " constant at The 600 Battery floating at end of trolley line. With littleload on the line. the change of booster excitation isoften accomplished whose field is connected in the through an intermediaryexciter. battery resistance Ri The the line? total resistance of the R The on 240 X 0. the battery is usually self regulatingboth as regards charge and discharge.363) A 4/0 trolleyhaving bus-bar volts. due to insufficient copper. Batteryat End of Line. Example. force 2.0 volts and a resistance of 0. cell has an 240 cells is ''floated. how station supply? The load current = When the load total = trolleyand track 4(0. This battery only steadies the trolleyvoltagebut tends to reduce violent fluctuation of the power station load as well. at a the station is mwntained resistanoe of 0. battery much is 150 does the . when a car is near the battery.362.48 ohm. ^Very poor voltage regulationmay at the end of a trolleyUne.05) 240 X battery electromotive ^ = at the does the battery supply and how = 1. the voltage at the battery should be high enough to charge it.0 = 480 volts. On the other hand. Jr ")-Bni-bar // X Bfcttetj Track Fig.24 ohms. At what rate will the battery charge is 0. be economical more storage battery at the end of the line.. (38.with ^^- ^"'P- battery will the .firstfind the 120 load of 96.4 amp. a remove constant it from current must be service. battery the line drop from the station to the power Under batterywill be 120 volts. the series generator.2 38. be checked current This may 600 480 269. (See Chap.making 480 volts at the battery.4 amp. Let II be the line current divided inverselyas the trolleyand and Is the battery current.6 amp. opened the As this is not Power current affect any That another one the so series that the Therefore if the circuit of any to allthe other loads will be interrupted. load just "float.6 volts. provided the voltage does same one cmrent are passes through each.2 will be amp.8 ^^ ^-^""^P' = -r24 1. ^^" That ^^ = 0. " Ans. 14.and the constant and Thomson-Houston current tranrformer operatingin conjunctionwith the mercury rectifier. . one not all in series with load be short-circuited when parallelsystem the load system the loads and the battery 111.8 + 14.24 is.24) 461.48) (Check) = = - Distribution.TRANSMISSION When is there to the AND load between no the OF station and 405 POWER the battery the current battery 600 . the loads are " In all independent of applied at any one point does loads.6 volts (111. II." The remaining battery resistance.) Both of these methods arc tend to maintain constant current under all conditions of load. = " station is already supplying 96.4 X 0. 461. Series - by calculatingthe voltage at the battery.a of the other change.48 Ib +Il Solving ^ Ib Il 53. 53. Vol.8 amp. Ib 1.. 480 - ' find the division of the at which 150-amp.48^72 1.a load it is desired to is usuallysuppliedto is.8 amp. permissiblein practice. In not of distribution another.24 ^ II 0. total station current is then 96.8 The The is 38. of which the Brush arc machines are examples. VII." 600 480 " a at the battery.24 + current 120 ^^ ^' To DISTRIBUTION at the amp. system by one of two methods.6 X 1. conditions the battery will neither charge nor discharge but these will "float. " Statioa Parallel loop series circuit. This is due to the fact that the copper only the current of any singleload. be dangerous to have such high voltagesin buildings.365.as shown in Fig. Open " 11 station loop series circuit. There two of connecting such series are general methods loads. 364.406 DIRECT CURRENTS Therefore. 364. parallelloop system the outgoing and return ductors con- always kept near each other. This system requiresmore copper than the other but facilitates testingfor faults and reduces inductive disturbances. the circuit is connected to the loads without reference to the separationof the two In conductors. In the open loop system. shown in Fig. the high voltageacross and so prevents the circuit being opened.this system is applicable narily because itwould ordionly to outside work.if the circuit be opened and thus introduced and ja constant current a very is maintained high resistance a highreacross sistance highvoltageresults. As the loads are in seriesthe a very rj Fia. are . the This system is economical of copper. resultingvoltage is high. Therefore. The advantage of the series system is the small amoimt of carries copper required. If the this paper punctures it lamp burns out. Fig. For this reason the lamps used on a constant current system are protectedby having a thin disc of paper between the lamp terminals (filmcut-out). 365. such as street lighting. ft.183 deg. cm. F.000 lb. (gram calorie) pound deg.u. 10.35 grams = 2.) kilogram ounce = 28. .452 cm. = == 407 760.5ft. Cent. sq.9 on of mercury mm. lb. Pressure 1 atmosphere 14. meter = mil sq. 1 sq. mil. meter at 32** 60** F. on sq.u.t.000 ergs joules 4. 1000 kg. mm. sq.76 Volume inch 1 cubic 1 liter 1 16.81 gram joules = 7. ft. gallon = gallon cu. 1 ton 1 = long dynes =981 ton 1 metric = ton = " 2. Cent. in. on at sq.233 ft.92 in. in. " 0. = 1. of water kg.-lb.000. (gram calorie) gram lb. in.t.356 joules deg.0 33. Fahr. cm.54 1 foot = 30. Cent. inch = 6. deg. at 32** F.000 cu.3 = = 0.) 178. F.7864 1 circular = 0.39 = cm.-lb.APPENDIX A Relations of Units Length 1 inch " 2.609 kilometers Area 1 circular mil == 0.2642 = 231 cu.1 = 777. W"ight 1 gram 1 1 (av.7074 550 = ft. 2.240 lb. (B.205 lb.94 702.000507 sq. 2205 W"yrk 1 joule (watt-second) 1 gram 1 J 1 1 = deg. 1.-lb. (B.70 lb. 1 sq. of mercury = = 1 lb.) kilogram-meter foot-poimd horse-power-second = 10. = 29. 1. sq. = 9. (gram calorie) = 252.48 1 mile = cm. of water weighs 62. . B ft.408 DIRECT CURRENTS APPENDIX 1 cu.6 Ih. 800 3.300 7.330 6.920 6.770 3.810 4.540 4.230 1. 10 Single-cotton covered 87.910 2.500 6.300 3.650 12.000 49.220 5.300 8.830 3.100 2.410 8.020 3.410 10.650 2.080 2.690 5. Solid Layer Winding* Wire Co.120 9.500 3. 5.000 12.270 1.303 1.100 5.5 Enamel 92.000 26.290 2.409 APPENDIX APPENDIX Table of Turns per C Sq.900 10.500 24 25 26 27 28 29 30 31 32 33 34 35 36 ' 5.155 23 1.5 11 109 105 117 12 136 130 147 13 169 161 184 14 210 199 231 15 260 248 292 16 321 304 366 17 396 374 458 18 488 456 572 19 598 556 715 20 772 722 865 807 907 21 1.) (The Acme Si"e.950 8.080 14.650 2.630 4.300 20.5 Enamel and Single-silk covered cotton Enamel and silk 84.200 7.780 2.900 21.075 1.800 14.400 23.460 4. Par.850 12.900 17.850 17.150 1.720 1.350 9.400 23.950 5.G.090 3.310 2.300 20.300 8.510 1.860 2.700 37 38 "Standard Handbook.610 10.440 5.950 8.000 31.075 22 1.650 13.300 .575 1.220 947 890 1.045 1.700 27.W. 9" 16. .600 10.900 40.630 6.410 1.425 1.430 4.520 3.730 10. In.910 2.330 1.570 6. Sec.010 1. A. 410 DIRECT CURRENTS APPENDIX Table of D Current-carryingCapacity in Amperes Under Various Conditions of Wires and Cables . . in this field and with pole of parallel its north the magnet.)is acting between them? 6.000 units.000 units. In problem 2 sketch the flux distribution when the bar magnet is perpendicularto the lines of induction. What the governs path taken by the lines of induction? does this law explain the attraction of iron to the poles of a magnet? is the objectionto the use of the bar magnet in practicalwork? 16. A AT the the needle? ON " "J true dip of from north the the north of a between magnet. a sketch.)is tending to pull them together? 7. = = .412 DIRECT is magnetic 14. What the induced inducing and CURRENTS induction? pole? does magnetic How may of soft iron to magnetic poles? attraction is the What of use a relation between is the What How "keeper" induction the explain the become a compass in connection with versed? re- horseshoe a magnet? general law 16. What force (inlb. Sketch . What pole is induced on the and in what direction does the force act? Make bar. The of horseshoe two poles a magnet are 4 cm. How the underlying the compound principle laminated 18. When it is 4 in. 6. resultingfield. Two 800 and m' poles of strengthm 1. from end of a long soft-iron bar. 4. In S Fig. apart. is inserted lines of induction polepointingto bar mag- two field is produced parallelpolar surfaces A bar magnet to the is indication of the I the arranged 2. it induces a pole of 300 one units on this end of the bar. With what force is the magnet actingupon the bar? Neglectthe effect of the other poles. What the by magnet exist in their vicinity? may of two horseshoe used in practicalwork? be shielded instruments sensitive may fields that may 19. problem 2 show the ultimate efifect the magnetic flux distribution of inupon creasingthe strength of the field due to the to the bar What occurs large magnet.what force (lb. true laminated or the bar over magnet? magnets from stray magnetic a bar magnetized by steel bar be In magnets? of means practice. magnet? Sketch the 3. What How have What advantages magnet? is the 17. A north pole of a bar magnet has a strength of 2. What Where are means 20. I lA. apart in air. nets two field around as uniform in Fig. If each has a strength of 1. lA.000 are 2 in.how bar a magnets may magnet? By magnetized be of electric current? electromagnetsand also by means needle does not point to the true north and State why the compass information in most south places on the earth's surface. How the ring and use necessary of What needle? compass the in order to determine is the PROBLEMS ^ CHAPTER 1. 5 in. exists between force (grams) is acting upon What an N-pole field? Toward pole will which the tend N-pole to be drawn? 160. of 500 units placed in this a another upon field of 50. A 413 PROBLEMS AND QUESTIONS magnetic two parallelpolar surfaces.provided turns rent cur- the direction of the the the to the poles at the ends direction of the current answer. How many from this pole? emanate is the flux density at a distance of 2 in. A field of magnetic QUESTIONS 1. per sq. current is placed with those of common mentioned one these of in a through be (5) may solenoid the may solenoid be known. Show how combined 7. within a this loop? bar magnet? 6. section and having a diameter is the approximate flux What in the rod? density 14.8 cm. plane surfaces having areas of 25 sq. 10. Near the second? Explain. In of a compass needle point if held over the what direction wire? If held the wire? 4. What away. in. cm. A singleloop of wire lying in the plane of the paper carries a in a clockwise direction. .000 lines per sq. 6. placed near the first surface? 11.000 lines and having the shape of a truncated exists between two parallel. What is the nature conductor carrying an and ON CHAPTER general shape electric current? direction of the current H of the magnetic field about What relation exists between the direction of the field produced about and a the the conductor? 2.pole4 force of 1. What and 60 sq. The current will the north beneath relations be shown to remember end the experimentally? What relation which exists between simple the magnetic field? in a conductor flows from left to right. force is exerted upon a unit N-pole if respectively. same wires tend to separate or come for the together? Give two reasons Repeat for two conductors carrying current in opposite directions.2 grams is the strength of the second pole? 150 units acts with polestrengthof 8. What are commercial uses of the solenoid? Name seven such uses. If two parallelconductors carry current in the do direction. per side. uniform 9.000 lines What is the strengthof the polesat the end of the rod. The flux densityin the crossnsection taken at the center of the rod is 15. from this pole? 12. cm. A lines of force N-pole has a strength of 100 units. whereby methods determined. Give be three Has several to form a What this 9* effect will be noticed if a compass loop any propertiesin loops similar long solenoid. A cm. What force would What exist upon the a unit S-poleplaced at this distance from pole? 13. How the above may rules enable one direction and 3. cone. in. A long steel rod has a square cross-section of 0. A pole of 500 units exists at the end of a steel rod of circular crossof 0. showing its generalconstruction. an a U-shaped solenoid attracts of operationof the telegraphrelay. CURRENTS Explain by the fundamental drawn 10. ratio of the cross-section of the field generators cores of a overcome be should What of some the approximate multi-polargenerator to the general rule should be followed in the yoke? What a magnetic circuit? Does placing of the exciting ampere-turns upon the of between magnetic leakage poles a generator representa direct loss of power? cross-section of the ON PROBLEMS 16. Show Explain the the applicationof practical one of the iron-clad solenoid. as is the disadvantage of the early types of magnetic circuits of representedby the Edison bi-polartype? How has the design of the the modem magnetic circuits of the more disadvantages of the earlier ones. A portionof a CHAPTER is shown direct-current feeder H in Fig. What dynamos. or When In what to flow in the feeders for tend the insulators? to move and what . of trolleysystem running upon direction. the solenoid upon practicaluse of this type of solenoid. plunger What and the position characteristic pulling the effect does the stop have simple solenoid. compass tion does the current in the feeder flow. out of the duct? 16A. 15A. Fig. armature.in Fig.and in what way are they more the magnet itself do than the older methods Does of handling material? work is handle iron it and steel? when used to appreciable being 14. 18. current Plot the relation between the pull on the of the plunger in the solenoid.414 DIRECT 9. Fio. Sketch a lifting magnet.the ordinary electric principle State a the principle whereby door-bell. 16A shows two positivefeeders a pole line and carryingcurrent in the same drops upon the track. into a solenoid when laws of magnetism why the plunger is flows in the solenoid winding. What effect does ''iron-cladding have upon of the plunger? State characteristic? 12. an in what instant. Where are such economical magnets used commercially. " 11. isheld above the feeder the needle deflects as shown. If the troUey wire a current direction will these conductors b the direction of the force actingupon a direc^ 15A.causing an enormous 16. AND QUESTIONS 17. polarityshown. method of connection? 20. 18A. ISA coils so shows that two they aid Connect simple horseshoe magnet. actuates the A coil D.in what If the polarity move? direction " . indicate the polarity direction will the plungerP tend to in what ^ is -f and terminal B is of terminals A and B is reversed. does the plunger tend to move? ^nn. is excited continuously hammering direct current. Assuming that one of the field coils of Fig. sketch the general appearance by this the magnetic field. Fig. coils one on a poles. Sketch the magnetic fieldbetween another. encircling device. If terminal of the ends of the plungerP. Fio. In hammer Fig. P. 20A a heavy iron shows liftingmagnet about to pick up "skull cracker" (used in breaking up scrap in cross-section sphereknown as a a . these the Fig.the two coils **buck" each other. Fig. page 27 is reversed. the plunger P.magnetic ^jiDflaD"ie Steel 20 a. with If the terminals a and h of the coil D are of the B b a Fio. 17A. Will the total flux be increased or diminished 19. of that is. 17 A is shown operates. 38. 18. a soft-iron plunger running in guides. the principleupon coils C and Two 415 PROBLEMS C are which one type of electric in series and connected in the positions shown. homogeneous material vary with its is specific resistance or resistivity? of a substance is fixed. What is the unit of What Explain. into the is What "fringing?" QUESTIONS is the mechanical 1. poles sequence the Sketch paths of the magnetic lines. Fio. The the current enters 21. 21A. How HI A "microhm?" "megohm?" have analogue CHAPTER is it defined? How resistance? ON are resistances connected a is the ances resist- in series? ances circuitto the conductin connected in cross- parallel may parallel? be bined com- equivalentresistance. that the proper north as shown. 22A shows the pole face of a generator and an armature Sketch the paths of the magnetic lines in passingfrom the pole face 22. length and conductivity What these of its individual parts when is the relation of the total conductance of its individual parts when how these latter a circuit to the connected are of 8. What this relation show the . Distinguishbetween 3. resistance of does its 6. May conductors.each two length and of the the with its cross-section? 5. Assume that the coil in the right-hand section of the excitingcoil. armature tooth. Sketch the magnetic lines and conditions. 21 hand A.416 DIRECT CURRENTS iron). "mil?" mil? is a square What A is the meaning of the term cirWhere is the cular circular mil? What relation does one bear to the other? 9. What mil usuallychosen as the unit of crow-section? What are its advan- . Fig. Fig. 22A. polea the polesexistingunder in the coils 06. tooth the from and these horizontal section of the magnet is circular. Connect Fig. If the volume and same material is a and how does it vary with equal volume. cdf ef^gh. relation of the total resistance of latter an of What Distinguishbetween conductance and generalmeaning of "per cent. What 2. conductivity?" is the and affected? resistance is conductance into What a section? From conductors. how is the 7. What of resistance? insulatingmaterials different resistances? 4. so mark tooth the to of rest the iron. in the multi-polarmachine shown the of Make leftis obtained. does its resistance vary with how If the volume its cross-section? is fixed and the length length? With doubled. of of C is twice the material. cube. Between the 18-in. what a of the cube 18 of copper is 1. 4 ft. A phosphor-bronzestripJ^ of 0.W. 23.5 in. X H a copper ui.000 ft. is that of D? what 26. and cm. and per cm. ohms.000 ft. A of in. What the are any What PROBLEMS A conductors. is the best conductors determine to one given size of wire? commonly used and why? Compared and the disadvantages of aluminum steel used as conductors? Explain.G.724 .02 What is the resistance of 5 miles of 000 copper per 1. cylindrical 29. edges? 27. mils be known? its cross^section is the unalloyed metals for if its affected by is the "temperature coefficient of resistance?" What temperature? What resistance of How is it used? 12. How another? one would temperature weight of of 1. 10 wire? 14. At what decreased resistance of to at the temperature? How resistance and 13.AND QUESTIONS such units tages over the number does as of 417 PROBLEMS the square mil and circular mils in a the square inch? What relation circular cross-section bear to its diameter? 10.a width of length of If the resistance is the resistance cm. What copper? length in is How cir. How the is its approximate wire be resistance of most of the resistance determined a copper in cir. ohms wire ohm. of No. the If the resistance same of C is 30 length. What same may resistance of copper be zero if the rate that it decreases within ordinary ranges this principlebe used to solve problems involving the temperature? relation do the cross-sections of the wires in the A.. X is its resistivity per A has twice the diameter If the resistance of B and is 5 twice the length is the ohms. Two enable does this relation the resistance and bear platehas rectangularcopper thickness of 0.C but the diameter what CHAPTER ON and but the cross-section of A a 2 wire? Which the metals? among with as readily is the resistance What weight of 1. same If the resistance that of B. A cube. per edges? 6 in. conductor cylindrical conductor B. of No.have the same is most advantages length.7 bus-bar The 40 ft. of A is 30 and D. long. ohms. plate between at 20** C. long has cube? Per a resistance in.724 microhms the 6-in. in. What a 1 in. what 24. A a the are of B? conductors.000ft.-mil-foot? a may feet and 11. bars What each of copper microhms of is the resistance per cm. temperature? in. what resistance oi A? 30.have same that of D.000597 28. Two is that By of is twice copper the When conductor? iron and are m material. (diameter is 410 mils)? No. If the resistance of copper is 1.724 microhms is the resistance of an inch cube at the same what 26. at 20** C. cube? 16 copper wire has a diameter of 51 mils and a resistance of 4. made resistance of copper up of 4 is 1. 6 ohms are ohm at 20"* C. bar ^ in.32 81. A 43il. X 1 in. The resistance of 500 ft. 8 wire is measured and found to What is its per cent.89. problem 40 are in connected what series.418 DIRECT weighs 0.what costs aluminum of cost shall cost copper mils is drawn between used 8.0000755 a its per cent. " conductor down $0. conductivity? be 0. of 25** C. two resistances of 6. what was 000. What is the are 6. another is the 120 of and 140 ohms and 110 in is connected parallel. Pio. What in series.20 per lb. the as conductance is of 2. is the resultingresistance? group of two in series with (Fig.. diameter and 8 ft.2 ohms 88. Three "and found resistance of 8. (Conductivity 86. conductances Three parallel. of aluminum s in. If copper of the bus-bar the cost 82.connected group of two parallel(Fig. If the three is the 42.length of No.00241 ohm at 20** C. in order per were be the ratio of radiating bars. total resistance resultingfrom this combination? group 96 .44A). that its diameter so the Neglect lb. 1 in. problem 30? H in. Resistance? resultingconductance? If the of of problem 38 all connected were in resultingresistance? 820 FiQ. long and 800 the ends that as the Specificgravity having is 268 mils. and cu. cube. 84. in (a) If aluminum surfaces? bus-bars copper 88. and 3. and 10 mhos respectively What resultingtotal conductance? of connected is the in total resistance? 41.5 ft. conductivity? each. resistances of 4.05 ohm. A be 000 the the same copper? ft. resistance of 41 ohms resistances What of 60 and 80 ohms is connected 44A. Ww^m*vnA^^^"v 120 Q 60 Q What of resistances. should (6) What aluminum lb.70. 43. and a to be 3. What is the total resistance of the combination? 40. all connected What is the total resistance of the combination? resistances of 8 and 80. thick and of the same in problem 31. long. ohms in parallel 82. A copper = to have is found copper resistance of 0. conductivity? 87.35 ohms. long rolled from electroljrtic 86. A 43A). in series with a in respectively. Determine the conductance of copper 580. Two 4 ohms connected are in parallel. of No. per bars for the copper substituted CURRENTS diameter a of 410 If the resistance of the is the resistance of the entire 0.3 ohms each. 44.000 mhos per cm.8. The resistance of a 4-ft. what would Spacers are radiatingsurfaces. conductances individual resistances be the would what parallel. conductor reduced been to 258 mils? has length when its diameter of a copper rod. 18 wire is measured at is What temperature a is its per cent. 800-ft. . and "20" resistance of 0. is meant 8. Discuss may appear. QUESTIONS 1. Estimate wire. Estimate wire. 1. power ical is the unit of mechan? What relation does it bear to the unit of power between what horsepower? 8. 62.007 ohm a winter of 100" temperature summer at 20" C. What relation does it bear to the units of electrical power? is stored or in which energy in which energy the various forms Describe the energy cycleinvolved in a steam-driven electrical . weight Of 800 the resistance and ft. 60.420 CURRENTS DIRECT feeder has A direct-current 68. Of 500 ft. the weight. of 0000. What Illustrate. of 16. What CHAPTER ON and how is the unit of electric current electric quantity? force? What What is the nature the are IV of mechanical is it related to the unit of motive potentialdifference and of electroof electromotive force analogies why? and of Can it be compared to voltage drop in a line? have over a line and pressure drop in a pipe? Is it possibleto supply power of line? the voltage at the load equal to the voltageat the sending end the in the wire the Is loss there to return a voltage generator as well Explain. What of* temperature F. What 6.'s and more no potential"? Is it possibleto have potentialbetween certain of difference of points? should 4. weight of 2. How a in the connected ammeter be connected never forms is the to use each law same way a as a voltmeter? Is circuit? a should Why an an meter am- line? relation does Ohm's expressed? Under Law express? conditions what In what is it most three convenient of these? series-connected are resistance? How are the division of current of each in ordinarilybe connected across fundamental 5.? What is the percentage change? Without consultingthe 60. What two or by "difference yet have emf.000 ft. 61.000 ft. in is its change the lowest between conductance the maximum F. the Table Wire resistance of solve the 1. of 0 bare copper Of 600 ft. taken two How at a may time? it be expressed in Differentiate fully care- and What is the unit of electrical energy and energy. of 18 bare copper 8 bare copper 24. Estimate wire. mils of 600 ft. 1. of 00.amperes of electrical power? and ohms. in the outgoing wire? Can potential exist without as a current flowing? is the nature 2. How voltmeter What branch? resistances combined parallelresistances in a to circuit parallel two-branch relation exists among equal an What combined? bear the currents equivalent relation does to the resistance the circuit when has three branches? 7. of No. Estimate No. of No. followingproblems : 13 bare copper wire. of No. What terms of is the unit volts. the resistance and of No.000 ft.resistance and cir. of No. 25-watt 66.of bus-bar? 74. The 250 voltage drop amp.1 volts at its terminals. What electric a value of 480 current 550-volt 67. A series lightingsystem consists of 118 lamps. the resistance? 73. each having a resistof 7. found to ft. a copper What is be 1. across is 0.7 volt. A carbon mains what and cold resistance of 330 ohms does it take does current has a it it is when operate? cold resistance of 40 ohms does it take current what its terminals ? across does current a field resistance of 160 when it take it is when ohms.580 amp. A mains? generator has What rheostat.26 millivolts. A rheostat has what To reduce 68.? 1. A storage cell has What and hot a 115-volt resistance hot first switched to it has attained normal 220-volt 66. includingthe flows in the field? a of 350 field resistance What to rheostat is the a resistance voltage across must a the the and the field take? adjusted in order to amp. what is the of the ohms.2 has ohms does current the resistance of the rheostat be should in which a current What ohms.25 amp.4 ohm incandescent resistance of 240 first connected and flows when filament CHAPTER difference of potential constant a current 64. How 421 PROBLEMS AND B. the relay over a line having a resistance of 30 ohms? ance 71. of 8. generator supplying this system? voltage is its hot What 72. operating conditions? the field current of 40 amp. power form does the energy ultimately? Approximately appear of a modem efficiency system? power A gram-calorie? What is the relation bedefined? tween is the over-all what is 9. the series field of What a compound livering generator de- is the resistance of the series field? .t. An incandescent lamp takes 0.u. What simple relation exists between the of feeder of transmission? and and ends efficiency a receiving power conditions is the voltage drop in each foot of wire inde11. a wattnsecond? a gram-calorieanda the voltages at the sending 10..6 amp.5 ohms an and connecting wires a total resistance of 0. A a to 0. 70.QUESTIONS In what plant.24 ohm and carries a current the rheostat? generator develop heating coils have a to supply resistance 25 to amp.-length the voltagedrop is the resistance across a per ft. What has 2.2 ohms and If the line resistance is 100 requiring 6. 110-volt IV isconnected What tungsten lamp 110-volt. at 110 volts. generator has voltage oven At resistance of 45 ohms. A telegraphrelayis wound for 150 ohms and operates at 40 millibe the circuit of the What should battery if it is to operate voltage amperes. Under what pendent How of the total current? is this principleutilized in solving electrical problems? be appliedto obtaining the power Can this method loss? Explain. When 6 the bus-bar carries 1.25 ohm. 69. lamp ohms. A carbon ON of 0. PROBLEMS 63. all connected in the magnet series.15 ohm What total resistance of 7. A direct-current the drop CURRENTS takes 6. has a resistance of 0.16J1. having being supplied from a 115-volt generator over 76.each having a resistance of 0. how 350. QOQQQ^''^ 0. of 0. four relays? 84.two feeders.012 ohm. are connected a greater If the 50-amp. and 31 : divide total is flowingin the two? selective relays connected 37 ohms what respectively. Determine take? If coil one what short-circuited. To feed and When among the other a trolleywire at a given point. S2A. ohm What is delivers 400 amp. 76A.what Fig. Two ammeters. scale and the other a 100-amp. If is the resistance of the '^ballast?" multiplearc lamp is 70 the arc across volts. instrument a resistance of 0. parallelthe 0000 hard-drawn the current demand the feeders and upon trolley? the system is 600 amp. their terminals when voltage across wire? ^^^ suppliedby the common 82 A.05 ohm.. 30 and 40 ohms in parallel. In problem 82 how will the is the 2 2 amp. sistance connectingwires having a redoes the lamp bank receive? 0. 20.. connect 77. at 110 volts.0 amp. 86.5 a current ohms. ^^o Fia. determine the current in each of the other resistances. instrument than 100 amp. 76ii shows a lamp bank.004 resistance of 0. electromagnet has four spoolsof 1 ohm each. An What ll"-volt mains. A 0000 a the series fieldwhen 80. 25. the series field? 81. 70.If the current in the 16-ohm resistance is 2 amp. amp. Two wires.422 DIRECT 76. a - 83. one having a 50-amp.002 ohm and the 100-amp. The is shunted and the series field winding of by ' voltagedrop across problem 79 how will the 400 a resistance of 0. the a in wire shown parallelare suppliedby a common If their resistances are in Fig.. does it divide .? the diverter between the generator divide amp.0012 ohm. In and having diverter a generator has a 000 trolleywire is 6 miles long hard-drawn annealed feeder. 20. trolleywire.15-n- FiG.one 250. per wire. copper and is their combined What is paralleledby resistance? What is the voltage drop in the feeder when of 100 current Four 82.000 CM. in parallel so as to measure current scale. to ''grounded" so becomes does current the magnet half of its resistance is that will the magnet current be? the equivalentresistance of 78. what will each read among flows in the circuit? when 130 amp. amp. circuit having four resistances a of 16.000 CM. to 6? a Gen. FiQ. A resistance of 50 ohms is connected of 75 and These 100 ohms.2 jO.2 -fl. 88. 150 and of three parallel total current of the How much each resistance? current system when 120 V. What each. 86A 86. S7A. 89A 89.l-TL Fig. - a shows generator from drop wire ab is 120 is H is zero 12 ohms volts. Fig.volt generator supplying lamp loads. and the voltage at the various a at each terminals. each. does the generator deliver? 0.305 6 gem tungstens. O.what to its maximum and a for The the distance? field current of total resistance of the If the line does the generator fieldtake when }4 is the mains? is the voltageacross regulatingthe value.1 -H- 0. cate Indipart of the system.2 -TV Lamp 10 -TL Load ' 0. shows the currents lamp is the What A. Field 80A drop wire. having lights. used a current the distance from 12A What 100-volt across take and what sistances parallelre- in series with 180 ohms. Fig. S7A 87. that of the field is 30 ohms. 86 a57 voltage at 0.QUESTIONS follows: 4 120-volt generator a the mains mains. it is connected does each resistance two connected voltage the contact x ^i the distance? (^oogle . 115.n.3 ohm resistance a 423 PROBLEMS AND ohms each. are in series with in turn group resistances of 120. 150 ohms supplying lamp loads of 0. 10 tungsten current loads The 290 ohms over are as each. lamps. IS-Tl. and shows Fig.2- 0. Lamp Load 0.3 . gMk- *^/////yi^ Powe^ " I I 260.what are power is lost in this shunt take? the heaters A 96.670 rating? 90. is the cost of the How much hours. I SUtio]^ Fig. 45 to many at 220 amp.000025 ohm. A no volts flow before a the temperature room temperature of 70" F.35 lb.of water. per gal.4 then 50 amp.200 amp. Determine 2 quarts of water at a room temperature of 25" C. 98. railway is fed by a 5-mile trolleyline of 0000 hard-drawn feeder parallels CM.takes a maximum power feeder..what is the greatest change of voltage that What is the load to the maximum load? at the factory from no occurs maximum load and half the at this load? of transmission at efficiency of 120 over amp.1 mile from a current station.-hr. A 250 at amp. 220 volts and delivers 20 hp.8 its ratingin watts? 01. A from amp. Assume that efficiency (Water (100"C). across 96. factory..) 101.? resistance of 0. how ampere-hours are delivered to the many lamp? the cost of heating 100.5 hours. If the station voltage is maintained 250. 200" F. for 3 miles. A generator delivers 1. series field of of the 600 at amp. The What ohm. weighs 8. to the boilingpoint the of the heater is 80 per cent. a 600 -S. at constant volts. 230 volts. If it has an of 92 per cent.000 CM.-hr.? (1 of the water gal. A water-barrel rheostat contains 30 gal. volts. Energy costs 8 cents per kw. resistance 92.) Assume 102.000-amp. shunt a the generator delivers 1.35 losses.424 DIRECT CURRENTS A gas-filledlamp takes 6. Four street car heating units. electric An A 250.water is raised weighs 8.what 1.being tapped this trolley . is its efficiency? What generator delivers 97. If the trolleyvoltage is 600 volts. What power carrying its rated current? 94.000 103A. copper. How long must How 99.000CM.each having a resistance of 55 ohms. compound a What What is is its kilowatt generator is 0. do connected in series. An electroplating at 20 volts for 2. when shunt takes motor 75 at amp. 98. 110-volt mains. from lb. A tungsten lamp having a hot resistance of 202 ohms is connected What is its watt rating? 110 volt mains. 103. At 4 cents volts for 60 at per kw.002 islost in this field when power has 2.what horsepower engine is requiredto drive it? bath takes 80 amp. and is consumed? energy requiredenergy efficiency under the above conditions? joulesare supplied to a 25-watt lamp burning 4 hours? K the supply voltage is 110. lOSA).. size wire is necessary CHAPTER the terminal at a distance The and what V voltage of a batteryof applying Explain.000 in parallel to the first load. 104A shows and another station.000.000-ft.000 CM.000. A by 104^. If. Solve the followingproblems not consult Do 106. power and a from runs of 500 amp.volt bus-bars. a 750. The voltageat the 200-ampere load of transmission? station voltageand the efficiency Fig. CM. 68 and 69.000 C M. A 40-hp. What size feeder is necessary. }i mile from the loads.000 Fig. the wire tables.000. are second load. the cable operates at a densitycorrespondingto is the power What is the total voltagedrop? 1. when miles it is 3K voltage at the end the from station and is taking of the line at this time? What of transmission? is the efficiency 104. 2. To what is the internal resistance of a battery due? Is this resistance a constant quantity? 4. what is the station is If the voltage 600.5 mile. 1. lengthof 200. 1.000ft. 500.000 CM. -)iMi^ Power Station BWlAmp. What is the two CM. of transmission? efficiency 108. f I "00 --j I I Amp. farther along.000CM.000 760.425 PROBLEMS AND QUESTIONS be The resistance of the ground return may half mile (Fig. and what 200-amp. cable 500.500 cir. the methods outlined in Pars. what loss under these conditions? 107.02 ohm per mile. motor is to be suppliedwith 230.in problem 105. What a is the effect upon ON power cannot exceed of 500 ft. mils per amp. What has an efficiency motor of transmission? is the efficiency is the QUESTIONS 1. considered as 0. of the station to be of 0. one of 200 amp. A 1. cable suppliesa certain power load is the total voltagedrop in the cable if the load is such that the cable is the power loss under these densityf What operates at the normal What conditions? 106. the first to the is 220 volts.000CM. 15 volts. Is it how may the current delivered to an external resistance be calculaf" ^t^^hc^ . 500. If the electromotive force and the resistance of a battery be known. A ^ supplied from the 600-volt bus-bars of a exceed The voltage drop cannot voltage. The voltage drop from of 90 per cent.000 CM. 1. load is station at distance a power 10 per cent. Why does the electromotive force of a what conditions are they the terminal voltage? Under load to its terminals? cell differ from the same? of the internal voltage of possibleto make a direct measurement How this internal voltage be it is deliveringcurrent? a cell when may calculated if the battery resistance be known? 8. in every voltage 110 the at car is the What amp. 1. what should be the sign When passingfrom a ? When When of the potentialchange and why? passing from -f-to passingthrough a resistance in the direction of the current does a rise or a What then should b^ the proper sign to use? drop in potentialoccur? When passing along the resistance in oppositionto the current what sign should be used? Why? 12. Under what conditions may to receive electrical a battery be made becomes What energy? relation does the direction of current flow bear to its direction the battery delivers energy? If a generator has a voltageequal battery. If the assumed direction of this fact indicated in the result? a current in a network is in error.terminals of like polaritybeing connected together? What voltageis raised above this value ? What " is meant by the battery floating? 6. how is .how should If their direction of flow be into account? potentialbe represented? A drop in potential? to a + terminal of a battery.what voltage must can applied? Explainwhy the voltage in excess of that of the battery alone is illustration effective in causing the flow of current. What two fundamental are principles How several currents taken meet at a junction. In should general. motive what is the resultant electroeffect is noted when the generator " force of the combination? How combination? the current may is the resultant What of the resistance if the external resistance be be found known? 8.how cells be may the resistance. What entire resistance individual cells be known? of the external circuit be found if the external 10.426 DIRECT CURRENTS short-circuited what the battery becomes current does it deliver? What that the cell develops under these conditions? of the energy 6. What is a very common of a battery receivingenergy? 7.how of the cell? What under cells? the the total K the resistances the resistance may these and current relation between relation does the current What found? most of the individual the resistances to the resistance the is the What of the individual cells are operate force of the combination of the delivered by each relation exists among the terminal voltagesof individual cells connected in parallel? is a series-parallel grouping of cells? What is the voltageof battery? How may the resistance of the battery be found if 9. How should a rise in " " 13. cells and and resistances of the individual How the current electromotive their arrangement grouped in the the an forces be known? to obtain the best economy? should cells be arranged to obtain the maximum output? power stated in Kirchhoff's laws? 11. K several cells are connected in series.what effects are noted when the generator is connected when to that of the to the battery. Before current first be be sent into a battery. Under conditions what conditions? current is the What in the batteries do is the electromotive parallel?What battery resistance and relation cells? individual entire battery be cell bear between in satisfactorily external not equal. . 1 ohm. How should these be connected that the maximum is obtained? so efficiency When the load requires 10 amp. CURRENTS flows? current is the What each voltageacross cell? 120. in parallel.006. A 126.what respectively. 0. are available.0026 force of each is 2.8 ohm current flows? much current the is connected What is the terminal does each cell deliver? A 122. must the four not certain load is such be less than that 6 volts.2 volts.5 volts. batteries A forces of (Fig.9 volt and cells be these a connected 50-ohm so as circuit? a of 0.004. What is the total batteryvoltageand ohm current does its total resistance? If an external resistance of 2.0. Each of two an internal has one What 0.2 ohm.6 ohms terminals. The battery of four consists internal resistances storage cells all connected of these cells 0.0. power may much how is absorbed by the resistance power in the battery? and the what is is connected its across 124. having electromotive 4 and 3 volts and resistances of 1. each having an electromotive relay over a resistance force of 0.0 ohm connected are respectively.008 ohm is the in it the two startingbatteries has equivalentresistance of the batteryconsistingof the parallel? What is the terminal voltageof the combined delivers 160 amp.428 DIRECT resistance of 12 what ohms.010 ohm.2 and 1. current positive positive resistance connected the battery terminals? What across through a 2-ohm is the battery terminal how and much each does current voltage battery deliver? Two and B .? tween How does this current divide be- individual batteries? 121. Twenty-four dry cells are arranged in rows electromotive force of each cell is 1. ohm. A telegraph battery consists of 12 gravity cells.128A). How should 20-ohm a satisfactorily u nder these battery efficiency most conditions? 128. What under these conditions? battery 127. What is the cells of problem across the terminals voltage of resistance a batteryobtained by connecting all parallel? When 119 in of this of the a battery.4 volts in parallel. K the electromotive the battery deliver when its terminal voltageis 1. two connected battery when resistance electromotive force of 6. force of 2.02 resistance to operate What is the of 0.9 volts? of six in series and 123.1 volts and the Twelve maximum Under and how difference potential amount of these conditions much is lost at its terminals each having an electromotive storage cells. what is the battery terminal voltage? What is the load resistance? is the battery efficiency? What 126. and the other a resistance of an of 0. The rows resistance of each is 0..003 and are in parallel.what battery how and resistance of 0. terminal What to flows terminal. Arrange the cells in problem 125 so that the maximum of amount is the efficiency of the current will be delivered to the load resistance.what current flows? Arrange the cells of problem 123 so that the be suppliedto a load resistance of 0.6 ohm. is its terminal voltage? 0.000CM. Two having batteries.0-ohm resistance to charge a 2-volt battery of a resistance of 0. of station A is maintained constant at 600 volts -aooo ft. a.000 ft. and that at station B is maintained 350. "i" Fig. the 2-volt connected is to the wire resistance at a I point ?i its length from the negative terthe minals (see Fig. at 580 volts.3 terminal through 6 volts and forces of 6 and electromotive of 1. 132A.000 center is 500 amp.15-ohm. }r^ 350. be placed upon the flows in the 6-volt battery circuit? B feed into the same distributingcenter. Across the terminals of a 12-volt. These supply current 1.0 and 0.000 CM. i^ T " " .. the (a) Determine 131. what point resistance wire that (6) At 132.2-ohm 130. The Two so the must current no sub-stations A voltage at the bus-bars and contact Fig. a resistance wire battery.120.000CM. When through 350.- 400. 429 PROBLEMS AND QUESTIONS sistances re- in positive are connected parallel. 129 A). two positive terminal (Fig. respectively. 500 AmpB. IZOA). through 400. the load at the distributing (see Fig. terminal and currents voltages of each battery in the if the 6-volt 130 problem batteryis reversed.000ft. cable CM. battery. how much does each station supply? How . terminal The of ohms is connected.000 CM. 130A. The positiveterminal of the 6-volt battery ohm . Determine and the terminal voltages of each currents *i^ + 8"^. of 2. Station A feeds a distance cable and station B a distance of 1. is connected negative terminal of the 12-volt battery. to the resistance is 0. 132A). 10 6-volt of whose a negative battery. Fio. battery is so connected that the current flows in at its positive is the charging current of the 2-volt battery? What What terminal.5 ohms to a 2-rv 128A. 430 DIRECT much does each power CURRENTS station supply. C. The station voltage at the subconstant at 240 volts. A tie line 1. distribution system. and distributing QUESTIONS acid solution and C at amperes.300ft. and how much is received at the center? distributing 188. long and of "{v. What is the nature may the four this resistance the elements of requirements for be reduced? In what cell increase its current a voltage does 6. terminals cell which of 7. type of work What electrodes and is it designed? What force of this cell? does the gravitycell differ from the Daniell cell? Which in the other electrode? electrode requiresreplacing? What changes occur What is the cell electromotive force and for what type of work is the gravity cell designed? .C and D. another a centers B.000CM. What a satisfactory primary of the internal resistance of a voltmeter a does way capacity? indicate cell? cell? In what manner increasingthe size of Its electromotive force? when it is connected If the to the circuit is open-circuited? a suddenly To what is the excess closed. What is meant A If metal is of the is flow between current them flow between electrode? an copper what other solutions? to another? by one metal being electrochemically positive what will to metal be the direction electrochemically positive B.100 ft.000 ft.iioo ft.Describe two generalmethods of reducingpolarization. Fig. and cell a secondary a primary 3.to what is the initialvoltage drop due? Explain the part*that hydrogen plays in drop over this initialdrop due? polarization. D is 2. equivalent.000 CM.000 CM.600. long and 2. and long 1. that to C is ft. of ON CHAPTER load similar of D.000. direction of the current What three other such 1000 and at D amperes. A radial feeder extends from a centers distributing The feeder to B is 2. B.that to 2. the voltage at each 500 Find amperes. In what 4. equivalent(per wire in every case). ^"^8 aJid 2. In what ^ construction used? are electrolytes is the electromotive way is For of the what Daniell cell. A A 133A shows is maintained to each of the J ft. VI in stripsbe immersed copper connected between them? a voltmeter dilute sulphuric If the two stripsbe replacedby two zinc strips? By two lead strips? Under the stripsbe obtained? conditions may a voltagebetween Would a voltage exist if the sulphuricacid were replacedby some Name type of solution? 2."i "--^y"-"-"*^ 500"000 CM. What if two occurs and a load a and C and At " is "". B connects line connects What within them the cell? through is the cathode? What the external will be the circuit? anode? The form is the energy stored within the cell? What changes take Distinguishbetween placein the electrodes when the cell delivers current? cell.000. What are 6.800 equivalent. Describe what the 8. C * 133 A Fi ^"*^ of the "^ "^ 1. show that the existence violate the principle lead storage cell does not in any way When the cell is approachin general.AND QUESTIONS Edison-Lalaxide the 9. occurs change principle 16. What is the electromotive stood idle for when some and new with compare is After it has dry cell when new? time? What is the magnitude of the internal resistance How it subject to change? does the polarizationeffect the internal 14. What of Weston a cell? standard a cell in distinction to the In practicewhat How two What way does the saturated uses quantities and is its how cell differ from cell be measured voltage of the Weston made be the characteristics must cell constructed is the Weston insured? In what permanency cell? normal the Cannot Why electrical common maintained? easilyreproduced and most are is the function of types of cells? of other the with ordinary voltmeter? an 12. What gases lead is observed are evolved to exist and from at different which times plate does in the each emanate? 17. of electric cells for the would account the materials in what approach change discharge of an emf in . In what Is a The What does way a dry cell resemble a type of common wet cell? dry cell really"dry?" Of what is the positiveelectrode composed? negative? What is the electrolyteand how is it placed in the cell? materials are placed between the carbon and the zinc and what are their functions? 13. ing governing the emf.what voltage in used are be allowed? cell should reduce electrolyteand What current? a per cell. In what What way condition dry is a should current voltage when due? principally is the cell's becoming exhausted cause of applications much is the terminal some of the a a Can cial commer- cells. Describe strips. What what chief force and of this advantage what is its terminal trodes elec- the cells type of cell? voltage when livering de- materials for the trodes positiveand for the negative electhe Le Clanch^ cell? is the electrolyte? What is its electromotive What When force? planning to use the cell commercially. storage cell renewed concerning functioning of the cell? it becomes when What two discharged? of the cell is necessary general types of storage the materials for proper cells are in use? commercial lying a very elementary experiment which illustrates the undereach in State the of the lead that of the cell. a voltage to zero? process of charging? of the In what way is the 2. Even although both of its platesare of lead.6 volts per cellutilized in the . does its electrolytediffer from what already described? 431 PROBLEMS polarization? materials What introduced are is the cell renewed? How For in the cell to type of work what is this cell best suited? 11. To what resistance short good cell deliver upon cell delivers current? force of a How effect? circuit? What Name this cell be temporarilyrevived by any means? 16.what voltage experiment. Describe In used? are way is the What is its electromotive What 10. what . What gravityof a fully-chargedbatteryhaving Plants plates? Pasted plates?. the What are the advantages and the disadvantages of pasted plates over commercial conditions demand Plants plates? What a pasted plate and of that of a Plants How does life the with a pasted plate why? compare plate? of the "Iron-clad" the construction Exide cell and 20. When a battery is received. Describe briefly its principaluse in practice. gravity place specific does the specific change during discharge? What gravityof the electrolyte of made of is these gravity? specific use changes practical what specialattention should be given to 26. What In what manner should the Under what conditions is each used and why? in lead-lined tanks be made non-leakable? How the are jointsand seams the tank? be lead in factors in What considered must plates suspended tank? a lead-lined wooden designingand installing the advanName 23. Whatthreetypesof separators are in generaluse? tages and the disadvantagesof each type. and what 27. and describe that Plants the two formed by this are plates briefly process 18.432 CURRENTS DIRECT during the charge and the discharge of change in the electrolyte the chemical equation? Why is a cell composed of by a Describe plain lead plates not useful in practice? Give two reasons. the two generalclasses into which storage batteries may be 21. What change takes the has ceased? after How the in charging Explain. What are What divided? types of plateare best suited for regulatingduty and for in stationarybatteries? Why? duty emergency batteries? two types of containingtanks are used for stationary 22. What the requirements of a vehicle battery that make are in the made different from that of a stationarybattery? What changes are tery plates? Separators? Specificgravity of the electrolyte? How is a batdiffer does from made In vehicle what a a stationary battery up? way indefinite period. What ing precautionshould be taken in dilutuse? for What is used simple device storage battery sulphuric acid for determining specific gravity? How is this device adapted for use with vehicle and the Faure or portablebatteries? during the charging period? change takes placein the electrolyte the is the effect of gassing on What specific gravity?. For what type of battery is each used? What kind commonly one precautionmust be taken in handling wood separators? Why? should be the specific 24. In what should the jarsbe installed? the wood How manner separators? should the platesbe placed in position? Why is an initial charge necessary 26. 10. What cell is shown process. Describe pasted process for making battery plates. idle cause What should be its duration? happens to the long periods? In What over be avoided? active material in what way If it is desired to a cell if it is allowed to stand injury to the batteryfrom this may withdraw service for an a battery from procedure should be followed? its design 28. in an Edison cell? In the chemical reaction that takes placeboth play? How on charge and on discharge.QUESTIONS AND PROBLEMS 433 of shipment? What battery in the manner special attention should be paid to the electrolyte? 29. . In what manner is the rating of a storage batteryexpressed? What is meant Can as many by the 8-hour rate? ampere-hours be extracted from a cell at the 3-hour If due? rate. Repeat for kilowatts per pound of cell. What is lost by a lead storage battery during its period of service? What With what should this loss be replacedexcept in rare instances? cumstances cirshould be care justifythe addition of acid to a cell? What taken in the selection of water 36.what part does the electrolyte and does its specific charge discharge? during gravity change construction of the Edison 39. them and with the the the of method plates holding connecting stating is used for this cell? What kind of a tank is binding posts.mechanical cell. is the positiveplate. What change occurs in the terminal charging period? What corresponding changes occur voltage? To what is the discrepancy between the cell electromotive force and the terminal voltagedue? Can it be said that the voltagecharacteristic of a storage battery is such that its use upon lightingcircuits is practicable? 35. What two of charging are general methods commonly the 3-hour from it? can In each method and employed? with pasted plateswhat value of current should be employed when the charging commences? When does it become to necessary reduce this current? What the are objectionsto pronounced gassing in a cell? How does the charging rate with Plants platesdiffer from that with pasted plates? 31. very is the About method great advantage of the constant-potential what voltage per cell is necessary in this method? one battery is justfloatingon manner may' the necessary a Does the generator of bus-bar and it is desired to charge tained? excess potentialfor charging be oba employed supply the entire energy necessary for charging? in the electromotive force of a cell during the 34. In what be of manner can absolutelyprevented? a for with use storage batteries? in the freezingof the electrolyte How does a rise of temperature a storage battery affect the rating storage battery? Compare roughly the kilowatts per pound of plate for a given cell at different dischargerates.in what example common should be taken care test by which of constant-current in the the connecting up determination method of the of the of ing. Of what composed. Name What a a simple What charging? 33. When it. polaritymay 32. What 37. Compare three the above factors for different types of cell. Describe briefly the. would What a rate as the 8-hour rate? at cell is apparently exhausted after it be possible later to extract To what is this difference dischargingat any further current be said of the overload capacity of a storage battery? 30. chargscribe battery? De- correct terminal be ascertained.the negative plate and the electrolyte 38. statingthe type of service for which each type is best adapted. brush such as is used positiveterminal with of the When is there any generators.07 volts and electromotive (a) What is the current new that VI CHAPTER maximum in such current a the cell can force? now which that manner electromotive an internal it can the plate (c) What is deliver V . 42.Give some battery. Show how the gravity cell is an electroplating bath which supplies its own current. State the advantages of the Edison battery over other types of storage of the commercial batteries. the approximate (6) What maximum force of 1.2 ohm. of a the lead cell? complete charge be assured? 41. supply and is used a electrode is connected is connected which in connection copper marked change in the plating upon copper Which with a to copper carbon to the the minal? negative tersulphate solution. electroplating 51. In what terms of a storage battery expressed? of true the ampere-hour efficiency indicator a efficiency? 44. State a simple method of producing 48. kw. 45. per is the efficiency Is 43. What are some applicationsof the battery and factors limit the applicationsof the battery? Compare the weights what with similar weights for the lead cell. State the reason why the ratio of the kilowatt-hours of dischargeat the 3-hour rate to those of charge at the 8-hour rate does not give the true of the factors which determine the efficiencyof a efficiency. A Daniell resistance deliver? cell has of 0. electrolyte? Explain. State some of the factors which of selection the govern a storage battery for any particularpurpose. Describe briefly the process of electrotyping. 49. when possible? 60. What is the approximate kilowatt-hour and the ampere-hour efficiency of an Edison battery? How can 47. What should be used to replaceevaporation of the electrolyte? Is required in the selection of water for the Edison battery any greater care than for the lead battery? Explain. The an is the size of the cell is increased area is doubled.434 the CURRENT" DIRECT advantage of this type of construction? and necessary what does care the For valve what is the valve puri"ose How require? is the battery mounted? In what does the normal rating of an Edison cell differ from that way What is the voltageper cell? Is it possibleto tell accurately condition of charge by readings of either voltage or of specific gravity? 40. Can copper be ON PROBLEMS 134. plated from a solution in which neither terminal is come? copper? What voltagesin the platingbath must the supply voltage overIs How these are electroplating voltages reduced to a minimum? considered a high voltage or a low voltageprocess? In what way are plating baths connected. What is the order of magnitude of the kilowatt-hour efficiencyof In The a lead storage battery? ampere-hour? Why do the two differ? does the cycle of operation of a storage battery affect the what manner efficiency? 46. . page How 113. How dry many purpose? 144.240. A hydrometer test of the electrolyte in a vehicle cell shows the specific gravityto be 1.2 volts and a short-circuit The of current test show 4 What amp. will be the is the cell voltage is used in cell in problem 141. operating at this time? At what (See Fig. 104. This rate is maintained charge. During this period the voltage in Fig.2 watts per candle. = = . What is the percentage by weight of acid (sp. The hydrometer in a pilotcell of a stationarybattery indicates a How hours should the battery be more specific gravity of 1. is the is needed and State the procedurethat what total volume should of acid when be followed the solution is mixed? mixing the liquids.84.approximately what does it take and what current is its voltage? 146. to having a specific gravity rises to = . 104. 1.2 volts.021 For resistance of 5 ohnis galvanometer amp.) 148. many curve according watt-hours? ampere-hours are delivered to the cell? How (Note: many Mark several equally spaced points on the voltage curve and take their average.how near complete dischargeis the battery? 160. How 1.210)weigh? 161.84)in the acid solution of problem 150? 162.98.gr. acid How much water 1.436 CURRENTS DIRECT having a the and 0. If this cell is one of an electric vehicle battery engaged in propellirig a vehicle. A certain flashlight has a 2 candle-power lamp whose efficiencyis If this lamp is operated by a singledry cell. It is desired to dilute a quart of concentrated sulphuricacid. 104.sp. If the cell of problem 147 dischargesat the 8-hour rate and its voltage of Fig. many left charging (Fig.) 147. how many watt-hours are discharged? 149.gr. what much how each. class condition. is its internal resistance? What does this regards the condition of this cell? 146. make of 1. much will 5 gallonsof battery in gallon of water weighs 8.000 ohms a electromotive the measure cell has in the wire AC value of current and galvanometer be zero? Under each of the 5-ohm coils? across to The of 100 ohms. A storage constant cell has an 8-hour for the 8 hours the of shown rate of 40 amp. gr. A dry cell shows an open-circuitemf. resistance a current 142.. of 1.in first 1. A acid (sp. as having voltmeter through a the the current galvanometer? through these conditions what Is this a Weston ohms in ^C will the current force of the read? resistance of 180 When resistance of 1. A voltmeter passes What will the Weston cell 143. page follows the 8-hour discharge curve 113.3 lb. of using the practicablemethod an attempt standard? a factory ignitionsystem on an automobile requires 6 volts for satiscells should be recommended for this operation.190. page 106)? 163. A storage cell is being charged at the normal rate as indicated by an as voltmeter A ammeter.185. part of the its terminals across charging period is the cell indicates 2. What lem.. What method Is specificgravity in a vehicle battery is found to be 1.? for how many 168. At 5 cents per kw. mains. ance resistbeing charged at the normal be in inserted series must with this battery? What percentage of the is delivered the to supplied battery? power 162.). what is the energy cost of getting the battery ready for service? to be 1. of the United of its freezing in the climate States? possibility . before it is ready for active service.c. If the booster generator of problem 163 has an efficiency of 78 per of 80 per cent.-hr. at the 8-hour rate is How ampere-hours charge should be ^iven it many just received new. many If the has it absorbed? is 95 ampere-hour efficiency ampere-hours per cent. total internal resistance of 0. 166. hours can it discharge 60 amp. A storage batteryof 115 cells is floatingon 230-volt bus-bars.8 volts per cell. 101 and 102.) (See discharge and how many current 169. A a normal 437 PROBLEMS AND QUESTIONS ratingof 40 amp. be the electromotive must (c)What (6) What current does it take at this time? force per cell when the battery ceases taking current? of charging is used and is this method a desirable one? 166.bar voltage is desired that the battery begin to discharge when On is have 230 volts. There are 40 cells in series and a 0. ampere-hourswill the battery of probIf the 166.6 At the beginning of charge its electromotive does it take? force is 1.c. what series resistance is necessary? What centage perof the power supplied is delivered to the batteries? 163. It is the bus. A battery is charged at the 80-amp. mains. The average chargingvoltage per cell in problem 154 is 2. If two batteries each similar to that of problem 161 are being charged in series at the same rate.B volts. 161.5-ohm resistance in series with the battery.5 volts when much How rate of 12 amp.. would be specific gravityof deliver 157 at the a vehicle battery is found of its condition fair estimate a of 1-hour rate? rating of 320 ampere-hours. which drives it has an efficiency cent. rate for 6 hours. The battery consists of three cells each having a terminal voltage of 2.. and the shunt motor 160.240. It is desired to charge a startingbattery from llO^volt d.0 electromotive volts After 4 to the charging per cell. At what value of should the charging be started if the platesare of the pasted type? current Of the Plants type? (See Pars.what current How will it discharge at the 3-hour rate? ampere-hours does it many this rate? at Par.battery having 164. to charge exactly necessary What capacity of booster is required if the normal charging current is 60 much How is delivered to the battery by the booster? How amp. it 2. A battery has a does the booster set take from power 166.200)what charge? How 167. (a) What current force rises hours 2.4 volts per cell. A storage battery of 50 cells has the bus-bars? what and ohm is charged from a 115. If the battery of problem 157 is of the pasted platetype.volt d. there Give The any reasons. 101.? power is supplied directlyby the bus-bars? much 164. deliver kw.) the weight in pounds. Par. terminal at an voltage of 220 volts for 8 hours before it is average amp. It discharges 45 its terminals potentialdifference across terminal voltage of 1.65 volts. What of principle D'Arsonval current led in the poles? placed between two What may many hours. What ** CURRENTS per of the the a capacity (a) What will be the approximate battery? (6)Of the total battery? (See 4-hour this platesof will be iron-clad" the weight rate. kilowatt-hours principle? 2. Of what importance is explanationsof this effect carryinga is the in the is the be current 3. cell at weight 106. 170. amp. Approximately how volt Edison many cells would be required for a 24- project? lighting It is desired to install a generator to charge a 60-cell Edison battery.2 volts.28 kw. page 117. is its watt-hour is its ampere-hour efficiency?What eflSciency? 174. of a 50-cell Edison battery 15 Par. An Edison battery of 12 cells is charged for a period of 6 hours at the terminal The voltage per cell is 1.22 kw. A lead cell is charged at a 40-amp. One ampere-hour will deposit0. rate for 10 hours with an average of 2. 25-amp. volts)? (See Fig.438 DIRECT It IB desired to install a 110-cell stationarybatteryhaving 167. efficiency? of copper upon the cathode 176.95 volts. A storage batteryin its discharged condition is charged at the 100It delivers 105 rate at an average voltage of 250 volts for 9 hours. of 24-cell vehicle a cells. of 1. What for 8H hours at an average amp. rate with an average its is what What its is watt-hour and ampere-hour voltage of 1. per kilowatt of this battery? 173. and how will be What kilograms of copper many utilized in the are and is 12 amp. of at the 8-hour rate? 169. How How how to flow for 6 process? Give is noticed? is allowed deposited and are QUESTIONS 1.3 volts.) 168. What will be the weight in pounds. the current the a coil this currents two CHAPTER ON VH what efTect placed in a magnetic field. at the 8-hour rate? designed to 108.843 gram is 12 volts If the voltage across bath. rate and the average terminal battery discharges 5 hours at the 28-amp. in an electroplating a platingbath 171. normal size generator is necessary What charging rate is 20 amp. amperes. If current common is meant moving coil adapted to measuring small is the coil suspended? galvanometer? How and out of the coil? Why is a soft-iron core the methods by the are ** this damping be accomplished? used to damping" read of a the galvanometer galvanometer? flection? deHow . The (kilowatts. is its kilowatt-hour condition.this battery to have a battery composed total output of 1. 108.) (See 172.-hr. What in the efficiency? discharged again 176. Is it What be caused may what How voltmeter of of the instrument? the movement ammeter? springscoiled the bottom the movement instrument heating 10. led to the coil? Weston of electrical to be inaccurate? factors caused these instruments the movement of the D'Arsonval the underlying principleof What instruments? the advantages of the shunt? Ayrton 6. Sketch whereby an one of "balance" that exists when a battery and arrangement of four resistances. Prove How the law of has been reached. Of what deflection in a Weston Is it possibleto use the instrument for instrument? of this value? Explain. Show currents? excessive 4. instrument an evolution is the moving coil pivoted? How used to oppose the motion are How galvanometer. a eter. remain of the shunt In what Does is In ammeter? constant? or What be ammeter an may internal shunt an in instrument Weston errors of made An 13. connections an voltmeter? the In the line? possiblefor a voltmeter to have more is meant by a multiplieror extension coil? In what manner the heating effect of may the the shunt? important respect does the voltmeter differ from is the current in the coil of a voltmeter limited when to measure and by several scales? to have external 12.when 11. How Sketch means is meant coil damped? Explain. the shunt and law does the current follow in dividingbetween 9. be measured by What is the this method? for this work and an the the than an State scale? one Explain. Describe shunt. voltmeter of the current? " that specialtype very low resistances? the connections that alone. measuring current in excess the of 8. galvanom- is the condition proportionality .c. construction a briefly Why are four posts or is used in that when Weston instrument terminals necessary? Show a connection with a shunt. What 6. What of and should resistance the ahunt the instrument? the the resistance Why WTiy are the top possibleto utiUze of the way general. What of hot wire instruments. Show voltmeter the and measuring Show 16. and why? used in of voltmeter should be used in measuring resistance by a order of magnitude of resistances that can sirable What specialtype of voltmeter is often deTo what type of resistances is this method can be used contact in applicable? especially 16. it is acting as a voltmeter. is connected used? voltmeter a differ materiallyfrom that across the value disadvantagesof 14. of the resistances in the may bridge detected? this condition of balance be measured. the the was that current the coil? two are early types of a What is d. electric current some of the be utilized advantages measuring resistance with a precautionshould be taken in connecting are What ammeter. What by a effect does it have-on the calibration of the instrument Is the field " and what is of "radial s cale? oppositedirections? Is it as a galvanometer? a order of magnitude is the current that will give full-scale 7.439 PROBLEMS AND QUESTIONS a galvanometer be protected from may What the connections of two types of shunt. 133 as they do in Fig. Give brieflythe procedure balance with a plug bridge.after measure method the other is ployed em- measurements? Northrup potentiometer whose connections are in Fig. What value factor besides the resistance of the insulation affects the other of the current has been adopted resistance?. What the variations voltages among provisionis made standard cells? What protectionis aiffordedthe galvanometer during the preliminaryadjustments? each of these units? What is the working current . What types of two bridge are in general use? Compare them of ease manipulation. 18. Was Which is the of this is the be known before the it necessary this to know method? What simpler is it desirable in practiceto know 22. in Fig. same positions 21. to 26.440 DIRECT 17. are Does the Leeds " the smaller decimal divisions obtained? What resistances of this are used in potentiometer? in for the 28. Show standard electromotive forces with in such this standardized wire? What '' method the cell is used? volts. flowing in standard as What do is the standard must be observed only one which circuit? be of insulation measurements observed cell balanced? What care Why results when give satisfactory a installation of in the potentiometermeasurements if a balance is to be obtained ? will of electrification time What in commercial precautions should cable testingapparatus? 25. In what does way the should be followed in obtaining a slide wire bridge resemble the Wheatstone bridge from bridge? Compare it with simplicityand accuracy. 138 differ materiallyfrom the simple device sketched shown Where the one-tenth 137? What volt minor changes are necessary? are divisions located and how are they utilized when obtaininga balance? How 27. Sketch the connections used in the Varley loop.1 megohm in circuit continuallyand does it introduce any appreciable error? 24. Upon what is arm the obtained? balance positionof factor the in the fault What of error What additional factor must determined? loop test? exist? Murray sources possible be can cable. plug-contact resistance. What nometer is it under desirable all conditions of circuit resistance? to Why keep the 0. 19. Give which the connections in whereby the earth fault in shde wire the Wheatstone standpoint of the be bridge may put to a locatingan practicaluse name method? Explain why the galvanometer and battery do not occupy the in the slide wire bridge of Fig. standpoint of the from CURRENTS convenience. 20. 124? method is used to obtain readable deflections of the galva23. 132. Upon what standard Against what the is a as " primarilyrest? regardspolarity nul standard in be calibrated and marked wire may how a Is it possible cell balance has been obtained. the insulation resistance of Why cables? is not always practicable?What Why is the voltmeter method the generalprinciple of the method described in Par. as a voltage-measuring device. At what values of meter friction is How this error practicallyeliminated? Explain. alone? By Is what means can " circuit? direct-current when the delivered to power delivered to that 32.adapted to What is the p. In what generalrespect does a three-wire meter differfrom a two-wire meter? 42. What does a watthour device any low resistance is being measured? a differ in construction? the instruments these be the relative positionsof the voltmeter should What Do source with moving coils circuit? Why to the What power? direct currents? Upon what familiar electrical its field coils supplied? are is the torquieacting upon is care Its the armature proportional? retardingdevice necessary and what must be the law of retardation? Upon what principledoes this device operate? load does friction produce the greatest error? 36.^ncpleunderlyingthe measurement of measuring currents? What does it have four posts? is a standard resistance? Why current? In what units of resistance are standard resistances generallymanufactured? Why is it desirable that their temperature remain normal and what means are adopted to accomplish this? instruments 31. What at light adjustment is made to correct the meter registration this at rather is than made loads? at adjustment light Why heavy 39. What two loads? 41. In their deflections instrument do way is it based? To armature? themselves? power being and the ammeter When measured? of the function a From what what the fixed and of connection manner when using this type of instrument necessary measure? meter 33. What What dial of a are of the are some a meter used of causes a to reduce friction in running slow? meter a watthour How meter? is the recording actuated? usually very important that a watthour meter Why register accurately? What load and measuring devices are necessary in testinga is it 37. Why is methods 36. 34.AND QUESTIONS 441 PROBLEMS is the maximum voltage measurable with this potentiometer of this be accuratelymeavoltagesin excess sured? for the device used increasingthe voltage range of the potentiometer in any way complicated? and how What is meant by a " drop wire the supply is at constant volt ate? it be \ised to vary the voltage when may 30. meter? 38. Describe are take a high a resistance is In what wattmeter. What is the fundamental relation between the energy registered by the meter? checking the meter? and What the revolutions of the disc measurements are made in adjustments are made to change the meter speed? What the center of the disc? Nearer is the effect of moving the magnets nearer the periphery? At what loads is this adjustment made? 40. Is this potentiometer. What are generallyused in measuring the power in a What 29. meter Describe in a generalway practicallyastatic and the construction therefore of a meter which makes enables it to be used near the bus-bars . Design a shunt which the line allow and current to will Ho" Koo. should It is used to resistance of 25 ohms. has instrument of 50 amp. the resistances necessary with deflection. be affected by stray fields? to CURRENTS elements two How in meter a these elements are likely safeguarded from most are these effects? PROBLEMS ON CHAPTER VH A galvanometer has a resistance of 351 ohms. can removed were through galvanometer? How of the galvanometer? sensitivity of 75 amp. current This resistance instrument of a shunt An has to a be internal resistance used shunt. this result with be contact What should much current compared with the in the shunt? current Find 183. resistance of Ko be desired that through the galvanometer? 178. 179A.. resistance a of 2 ohms. toB. termine dethe current through the when 1 milliampere ^ iA/WW\^^VVV\A'VVVVAVVWVVV% galvanometer Koo of the line current pass = flows in the line. shunt through the instrument It is desired 5-scale ammeter ohm. An Ayrton shunt (Fig.01 moved Line 1 If the line current what those it measure be the resistance flows through (Fig. When the is 2. now pass the ultimate reduce the line contact of problems 179 and would current the shunt that ISO when Repeat problem 181.442 DIRECT What carrying heavy currents. passes What The a to measure has be the a resistance of 0.001 set at the sistance point (the reAC 10 ohms). point at 179o). determine the current the through galvanometer when FlO. of 0. What should be the this if it be desired that for with shunt use a galvanometer the total current of the line pass through the galvanometer? If it 177. 179.00075 the instrument? Through measure ohm. being of the shunt has under and the instrument milliampere. 180. The resistance of a certain galvanometer is 495 ohms.000 It is used to shunt a galohms. of shunts for measuring the instrument currents of of problem 182. 184.179A) has a resistance from A to B of 10. Hooo pass through the galvanometer.000 0.01 with instrument? Googk this . vanometer resistance of a having 2000A shunt ohms. the resistance AD 100 ohms. 150 amp. Compare If the shunt 180. a How the shunt? What in millivolts? a alone is available. fuUnscale and 500 amp. current a D is 1 is moved the 50-scale millivoltmeter A 182. much current is the ratingof 185. conditions? these it be How neglected as much does It is desired at full-scale deflection. HiUiamperv- the line to the 0. An current of 60 amp. . 3. 14 wires a and conductor 6. a tank a of water slide wire the balance is obtained. short-circuited and grounded at the are is a single00 looped to one conductor of another cable which conductor of the faultycable 00 at the Cables. its out entire loop resistance to 0.long. Wheatstone a connected 128.wound in to locate the fault. perfectconductor is connected to the of the faultyconductors to the 100one 89. 1. unknown An wire bridge. What is the value of the unknown resistance? 200. balance a What and to have the bridge.100 in problem is obtained? a fault in its Murray looptest is cm.000 is obtained when P 58. long.200ft. "^L-qr x-^'-vI "^ Fault St-0000 Condi I Fig. the faulty one parallels cable of 4/0 copper is 3. resistance is balance isobtained? a resistance known M unknown is the value of the unknown the best values of M ohms. end of the bridge. The the known as resistance the slide wire when reading on It is immersed when cm. is looped back through a perfect00 conductor.72 arm is obtained value is known Wheatstone a the measurement end of the one 141. ance are arms (See Fig. In a = = = .reads is the distance from one end 18. A resistance whose What of the insulation of the field circuit to megohms of the machine? the frame is measured by resistance of 100 ohms of means slide 100-cm. 202^4. (See Fig. conductor in The of the slide wire and balance A Fig. readingend end.4 cm. A cable insulation. P at X bridge between " balance a What connected are to 199. arm ohms. 198. long.) A bal1. used 1. page ohms. 132.4 of the cable to the fault? 202. far end. One in a cable containing two No. 10 = read when to be between X at and N as shown N in = resistance? 10 and 20 ohms Fig. each 8. 203. a is inserted at the lOO^m.600 ft. long. 134. 128. page If the unknown to use? (See Fig.000 ft. How far out on the faulty located? Varley loop test for a fault in a 1/0 conductor. resistance be used 10-ohm a on is known reel. page 149. A bridge the and Af resistance is P. long.426 ohms.000 is 141. is known be The two to are looped at the grounded. as shown low cm.200 ft. Due same installed An to a bum-out two-conductor both conductors To locate the fault point. The of the bridge measurement far How the shows be ohm. page 146.) A balance is obtained when the slider reads 32.5 ohms.70 is fault? 204. what 201.444 CURRENTS DIRECT is the resistance in What In 197. what will P 16. this conductor The ratio and N M 10 ohms.4 cm. is obtained is the bum-out at 202^. If will be the 199.) When 1. and The o. P is then adjusted until this galvanometer galvanometer (Fig. 209 cell.far end the Varley loop test made. 12. the other conductor. page The short circuit is then set at 0. What is electromotive force of this cell? is It 209. arms of circuit.0176 volts is connected connected are cellhaving voltage of the storage are in the standard cellcircuit stands unplugged in P. The ratio and rheostat arms means a standard bridge (Fig. FiQ. P to be 890 found and is then read ohms.0 after the cable has been charged for 1 minute. It is desired to measure the terminal voltage of a storage batteryby of of a Wheatstone cell.C.is connected across a voltmeter voltmeter A) and is known the two at the is connected 115 volts to have ratio arms is an 115-volt point. two A balance ohms. to deflect the M arms same in series with is connected ductor con- N with P way P (Fig.207A) and a standard across at coil 1 . is of such force and deliveringthe small when same Fia. page 149) are each set at 100 obtained with P.. 1. 150. 207^. Snpplj 2266-0. is the A3ni"n 135. What is the terminal battery? 20-0.100 ft.which volts.134. resistance in megohms per mile? 207.0180 box a bridge A standard The (Fig. desired calibrate to potentiometeris available. The cable in problem 205 is its insulation What is 1. putting galvanometer deflects 19. and a balance obtained when P In which conductor is the fault and how far is it from the home ohms. long.the galvanometer deflects 12. What shunt is the insulation resistance of the cable? 206.8 cm. 000-ohm a an The . No in with the parallel impressed upon this electromotive in series with a force of key and .050 not capable To comparatively large voltage are sensibly required by the resistance of terminal current of another force electromotive cell which is deliveringany appreciablecurrent. insulation test of an When a cable the connections made are as the cable is short-circuited and in Fig. " ~ Storage r nt Batter7 D. the the cable in and removed.8 circuit. 2. galvanometer 1.050 additional ohms when zero the terminals of the storage battery across electromotive force of 1. its negative terminal is point a and its positiveterminal to the point h through a 207 A).0001. 208. storage battery of problem 207 The J- Zi a zero. as the galvanometer is found and be cannot 445 PROBLEMS AND QUESTIONS 0 and P = P is then " = . the its electromotive that capacity ohms.6 = end of the cable? In 206. shifted in over series with 6. cm. of to the connected key and reads the the measure 209^. with the shunt set at 1. volt mains. 2.266 ohms are 210. of the meter is the per cent. as shown in Fig.0. is connected across meter. are 214^. of the type shown suppliedwith current from which has a resistance of circuit. Thirty meter be to is (problem 212) It takes 62. an ohms. amp.6 cent.volt. accuracy be made to bring it nearer load meter watthour the average ammeter and the time is found 1. Fig.200 ohms.6 seconds.. error by has terminals.000 the ammeter is the true power if the instrument resistance rheostat.0008 ohm 120 20 ohms with the point? power and polaritybeing observed and proper The galvanometer reads at this voltmeter CURRENTS by connecting the by meter volt- outside the ammeter? In 212. h-a ^ -ffi '^" T T o T A/yv Fig. lamp 117 be neglected? power 211. The unplugged in to 25"watt a The ammeter. 2. in A calibrated voltmeter is connected in . 214A.4 amp. is the What What adjustment should registration? the average voltmeter reading is 21. the lamp? What per cent. 1 volts. 214. In measuring the power taken having a resistance of 0. per is introduced error is introduced error a is introduced ammeter directlyacross of the a with resistance What volts. the directlyacross used.000-amp.23 taken by What P. in order for the of the accuracy per be made to to registration? 1. 220. 148. reading is test a revolutions of counted are is constant What adjustment The should voltage is still 118 volts.0 amp.current a volts and 118 nearer the the two point? correct 232 V.what meter 213. are is connected which value the true the voltmeter zero correction voltmeter. What is reads resistance. ohms unplugged key depressedwhen should be applied to the are tungsten lamp is beingmeasured the When resistance? current? What and the low a When meter volt- a of 12. is connected reads 0. revolutions. What cent. In order astatic watthour coils to make a laboratory test of a 2.an voltmeter reads 70 meter am- resistance of having a the voltmeter. its current a 4-volt storage battery and its armature the 2322. but disc to make at this meter bring it If the at this load? the correct dropped seconds 42. direct.446 DIRECT galvanometer.page 167. the in these two arms.which the voltmeter reads amp. 40 revolutions in 45.980 amp. makes meter cent. and flux. does the magnetic flux return If the excitation be decreased values? What is a How the magnetic flux be brought back to zero? to zero? may What Coercive force? does cycle? A hysteresis loop? Remanence? of in Digitized by terms energy? vjOOglC represent hysteresis factors may the 0. Are dependent ampere-turns relation is the numerical What alone? current on On turns alone? magnetomotive force and ampereturns? largerunit. accuracy for this test? external shunt an terminals current corrected voltmeter 1.mmf. How its basic unit of reluctance? In in the electric circuit does reluctance is the combined? related tance to reluc- a magnetic path permeability? How flux magnetic related to its correspond? length? To reluctances are in series parallel? is it usually necessary to represent the relation between magnetizing curves? What force. by generalshape does Why lower part of such saturation? How may does the 5. State as To is of is due what method law a Why magnetic problems? 7. is the per circuit and armature 447 PROBLEMS ways readilyconfined to definite paths? In a generalway how does the with that obtainable precisionobtainable in magnetic calculations compare flux be in electrical calculations? 2.AND QUESTIONS the parallelwith the in series with The is 150. How to conductance? is meant what between is the such a by curve? variation of to in the relation between electric circuit does of trial and error is the sometimes magnetomotive flux. reads The required current of the meter much How QUESTIONS 1.8 seconds. relation between magnetomotive for increasingvalues of magnetomotive force differ from that for decreasing to zero.in iron and steel. If the magnetomotive force acting upon a sample of iron be increased and the definite value and then decreased again to zero to some from zero be the and does force flux curve plotted. and this law correspond? in solving necessary force acting upon a computations centimeter How inch units? In units? in are magnetization curves plotted in order to reduce computations to the simplest basis? 8.4ir be eliminated from . have? curves variation electric resistance 6. Upon three what How circuit dependent? The upper is meant from B-H with permeabilitycompare heating? governing the What part? be obtained permeabilitycurve a the simple law reluctance.the gilbertor the ampere-turn? To what quantity in the electric circuit does magnetomotive force correspond? is reluctance and to what does it correspondin the electric circuit? What Which is the What and What To 3. In what what In meter this load? at would power be How stant con- the ammeter much What is power required if the meter ON CHAPTER VHI does the magnetic circuit resemble the electric circuit? do they differ from each other? Why cannot magnetic way two The volts and nected con- volts? supplied at 232 were reading is 232 is ammeter of the meter. of its To the How is permeance by permeability? quantity cross-section? 4. a bar magnet. How is the geometricalpositionof the lines of induction related to the ** this relation suggest the term in a circuit? Does current linkages? these linkages be calculated? relation does inductance What How may bear to the total linkages? 11. a general way. Is it possibleto produce an electromotive force in a circuit which is insulated from else? in is motive electrothis everything How. show that to an change by alteringthe value electromotive of force is induced. motive electro" force have in the and coil? Is it when as the bar magnet reaction will be produced between What inducing agent? Upon what two factors possibleto determine the these factors inserted was the induced current induced electromotive of this electromotive force depend? force in volts if known? are 13. force produced? If an induced current is allowed to flow in a coil.-energy? Upon what two factors does it shown that this condition .448 DIRECT CURRENTS is the 9. why is this tendency of the does rent cur- persistdue? is the nature of inductance mechanical property does as does the effect of inductance circuit is How it regardsits effect upon correspond? manifest it be itselfwhen circuit changes? the current of a is not can interrupted? To what is this arc due? Under what conproduced by the current alone? ditions in practice may it become How this menace a menace? be may partiallyor wholly removed? What personaldangers may result from opening inductive circuits? force of self induction 16. What the direction same the 12. what does it indicate constant" In a time value? of lag of a current in a circuit have any quantities regards as practical importance? 16. How How the hysteresisloss related to the loop area? may under How loss be calculated is the loss related to practicalconditions? flux density? What is the Steinmetz the maximum Law? 10. If the flux in current What does value is Lenz's Law? What linkinga coil be made the coil itself. Is it possibleto calculate thi. be withdrawn from a coil. is the relation of this electromotive flowing in the the current it be may How coil? builds up 14. Upon what three factors does the electromotive depend? of a magnetic flux require an the establishment Does expenditure of lished? estabenergy? Is energy expended in maintaining this flux after it is once field coils? What of the power becomes requiredby electromagnet Give examples of electromagneticenergy manifesting itself. If not inductive circuit carrying a current the current to What To an what How die out immediately? To what be short-circuited. will the induced for example. what reaction will exist and the inducing agent? this current between If the inducing agent as. the the to its Ohm's is the "time expressed? circuit? Does does force to the direction of the current this relation affect the rapidity with which the Law circuit and by what two general way. 18. What How is mutual induced How inductance defined? How it be utilized to determine may voltage? the mutual may Explain 20..400 turns exciting coil has ampere-turns way total resistance of 160 a across it the two with that of the plunger. ON CHAPTER certain electromagnet has surfaces Vm excitingcoils.219A. same now Another connected What coil is connected is placed one and ohms. (")? What In 219.each of which has these two coils are connected in series. Is it possiblefor a magnetic flux produced by one coil to induce an 17. act is the problem In a the series with What pere-turns am- Fig. induction? how How inductance the of two be circuits be materially increased? action of the induction is the primary current this current that which in the second factors does this electromotive three the coil from force in another coil depends mutual upon interruptedand why is it necessary interrupted? 21. circuit? force in gilbertsin problem 215 (a)and 217? certain iron-cladsolenoid.How depend? 449 PROBLEMS AND QUESTIONS the may before opening of generator fields be very energy the circuit? duced. 219A. what is the 2. this mains? similar to this magnetic circuit ampere-turns? 1. the reluctance is negligiblecompared inserted the lines of 20 in magnetic magnetomotive on are coil in every the same on 120-volt mains. When induction passingthrough the central of the the core are yoke plunger is observed . what is the line voltage in (a)? What is the line voltage in (6) and what are the ampereper coil and certain turns 217. Explain why the coil produces a hot spark. 216. A and the has 120-volt when the across 218.200 turns.Fig. How does the electromotive this in any correspondto the way of insertion bar a magnet direction of the induced is closed the first is insulated? production of electromotive force by coil? What voltage in the secondary to its direction when Does primary the the is the relation of the when the primary circuit Upon what circuit is opened? force depend? Is it possiblefor all the flux produced by one coil to hnk another? " " is the definition of the coefficient of coupling of two circuits? 19. Upon what two factors does the pull between magnetized depend? How does this pullvary with the flux density? PROBLEMS A 215. If one of the coils in problem 215 has a resistance of 80 ohms and the other a resistance of 60 ohms. materiallyre- gas-lighting spark coil utilize the electromotive force of self induction in its operation? How is it connected in the circuit? Show that the spark coil can be considered as a reservoir in which magnetic energy is stored and later liberated. (o) When total niunber of ampere-turns acting on the magnet if 3 amp. are supplied the line? from and the total current (6)If the coils are connected in parallel is 3 what is the number of supplied ampere-turns? amp. If the iron pole piecesof problem 223 are and have axial cylindrical is 1. 227 A shows branches. 225A shows three portions of a magnetic circuit.? 221.5 in. of the circuit. apart.000 lines. The iron has a bility permea- . of 200. in diameter electromagnet are the At re- is the reluctance air-gap. 80. Compute the reluctance of each portion and the total reluctance of the combination. cross-section is the flux and and 1.200? permeability lengthsof 1 in. luctahce 223.000lines. Compute the reluctance of the magnetic circuit shown of two 227.Compute the reluctance which are similar and which are each half and of 6Q0 the total reluctance throughout. and per sq. in Fig. between The two iron 226A.what is their reluctance if their 226. 6 in.450 to increase from at this flux 350 to of a A carries a permeabilityof plunger. the plunger density? A steel field core 220. What this field core at this flux density? oppositeends of pole piecesof an and are spaced K in. a magnetic circuit composed of in parallel. 226 a. Fig.? Fig. in diameter. density in diameter.280. long and 4 in.000 field core of a dynamo per sq. Fig. magnet flux of is 4 in. is the What 52. lines per sq.000. cm. in. 224. is the permeabilityof 700. The 222. it has lines a is 3 in. in diameter dynamo flux of 1. forming of this gap? Neglect fringing. 226A.. 226. in. Each portion is circular in cross-section. cm. and CURRENTS DIRECT is the What circular What flux carries a netic mag- density in lines per sq. per sq. in. What yt^sMO At-900- Fig. . 452 CURRENTS DIRECT Fig. 237A has a yoke of cast steel and pole of Fig. 154. page 177, piecesof cast iron. Using the magnetization curves determine the ampere-turns necessary to send 120,000lines through the airNeglect fringing. gap. The 237. magnet shown in ClrcnUr CroM- FiG. Fig. 238. field cores of cast are steel and sheet of cast iron the shows 238A has a has and 238A. magnetic circuit of 4 in. square. are axial length of 3.6 in. steel and net cross-section a of 2 X a The over 6 in. 2-pole d3mamo. armature The is of O.H. the iron;the yoke is Using the magnetization Fig.154,page 177, determine the necessary field ampere-turns flux density of 30,000 lines per sq. in. in the air-gap. for an average that 239. Repeat problem 238 assuming the air-gapto be 0.075 in. and field the and enters in armature. the flux cores of the yoke only 80 per cent, curves of (Leakage factor ^' 240. iron Determine = = -^ the 1-25. j hysteresisloss operatingat densities between (Use data of Par. 143.) in ergs per cu. cm. 30,000 lines per sq. in. per cyclefor positiveand cast tive. nega- 241. transformer A yoke of silicon steel has is the hysteresis loss in ergs per density is 40,000 lines per sq. in.? What In 242. cu. produces 1,200,000lines of induction. of 12 amp. of lines induction turns, 2,000,000 243. When Assuming 244. remains 243 Determine that in the total constant, determine when in. flux linkages? . What of the circuit? certain excitingcoil of 2,000 the linkages? coil. What are a link the its inductance the turns cu. of 5 amp. henrys? permeability of the magnetic circuit the the inductance In of 600 current turns, a are flows in current is the inductance What are of problem is doubled. the current when doubled. closed magnetic circuit of cast steel the net ampere-turns per in. The cross-section of the magnetic path is 12 sq. in. and its net 246. 20. are a volume is the inductance What linkagesper ampere? the are What a cycleif the maximum in. per certain electromagnet having 800 a 453 PROBLEMS AND QUESTIONS a length is in. If 1 amp. flows in of the circuit using the curve 30 inductance exciting coil, determine Fig. 154, page 177. the of the Repeat problem 245 for an excitingcurrent of 2 amp., or double the in problem 245. To what is the change of inductance due? the excitingcurrent 247. When of an electromagnet is flowing,there are 1,800,000lines of induction linkingthe circuit. The excitingcoil has 2,400 If the exciting current turns. is interrupted,requiring 0.5 second to is the what the induced completely rupture voltage across arc, average the ends of the excitingcoil? 248. Re-compute problem 247,assuming that the circuit is interruptedin 246. value of that 0.2 second. 249. A certain electromagnet has of 5 ohms and is connected of the magnet? cent, of its ultimate How constant per this instant? values If the 250. what the in the the time current to ultimate value? In which problem of the 63 per Illustrate by henrys and What current will be the value by current a a ance resist- is the time reach to of the current sketch, marking 63 at the electromagnet of problem cent, a of sketch its ultimate and compare How 249 be doubled, long does it take value? with is the What problem 249. given value of current first reached? 261. Six amperes flow in the excitingcircuit of problem 247. Compute the induced the circuit is opened in 0.5 .second, electromotive force when using equation (75),page 191. 262. If the excitingcurrent of problem 245 is reversed in 0.1 second, the ends of the excitingcoil. the voltage induced across determine V of 2 henrys and 253. A certain generator field circuit has an inductance the field The terminals must carries 100 amp. induced voltage across time which exceed is the minimum be allowed not can 1,000 volts. What in for opening the field? How much this field? is liberated opening energy the What is the average during opening period? power 864. Repeat problem 253 with the total field resistance doubled by means is the of the circuit become? constant reach What rise of the it take of 2.8 mains. problem. resistance does 110-volt long will value? Illustrate the involved inductance an across a of the field rheostat. . t 454 DIRECT 255. coils A Two placed that and but are B, Fig.255A, are insulated electrically of the flux produced by one of the coils links 80 per cent, has 120 turns Coil A other. CURRENTS and coil B has 200 turns. When 2 the amp. flow in coil A, What the A lineslink B? 220,000 lines link the coil. How many coefficient of coupling of the two in circuits? If the current in }^iosecond, what induced voltage results in 5? In A? so is terrupted is in- Fig. 255 a. The 256. by of 5 flux that same problems and in A by 2.0 amp. voltage is induced in A upon What voltage is induced in 5? in henrys the mutual inductance Determine 255 produced is produced interruptingthe What 1.2 amp. in 0.1 second? 257. was 256. What is the self inductance of coils A of A? 1.2 and in B amp. B, in Of B? B .1 Fig. 258^. 268. iron with Coils A core the as and shown other. B in of problem Fig.258^4,so 0.1 amp. in A 255 that now are now linked magnetically by all the flux of practically one produces 200,000 lines in the an links joint magnetic circuit. 269. what what rate If the in B the current must be in B is 0.05 amp., current interruptedin is In self inductance The of the circuits? produce this will same flux? Oi B? of A ? in A of problem 258 0.1 amp. in A? force is induced electromotive If the inductance At in B amperes many is the self inductance What A? How 455 PROBLEMS AND QUESTIONS 5? Of B? interruptedto in what second, is the mutual What of A? 0.05 induce 10 volts in the circuit be time should opened? and other flat pole The 260. a electromagnet are in contact with each 2,000,000 lines passes from one to the other. If in. X 5 in., what force in pounds is necessary to pull piecesof an total flux of each cross-section is 4 these pole piecesapart? ON QUESTIONS 1. If two each insulated ellipsoids near CHAPTER other IX are connected to the terminals will the what electrostatic machine, upon portions of the ellipsoids an density of charge be greatest? Would any considerable change be observed of charges if the wires shown that charges are be were disconnected? How can it "bound.'* force exists between What machine to the in these two charges of unlike sign? What is its direction? charges of like sign? positivecharge is brought into the neighborhood of an insulated is the What and uncharged ellipsoid or sphere,what phenomenon occurs? relation of the induced charge to the inducing charge? Distinguishbetween it be shown experimentallythat free and free and bound charges. How may bound charges behave differently? 3. How does a small positiveelectrostatic charge act when placed near two conducting bodies between which a difference of potentialexists? Can For 2. If a the distribution of electrical stress by lines in Where them a do manner is the effect in electrostatic lines beyond magnetic circuit and 5. If a needle or such bodies be sented reprebution? showing magnetic distri- electrostatic lines originateand with lines of induction 4. What in the air between similar to that used in a a and terminate? Compare lines of force in this respect. dielectric medium certain value? of increasingthe density of Is this same effect noted in the in the electric circuit? other sharp projectionbe raised to a what high potential, at this projection? What is the condition of the air in this region? What is the effect of a further increase of potentisd? Distinguishbetween an insulator and a dielectric. Name two substances that are good insulators but poor dielectrics; sulators. good dielectrics but poor inis dielectric strengthexpressed? In what terms 6. What is the effect of applying a voltage to an electric condenser? is the order of magnitude of the time requiredby a current What to charge such a condenser? To what hydraulic Why does the current cease to flow? this be can compared? phenomenon effect is noted 456 DIRECT 7. How How it be shown can that electricity is actuallystored in a condenser? quantitywhich can be stored in a condenser vary with the the does CURRENTS What simple voltage? and voltage? relation does this give between is the usual effect of insertingsome 8. What air between condenser plates? What to what charge,capacitance dielectricmedium other than is "specificinductive capacity" and What is the dielectric constant magnetic property is it analogous? Of rubber? of glass? Of mica? is the 9. How determined? condensers equivalentcapacitance of To connected electric circuit condition is this what is the equivalentcapacitance of condensers connected the electric charges on What is the relation among determined? connected of condensers in series? equationrelatingto circuit is the the parallel analogous? 10. How number in in series each of a To what equation in the electric of condensers capacitance equivalent in series similar? in series be each of a number of condensers the voltageacross if the line voltage and the individual capacitancesbe known? 11. How can calculated voltage relations dependent at all upon the insulatingproperties of leaky condensers, upon what the does of the dielectrics? In the case ultimate voltage distribution depend? Are these 12. How it be shown may Upon Upon what 13. that electric energy be can stored in a denser? con- factors does this energy depend? factors does the capacitanceof a parallel plate condenser what of depend? What is the effect upon the capacitance of changing the area them? Of substituting the plates? Of decreasing the distance between hard rubber or glassfor air? employed in the measurement capacitance? Upon what fact does the ballistic galvanometer method What relation exists between the quantity passingthrough the 14. What two and Should methods are commonly pend? de- vanomete gal- ballistic throw? its m'aximum be made the measurement of upon "charge" or upon "discharge? " galvanometer calibrated? bridge method of capacitancemeasurement. Compare of resistance measurement. How it with the Wheatstone bridge method the from formula differ for formula does the bridge capacitance employed of power and what simple What is the source resistance is measured? when detector is used in the capacitancebridge? 16. How Upon what principle a disconnection in a cable be located ? may this Is method of measurement does this method applicable if depend? the fault is grounded? Explain. How 16. Describe is the the ON PROBLEMS 261. the condenser capacitance of its platesis (a) 220 has a potentialbetween flowing at a uniform be charged in 0.2 second current may A 12 m.f volts? is necessary in each case? rate IX CHAPTER . What is its charge when (h)440 volts? in order that the (c) What condenser QUESTIONS of 760 volts. What What is the 263. is 0.002 coulomb? found be potentialacross How long in capacitance of be the should a 457 PROBLEMS 70 microcoulombs It is desired to store 262. AND condenser a . potential a the condenser? condenser 40-m.f at in which the charge of 1 milliampereflow in order to charge this condenser to the above potential? 264. A certain condenser consisting of two parallel plates,with air as has A 0.00012 m.f. of slab of tween dielectric, a capacitance glass is placed beThe the plates occupying the entire space. capacitance is now to 0.00072 m.f. condenser of must a current is the specificinductive What capacity of the glass? problem 264 is charged to a potentialof 300 volts between Glass is then inserted plates and the supply then disconnected. between the space. This insertion of the glass the platescompletely filling in no way changes the value of the electric quantity on the plates. What is after the of the condenser the insertion voltage glass? 266. A plate condenser,with air as dielectric, has a capacitance of 0.0012 The 266. ni.f. and 300 immersed in its terminals. volts is impressed across bath a of transformer oil having the voltage supply remaining connected. before 267. Four condensers and each in what must condenser is then dielectric constant a is the charge What on of 2.5, this denser con- in the oil? after immersion connected are on and The having capacitances 12, 16, 20 220-volt mains. across parallel be the capacitance of a and What 30 m.f. tively respecis the charge singlecondenser to replace the four? 268. Three connected condensers in parallelacross 400-volt mains have is the capacitance of What charges of 600, 800 and 1,000 microcoulombs. the and three? each what singlecapacitance would replace of problem 267 are connected in series across 269. The four condensers each is the voltage across of them and what single these same What mains. What is the charge on each condenser? condenser would replace the four? 270. Four condensers connected in series. The voltages of the condensers are densers are 50, 70, 80 and 100 volts respectively. This combination of conof be replaced by a singlecondenser 6 m.f. having a capacitance can What is the capacitance of each condenser? What is the stored energy 271. A condenser has a capacitance of 20 m.f. In it is 100 volts? the voltage across in the condenser when 200 volts? what ratio is the energy increased if the voltage is doubled? condensers 272. Three having capacitances of 20, 40 and 60 m.f. respectively in series across connected is the are a 600-volt supply, (o) What is the of each? each? is the energy (c) What (6) What voltage across energy of the system ? 273. Determine of the three condensers energy of the system when the same connected in parallelacross voltage. the stored problem 272 274. air condenser An connected are consists together as one plate between terminal intermediate are 12 in. X 12 in. and capacitance of this of three the condenser? the two and the other outers. plates are plates. The spaced Ke The outer two terminal ones is formed dimensions in. apart. are the of each by plate What is the Digitized by CjOOQ Ic 458 DIRECT 275. If the space filledwith CURRENTS the between having paraffin, a platesof the condenser dielectric constant of of 2,\,what problem Is 274 does the capacitance become? is to be made of alternate layersof glass high voltage condenser of 8. the glasshaving a dielectric constant and tin foil, The glass is ^4 276. A in. thick and How plates and sheets of tin foil are many having the tin foil is 2 mils thick and its dimensions capacitanceof 0.02 a m.f.? 3 in. X to make necessary If the glass platesare is the siae of the completed condenser? 277. In a bridge measurement of condenser are a 4 in. condenser 5 in. X in., 6 what connected shown as 100, Rt capacitance? Ri = In 278. a in Fig. 183 1,242,Cj = test for a (6),page 0.4 m.f. = capacitance the bridge is When 213. What a balance is obtained is the value of C", the unknown cable fault the apparatus is connected in shown as In the capacitance measurement of the part x the Fig. 184, page 213. In the measurement of the galvanometer has a ballistic throw of 4.2 cm. capacitance of the perfect cable plus the looped end of the faulty cable If the length of each conductor is 1,800 the deflection isfound to be 16.4 cm. ft.,how the far from point of test is the cable broken? ON QUESTIONS 1. In what How flux? The varied? linkingthe coil of a generator armature does this voltage vary with the speed? induce voltage? How is the flux way does this X CHAPTER The number of turns in the coil? 2. If instead of regarding this voltage as due to the change of flux linking it is considered as being due to the individual conductors a coil, cutting in If is the the result affected? considered ultimate is voltage flux, any way how does this to the cutting of lines by individual conductors as being due ? flux The density The velocity voltagevary with the length of conductor? of the conductor? definite 3. What emf ., flux? relation exists among the conductor direction in which the What simple rule enables of the one emf. direction the and moves to determine induced these in the of induced the direction of the relations? rotating coil,(a) when its plane lies the coil is in the plane perpendicular to the flux? (6) When its sign? Explain. parallelto the flux? Does the voltage ever reverse in 5. How current the a coil be alternating produced changed to may is the effect of adding coils to the rotatingmember? direct current? What what due? the "ripples" in a voltage wave To are 4. What 6. In what coil type? is the value is the open way number of coils and 7. Name two turns serious be the (Fig.192)? types, even fasten conductors the surfaces Show that though the same. objections to the ring winding. How the drum winding? What two methods in on armature force is different in the two objectionsovercome and different from* the closed coil type of armature type is the gramme-ring Which the resultant electromotive a of armatures? Which are are these used to is the better method why? 8. What is meant by "coil pitch" and what is its relat^^Si"CP^l" pitch? 460 CURRENTS DIRECT Is it always 20. possibleto fit a winding wave of slots if all the slots fixed number to utilized? are having armature an What Explain? a shift make- accomplish the desired result? may 21. If the number of pairsof poles is even, is the number of commutator of of is odd? if Answer the odd? number even or pairs poles segments be used to is the minimum 22. What winding? What would sets be used two of brush sets that number is the maximum and why? be used in can a that it is possible to use? number is the maximum Why wave When number usually desirable? winding? In what of poles? How paths way winding? paths in a duplex wave winding? A triplexwave many is it A lap winding? and 24. When desirable to use a wave winding why? Give specific reasons. other 26. In addition to forming a part of the magnetic circuit, what function does the yoke of a generator perform? Of what two materials is it made Describe a process whereby the yoke is made without and why? casting. 26. Of what The pole shoes? materials are the field cores made? What the of Where each is the sections? used? two are core generalshapes If not, how isit built up? 27. Is the armature a solid casting? By what in How the held methods two are are stampings produced? they position of the ventilating when What is the purpose placed upon the armature? How many is the number 23. paths there in are of such simplex wave a affected by the number ducts? 28. Sketch methods general types two used are of slot. Where to prevent the conductors from is each used? What being affected by two ugal centrif- forces? 29. Of what is the commutator segments? How connections made? What usuallymade? What the is the purpose made? of the pressure brushes? is used insulation is used Of what the brush? on between are material to hold the brush of the plating on are the coil brushes the commutator? is the purpose What of pig-tail? PROBLEMS A coil 20 279. in What clamped together? How the segments is the purpose What 30. are a uniform is the What (") If the ON X CHAPTER having 50 turns, rotates at a speed of 600 r.p.m. magnetic field having a density of 200 lines per sq. cm. (a) in the coil? induced voltage average flux and the speed are both doubled, what average voltage is cm. square, obtained? 280. a A wire 40 magnetic volts are 281. field induced at a speed of 2,000 cm. long moves having an intensityof 6,000 lines per cm. between the ends A uniform magnetic field perpendicularlythrough a coil 40 per second sq. cm. through How many of this conductor? is just sufficient in. X 12 in. The in cross-section to coil has 80 turns. pass If QUESTIONS the coil slides out what AND 461 PROBLEMS from this field in 0.001 second voltage is induced due to the change in flux and at a uniform linkingthe coil? rate, What voltage is generatedby the cuttingof the flux by the individual conductors? to the 12-in. one parallel (Work with the coil slidingin the two directions, side and one parallel to the 40-in. side.) 282. An has 40 slots. Design a 2-layer, armature 4-pole,simplexlap a winding, in which the back pitchis 21 and the front pitchis 19. Make winding table. 283. Repeat problem 282 making the front pitch21 and the back pitch 19. Which winding is progressiveand which is retrogressive? 284. Design a 2-layer, 40-slot machine, simplexlap winding for a 6-pole, choosing the proper pitches. 285. An 8-polearmature has 128 slots and 6 winding elements per slot. Determine a correct value of back and front pitchfor a simplexlap winding. Sketch a few slots with their winding elements and connections. How commutator are necessary? segments many 286. Repeat problem 286 for a winding with 8 elements per slot. delivers a total current of 287. A 6-pole, simplex,lap-wound armature How 220 volts. 228 amp. at ture? many amperes per path through the armaWhat is the How of the volts kilowatt rating path? many per machine? 288. If the machine of problem 287 had Per brush? be the amperes per path? 289. Repeat problems 287 and 288 a duplex lapwinding,what would for an 8-pole,200-kw., 220-volt generator. 4-polearmature, the winding to winding table for a 60-slot, There 2 winding elements per re-entrant are winding. duplex,doubly 290. Make be a a slot. 291. Repeat problem 290 using 61 slots and making the winding singly re-entrant. has 33 slots and 2 elements per slot. Design a 4-polearmature winding for this armature, having a back pitchof 17 and a simplex wave Make front pitch of 17. a winding table. (Check the pitch,using equation 100.) 16. 293. Repeat problem 292 making yi, 19, and y/ 294. Attempt to place a similar winding upon a 34-slot armature. Then omit one slot,using a dummy coil,and repeat. 295. An 8-pole,660-volt,60-kw. generator has a simplex wave-wound How armature. amperes per path? many 296. Repeat problem 296 using a duplex wave winding. 292. A = = ON QUESTIONS 1. A What certain armature are has a the separate effects CHAPTER of conductors fixed number on the induced the is doubled? on its surface. voltage of (1) doubling the enteringthe armature; (3) of pathsthrough the armature fiux armature; (2) doubling speed reconnectingthe armature so that the number of the XI 7. In the in fieldcurrent? 5. Is there any difference between increasing values of field current Explainany 6. field current of the generator same as abscissas and the induced voltage at constant speed as ordinates. What is the criticalfield resistance? What tests and remedies should be the generator buildingup. shunt generator. a of high resistance? how Is the fieldof comparatively Explain.for the current ous directions in the variindicating multi-polarmachine. Sketch a curve showing the values of armature motive magnetosurface. (2)Using a drop wire with the field. In CURRENTS given generator. The generator a abscissas as and the flux leaving polesas ordinates. the connections used in determining a saturation the connections of curve. Sketch the saturation obtained curve with with decreasing values? and that obtained difference. Show the effect of the above flux on the distribution of the total flux is the neutral surface. curve relatingampere-turns of the fieldand the flux of one north Why is the first part of the pole. Which Which conductors produce a forward field? in fieldto the brush generator what is the Into what two components can a is the effect of each on an component? produce a demagnetizing effect? armature cross-magnetizingeffect? the armature. each of which 10. Sketch the conductors on loaded 15.why does not the flux start at zero value? line? the At curve a straight practically higher values of field current whydoes the induced voltage increase less and less rapidlyfor any given increase armature 4." ashunt What limits build up? can Give three causes. Give two reasons why the generator should be separatelyexcited. (1) simple fieldrheostat. What When axis? How machine? is the relation of the direction of the armature brushes the moved are resultingdirection of the armature this be resolved? What 13. Show that a similarityshould exist between two curves plotted as follows a : 1. How along the armature made in the brush be must position? change zone affected? What . Show that Ohm^s Law can be expressedgraphically. Sketch low resistance or Explain in detail voltageto which a 9. The field ampere-turns of of its north one 2. What What does it affect the positionof the neutral plane? effect does the change in positionof the neutral plane have upon the brush position? flux in a 12.462 DIRECT 2. upon what two factors does the induced voltage depend? If the speed of the generator be maintained constant. 14. Show the flux produced by this force along the armature magnetomotive force when acting alone. upon what factor does the induced voltagedepend? 3. prevent may the machine used for each? in is the generaldirection of the flux produced by the current effect does this have upon the resultant What the armature conductors? 11. togetherwith the poles. What two quantities in when Ohm's Law this manner? are expressing plotted Using a 8. generator "builds up. a conductors. of principle ideal commutation tribution curve assuming uniform current dis- the brush. Why does the machine finally"break down?" follow the from short-circuit the curve does return obtained not curve Why current? with increasingvalues of armature 30.what is the of effect of arcing on for the commutator? eliminatingthe Why of the cause arcingbe a reason appearance arcing as soon as possible? Why is it not desirable to use emery paper or cloth in grindingbrushes or smoothing the commutator? 26. What is the relation of the polarities of the main polesand of the the of direction to commutating poles rotation. Name four methods reduced.in a generator? In practice the commutating polesadjusted to the proper strength? how are 29. Sketch advanced How commutator points to the fact that by the brushes is not due? How may over the carbon? taking Why of or even coil a them so are current conduction? pure it be reduced in To eliminated? methods. Sketch the characteristic. Sketch over an 463 PROBLEMS reaction is either eliminated by which armature each method. What coil? in such a current over 20. effect of having voltagesinduced in a coil during the What limits the current time that it is being short-circuited by the brush? is the 18. 27. What affect the uniform the brush? 19. general. 23. State the 17.the same of a commutating pole.AND QUESTIONS or 16. during the commutation evidence the what is "high mica" 24. Why What are vents preload is from "unbuilding" as a generator applied? ' . Why is the commutating pole connected in series with the armature? Why has it an unusually long air-gap? 28. (6)brush too far does armature an is the undergoing short objectionable? 22. upon What is the effect period? What effect does the relation of the brush positionto is the advantage of copper brushes brushes used almost universally? two too order of magnitude of the voltages induced circuit? If the voltages are low what makes from Name back. (c)brush What What distribution of followingconditions: (a) Brush coil have self inductance? the voltage of self induction have the neutral zone? carbon for the commutation of this self inductance 21. Sketch the connections used in obtaining the shunt characteristic. In should any wide. What changes occur in the flux at the geometricalneutral of a generator What is the effect of these changes upon the brush as load is applied? position? Why do the brushes have to be moved ahead of the load neutral plane? 26. Give three reasons the voltage of a shunt generator drops as why these three reactions cumulative? load is applied. too Why do these currents curves far. Show in order to obtain that instead of moving the brushes forward the proper result may be obtained by the use commutating flux. of a How series generators be used to control the voltage at the end Upon what portion of the characteristic does such a generator may feeder? operate? Sketch the connections. How may Is such taken 46. In what curve. a What a precautionsmust be taken in the booster? affect the generator tic? characterisit be drop in speed chargeableto the generator? How may the speed of a prime mover into consideration? State one essential difference between a unipolar generator and the to prevent the armature being ordinary type. What is case? by generator regulation? Does regulationindicate that per cent. Show may total power objectionabledrooping characteristic improved? is the What generator? What the How the are additional veloped de- effect of the Sketch the characteristics of connection "short the upon and shunt" nection.a^ . the shunt upon how explain.464 DIRECT effect does 31. in each same rated speed have an a separate series fields? two is the effect of speed upon the degree of compounding. may it be utilized? for desired degree of compounding characteristic and how does the series generator differ fundamentally from the shunt In the type of load that it supplies? generator in construction? 40. of the shunt connected turns do they differfrom the shunt field turns? the difference between "long shunt" and way largevalue of the for supplying one a be determined? armature may generator be in what a adjusted that so generator is a desirable Explain. Name a very common types of machines. characteristic and of series turns the number a isthe armature What be determined. is meant by the "total characteristic" 83. installation and operation of such 46. What design is necessary is the advantage of this type of machine short-circuited on itself? What over are the ordinary type and its disadvantages? for what type of work is it best What adapted?. Name two Why are specialcommutators necessary? of transmission? Thury system power " the by the right- common Where is it used? 44. 43. con- characteristic? flat-compounded and an is each used and why? imder-compounded generator. How is the degree of compounding in a generator adjusted? When do generators have over-compounded. if the What in each case? no-load voltage is the same Compare this with the effect 37. Describe the external characteristic of the series generator and show How its relation to the saturation 41. What lamp loads? is its relation to the shunt within How characteristic? an the How of a 36. of speed 38. Show may 39. is the What " use of the seriesgenerator. does the machine way "build up?" What is meant Why is it desirable to operate upon side of the external characteristic? criticalexternal resistance? hand 42. Where 36. What CURRENTS runninga generator at higherthan its characteristic. 34. provided that the field current upon the no-load volts the are is meant 32. there 300 4 poles and are wound is wave machine making two parallelpaths through the armature. what is the rating The 297.. armature between flux per There 400 are and field shunt pole and ampere-turns per pole.lap-wound machine surface.? What is the induced voltage when 1. When required for problem 301 speeds in problem is 301.m. taken for the saturation curve 301. running at 600 r. The The surface conductors on the armature.p.when the generator of 550 r.p. Plot this saturation The 302.m. has per and then replotit for 550 r. 220-volt generator. the Determine gap operatingat 304.m.m.the Tirrill regulator? What is the Of the relaymagnet? Why cannot control magnet? of fields of machines the to largecapacity? applieddirectly of the main function this regulatorbe How of principle is the basic 47. rotates the armature at 800 r. The followingdata were 299. etc. What 465 PROBLEMS AND QUESTIONS it be may appliedto these machines? XI CHAPTER ON PROBLEMS pole faces of a shunt generator are 8 in.m.p.220-volt generator. the approximate of ampere-turns number and for the iron at 220 volts. the poles at no load is 47. and field resistance is adjusted so that the machine builds up to 220 volts.p. 300. across A generator the armature. square and the average has machine flux density under the pole is 45. the pole faces are 12 in. 303.000 r. does not build up and what results field is connected shows What 4 volts.600 lines per sq. In an 8-pole.p.m.? 298. If the current per path in problem 297 is 20 amp. is the When probable remedy is suggested? . of the machine in kilowatts? Repeat problems 297 and 298 for a simplex lap winding.the speed. square. conductors If the armature is lap wound. in. generator of problem 301 is conductors 440 turns curve the on pole. the number of conductors. a voltmeter across this fieldcircuit is opened the voltmeter reason that the machine When What field current the shunt the armature reads 7 volts. per slot the rated load? at to give no are voltage necessary of a 20-kw. Plot a curve a 4-pole. the generator of problem 301 is operatingat 600 r. remaining the same. in. the criticalfieldresistance for both Determine Determine the field resistance necessary volts at each 305..000 lines per sq. how many 750 r. what flows through the fielddue to the residual magnetism? current What the induced from voltage results from this last voltage? 306.p.p.m. The flux density under is The speed of the machine 16 There are slots per pole on the machine. this field current? fails to build up. for the generator to build up to 220 speed. armature resistance of generator is 550 armature resistance volts when is 0. maintain the voltage at the load constant at 230 volts from . demagnetizing and cross-magnetizingajnpeTe-tums are there on the many when the generator delivers 120 amp. should be the terminal What that it shall regulateto within 6 per cent. A 75-kw. izing demagnetmany the surface of the armature generator deUvers conductor. distant. At the same resistance? is the armature taken by the shimt field. flow in the commutatingof commutation full-load current pole circuit. The rated of the generator is 80 amp. The voltage of voltage is being induced a shunt If the delivers 100 amp. amp. What are amp. The the generator is neutral flux of Repeat problem 307 809. the generator. CURRENTS are of a 25 How there? many magnetizin de- there? 10 space grees.000. A compound generator has a no-load voltage of 230 volts. equal to the no-load volts? It is specified no-load voltageof 119 volts.3 the ohm. What is the What power is being generatedin the armature? is 250 ohms. The most dition satisfactoryconis obtained when 60 amp. in the flux of 1. 316. Repeat problem 310 for a generator having the same of poles number and armature conductors and deUvering the same but with a wavecurrent. advanced magnetizing ampere-conductors are and cross-magnetizing ampere-turns 310. wound is the ratio of the kilowatt capacities of the two What armature. a carryingits rated load and plane.8 resistance The armature amp.000.000lines.220-volt shunt generator has 228 volts induced in its armatime 12 when it is deliveringits rated load at 220 volts. regulation? Why is the induced voltageat rated load is its per cent. a the brushes when 240 conductors the brushes is the resultant flux? s"turation. what in the armature? ture 314.466 DIRECT no-load 807.08 ohm.. What not The no-load voltage of the generator of problem 314 is 234 volts. A circuithas conmiutating-pole a resistance of 0. voltagewhen it delivers its rated load? A shunt 316. de4-pole generator are advanced The armature How is lap wound and has 496 surface conductors. armature? of the electricalefficiency 319. There The and cross on If the brushes advanced are 50 are making how 15**.what 308. bi-polar flowing amp. a The 200-kw. What this across the be must a shunt to be connected commutating-polecircuit? terminal 313.over a 1. are itselfproduces armature the effect of in each bi-polargenerator is 3. It supplies 318. brushes of a machines? 312. load. a of the geneis the total power being developedin the armature rator in and is lost the armature this much of How in problem 314? power much is available for deliveryto the is lost in the field? How much 317. It is desired to cable. The are When no-load glecting Ne- 30**.000lines.000. how generator has What external circuit? delivering50 terminal voltage of a generatoris 600 volts when resistance field shunt the ohm and is 0.? armature 311.situated 800 ft..000CM. . How it be can shown resistance alone does not that taken ? coil value? zero In what To field a should be made tem? sys- armature? determine any the of a Why by a necessitybe generatinga voltage when it is rotating? What is the relation To the direction of the of this voltage to the direction of the current? appliedvoltage? tage? electromotive force greater or less than the applied vol9. How How change have per of upon cent. other simple the direction the direction of the force enables method to one of be can determine this relation? 6. In what to a motor? what are very In the motive electro- the armature? important in consideringthe ability suit- work? does the torque of the shunt motor vary with the load? Why? Demonstrate. does the speed vary with the load? Ordinarily is its 16. Why are the torque reaches its when large number a of conductors upon the armature desirable? three factors is the torque of an armature proportional? factors two what b the machine. What In what is torque? In the metric 6.to torque proportional? one d. State convenient a rule by which the relation among the current. how shunt two the load is tion? reac- the the generator? a force? 14. What generaleffect of direction of rotation for one case of a motor? applied of the interpolesand does this relation compare How with a The current flowinginto characteristics for commercial motor what motor is its firsttendency? does this tendency affect the back motor. What motor a the fieldflux does this movement on is the effect upon the speed? the main poles.the What brushes have? the speed of distorted by armature motor a direction should the brushes be moved In what similar does quantities two direction is the flux of 11. When of the as is the relation between 12. To of taken what load? when extent By is the the speed removal the series motor is of of a vary with the load? How does load? series motor load? What being installed affected by the application should be precautions for industrial purposes? . Show that units is it expressed? In the British system? coil carrying current when placed in a magnetic develops a torque. In what positionof the coil is the torque a maximum What to the armature When is it zero? change in the connection 7.468 CURRENTS DIRECT 4. How does the flux in a series motor this affect the variation of torque with 17. Is the coimter Why? By what quantity do the two voltages differ from.upon depend? 10. the direction of the field and What determined. effect does armature What reaction speed with load excessive? the speed? is meant What by "speed regulation?" Does the have as regards a motor's perspeed regulation any significance formance? To what general type of work is a shunt motor adapted and why? 16. What a load is appUed to 13. each of current amount motor must motor other? Fundamentally. is the advantage voltage release? why? What two functions controller perform outside actual startingduty? 31. What is the nature of the speed and torque characteristics of the differentially 21. Exin startingthis type of motor? is the effect of reversingthe be reversed? What precaution is necessary may motor a line terminals? 24.QUESTIONS 18. What boxes made? The largertypes? . Of what material are resistance units for the smaller types of starting 33. What two additions to the startingresistance of Fig. Sketch the connections of the no-load 30. In what way do the windings of a compound motor differ from those For car AND of what reasons shunt motor? a shunt In what A series motor? two with ways. What of the back the arm? effect motor stopping by throwing starting of 29.304. 299. page 335? How is this starter operated? 32. Sketch the connections incorporatedin a 3-pointstartingbox? of a Why? Show that the startingresistance which is in series with the 3-point box. When the are release of series motor the over controllers used no- and What starters. To PROBLEMS 469 what general types of load is a series motor adapted and why? is it especially to street adapted -railwaywork? 19. page 330. What factors are plotted in giving the characteristics of a street motor? Why? 20. a hold-up magnet in series with the shunt field? 27. " M. respect to the the series winding be connected? winding. 26. How Is this type of motor in general use? plain. principle the current when controller operate? Why do the plungers remain down is large? Why do they rise and close the contacts when the current decreases? When is it used? is the principleof the magnetic blow-out? 34. is to short-circuit this resistance on starting? How Why is it necessary this accomplished? 28. may speed characteristic of the cumulative compound motor? What has it the series motor? over advantage For what general type of work is it best adapted? 22. advantage that of motor the connections having operation is this objectionis of sirable? 3-point box undethe of use a 4by What is the principle a overcome 4-pointbox. Upon what do the plungers and solenoids of the E. Under what conditions Show Why? Sketch point box. The is the What torque characteristic? motor? What 23. What two are advantages of automatic starters in medium motors? out In resistance the largersizes of motors? in the type shown in What may a sizes of limits the rate of cutting Fig. How is the should a shunt motor be stopped? Give reasons. shunt field when the arm is in the running positionhas little effect upon the field current. Why is starting rheostat a for necessary direct-current In what circuit is the startingresistance connected? connected in the line? motors? should it not be Why 26. Sketch the connections of a starting box containingthe fieldresistance.G. a 4-motor its are car. Can by "dynamic braking?" Where is it used? a of braking? be brought to a standstill by this method motor armature Explain. the Stow motor? be obtained with this motor? principledoes the Lincoln Upon what advantages? 40. type of brake output of the type lend itself to ready calculation of torque and power brake the and arm motor? by the dead weight of Explain. general principleunderlying the multiple-unitcontrol? is the What is the train line? What 44. What speed equation is varied in the Ward-Leonard How many machines are necessary in this system ? speed control? is its chief advantage and where has it been used extensively? Name system of What disadvantages. 41. in this a simple type What type? 48. What how can is meant Describe 47. of a of these factors is varied? the of control? Name two serious advantages of this method disadvantages. In what what and it be determined way principleis the is a correction be made? of rope A bundle is 800 How balances coolingprony are sary neces- brakes? a ON sq. is especially of speed obtainable? What adapted to type of motor range Name this type of speed control? 39. What motor operate? What control of railway motors? by series-parallel Sketch the half speed and the maximum is meant Why speed is such control desirable? connections 42. 43. 36. What is regenerative braking and where is it used? the efficiencyof a it is desirable to know occasions where 46. How Give other reasons two why automatic objectionsovercome? three it is reasons control is desirable. brieflythe Name sequence of closingof the contactors in starting a train. w^ith speed control of good commutation.470 CURRENTS DIRECT 36. method common part of the a magnetic fieldwhose bundle of wires which sity den- lies . What two factors only In the armature motor? What be varied in obtainingspeed control can which resistance control. brake. That XH CHAPTER of 16 wires lies perpendicularto lines per many of Upon speed counter differ from a tachometer? method of based? speed measuring magneto-voltmeter does PROBLEMS 328. Give on these are in a 2-motor In car. objectionableto place the main troller conwhy the platform in the largersizes of electric car equipment. What is the principleof the multi-voltagesystem? How are coarse Fine adjustments? What is the objecadjustments of speed obtained? tion are to this system ? factor in the 87. What principleis involved Why can a wide of range in the speed. Give two Does this motors? is for often used What loading motor. two 38. What is meant 46. cm. What factor method? in speed equation is varied in the field control the What limits the two distinct advantages of this method. and is 50 amp. What veloped kilogram-meters is detorque the current is 5 amp. What counter it is taking 80 when running as a the armature 338. and the armature when the takes 30 amp.the resistance of 0. (See Fig. 471 PROBLEMS AND QUESTIONS kilograms is actingon the entire in each wire. 286(o). Obtain the result in pound-feet. at 110 volts? motor of a 4-pole shunt has rotatingat 1. A pulleyhaving a diameter of 14 in. from If this the mains? the line? The What electromotive 420 same machine surface were force when conductors force does it develop when flux is 2. What net torque in poimd-feet is developed by each pulley? 331.000lines per is its terminal develop armature be its internal electromotive delivering80 amp.page 313.04 ohm. What cm. What the flux remaining constant? 50 amp. in conductor lie in the magnetic field. of the forces the directions indicating acting.2 ohm. ? resistance would what force does this motor armature wound. wave from amp. The distance from the center of the first gear to the point of contact of the teeth is 6. 336.) of problem torque is developed? current motor has a 333 is halved. back What is 0.. belt. it take would current (60 amp. of contact What The pressure between is the torque in pound- feet developedby each of the gears? 330. drives 50-in.) The distance across and 14 in. requires amp.in this fieldis 25 bundle when being force in flows of 12 amp. voltage when Its armature the motor takes . When the also halved. current a the long. respectively. is the torque developed motor torque.the pitch circle having the teeth at the point diameter a of 13 in. What The this motor of armature a is connected force of 105 shunt across volts. When the flux density in the air-gapof a shunt motor is 45. torque is is the torque available at What losses? the motor required to overcome the pulleyin each case of problem 333.5 in. in.000 lines per sq. a a The constant? 336. When of problem 333.? Sketch by the coil when per conductor the coil and the magnetic field..m..-ft.. is 400 lb.p. removed from the armature the load is entirely the motor What it 8 to armature keep running. of active this coil parallel to the field is 12 in. A coil consistingof 16 turns of wire lies parallelto a magnetic field having a strength of 30. Repeat problem 331 for a similar coil in which the current in each conductor is 8 amp. flux is When motive electro110-volt mains. 333.the direction of current in each? same 329. A gear having 130 teeth drives another having 60 teeth. in.500 and 300 lb. and the strength of field is 40. it develops a counter the What armature take? What current does if it connected were across the mains same while stationary? 337. per sq.400r. assuming that the no-load torque remains 6-in.000 lines current is 60 amp. 332. pulley with respectivetensions in the tight and loose sides of the belt are 1. the motor develops 80 lb.000 lines per sq.500.? 334. generator is The electromotive pole. in. before The motor the second of problem contact 351 reaches 25 per of the starting resistance cent. resistance develops 65-lb. It has a speed r.05 ohm is added to the flux 20 per cent. of motor reaction. of its rated is reached. What is its speed at its rated load? regulationof 3. if the terminal is its speed when problem in of the motor does the armature current voltage take 338 and flux constant? 340. 600-volt from runs mains is its speed at 60 what and and at amp. The has motor The total line current and is 50 its amp.m. amp.p. 10 amp. armature an has Assume When 90 taking from amp. the line? 351. By what flux of problem 340 be decreased in percentage should the it is at 6 amp? order that the speed at 40 amp. and motor with start is rated at 44 amp. a series motor Ib. When speed this . 560-volt series motor A its speed is 480 line? series field resistance of 0. between This increases the motor problem 340. motor resistance its armature 125 per cent.? Neglect reaction.15 ohm.? that the saturation curve Assume of the iron is a straightline. current.100 r.p. from the line it develops 220 takes 348. armature 343.m.04 a at runs 90 700 when r. current zero Assuming that the increase of flux is proportional When the find the 40 to running at 5 speed at current. The motor of problem 348 has an armature resistance of 0.p.m.2 ohm.? At 90 amp. 344.000 r.0 from is its speed when the hne What and runs at 1. 342. reaction. that the saturation curve is a straightline and neglect armature What reaction. armature an 220-volt mains across what has motor at runs is 40 current nected con- At 1. amp. A shimt is 1. torque.1 ohm. from is the What speed motor of problem it takes 349 when 230 volts.m.2 ohm. When 40 amp. amp.m. from the isits speed when r.p.p.p-m. rated at It is desired that is 0.360 r.-ft. Its field current What should be the the initial starting resistance? 352. amp. force of the armature? electromotive of field resistance of 100 ohms a of 0. problem 344 the line.100 r. If it ohm.472 CURRENTS DIRECT 339. What series field resistance of 0. A motor 800 at when runs running light. armature compoimd winding having a resistance of 0.5 per cent.m.2 ohm and motor from 50 amp. the speed is adjusted to 1. and line the it takes 40 amp. What is the torque at the pulleyin problem 345? regulationin each case? 347.0 amp. taking 15 amp.-ft.p.? 350. 349. be the same as Neglect A 341. 220-volt shunt A has armature a is the back What 346. A shimt speed will it it takes and 5 amp.05 ohm a resistance of 0.internal torque when internal torque does it develop when taking reaction. is its speed the 50 when from line? What and 15 taking taking amp. from the line? Neglect armature the motor of problem 344 is running without 346. What from the hne remain 1. Neglect armature amp. When load it takes 7.. taking 40 amp. and 40 amp. its armature when nm When resistance of 0. What torque does it develop at 60 amp. when the touches arm the third contact. What is its efficiency (6) The motor load? 360. M2. When 7 hp. 354. page as It Fig. Calculate the horsepower output developed by the rope brake shown It is running at 1.p. 85 per The cent.120 r. armature an 600 insertingresistance by has motor are 342). 317.p.p.000 r.p.130 r. 351 should current again be 43 amp. (r.m. 362A. page 352. armature (o) What horsepower does this motor develop? at this input is 49 amp. in amp.2 in Fig.m. reading of 36.m.? armature 366. amp. speed of The dead unchanged.8 lb.m.what 362. 363.AND QUESTIONS contact should reached IB it is desired that the armature be the resistance between 473 PROBLEMS the first two be 43 amp. Repeat 1. . control for 300 at 44 connected the r. (a)What torque develop at this is the If the is 18 amp. current What contacts? reaches half speed when the startingarm problem Find the resistance between the second and third reaches the third contact. the speedof the balance reading is 32 lb. The is 2. does the motor and the other reads 4. When 220-volt A shunt takes the armature is desired to obtain r. 600 at the by is when of What kept constant? 368. page 349. the length L is 2 ft. In a is being suppliedby current is the over-all What of eflBciency . similar to that shown is 10 in. and at 220 a volts. the diameter The One balance reads 19. the line it from resistance of 0. page 341 runs speeds can be obtained r. Af 2 delivers line voltage is 220 volts. 23 lb. of this system use the motor 1.500 r. brake similar to that shown in Fig. in Fig. the dead weight of the arm is 1.p.8 lb. how much the line? the system? 369.p. at 220 volts. cuit..400 r. The of motor The contacts. weight of the 361" In a problem The arm brake 359 motor remains for a input is balance now amp.310.p.. 355? and motor mains 110-volt ohm.m.319.p. at 44 in the armature speed will the motor takes 22 amp. speed is 1. the across if the shunt Neglect the laRa field drop in armature.m. What load? at horsepower (c) output? input (6) is its efficiency at this load? 110 volts. In a Ward Leonard system of speed the efficiencies of the machines follows: Afi (Fig. 362A.m.m.at resistance what 366. 309. cir- when run the armature to 354 A at percentage of the line power What problems runs in circuit.83 per cent. . 80 per cent.3 lb. Repeat problem 354 is delivered 367.15 external resistance is necessary? What this external With 4 amp. PiQ. ^-^^-^^^^^^ ^^ of the drum CjOOgle . 474 CURRENTS DIRECT QUESTIONS L Is it useful otherwise? or 2. In a such measurements make measurements objectionsare known are is the formula Why motor? a the may machine a Why any not can- be shown by using the fieldcurrent as a errors partiallyneutralized? advantage of the opposition Upon what principledoes this method depend? in the oppositionmethod? to make assumption is it necessary error? this assumption introduce In this method how appreciable then adjusted? What the two machines started and instruments are and what measurements State the are disadvantages of necessary? 11. For method determining the over are errors of the flux and measure other efficiency? its stray ordinarilyoperated in order to measure made? To wliat is the stray power measurements are is the flux adjusted to the Does is how losses stray power introduced one of these what is the method? proper flux adjustm^it have the the speed and if so how effect upon are any readjustments made? is a set of stray power desirable? 9. 12. For what curves purpose entire the the stray power of the machine over operatingrange with errors What machine power? What then equal? 8. How value? particularload at any for generator be measured have the upon difficult? ent generator differ- a directly? What What effect do precisionof the results? there to direct measurements is of a how stray power measurements. temperatures? 14. its efficiency can from of that 6.electrically loss made small? is the eddy current is it due? to what is lost within electrical apparatus? in detail its effect groups can the losses under Name determined. Into what on the apparatus. Show be calculated. the insulation withstand the of highest pany spot" temperature and what difficultiesaccomName method by which an approximation of the one be reached. or a gejierator they indicatinghow they readilydeterminable? constitutes the losses of the second group? 3. What Does are used this method. motor a the first group. are Explain Xm the losses in either three classified? be which of the energy becomes What CHAPTER ON How the are losses what How do they depend? is meant by pole face loss and Upon What is it reduced? How all the losses except the copper loss grouped as one? Why Upon If it is desired to duplicate stray power do they all depend? what losses under two different conditions of load. are constant? that if the losses in 6. What A gas determines engine? 13. State the An electric machine? effects of excessive electric machinery. How of efficiency conditions practical in the 7.what two factors must be maintained 4. What Are or mechanically? supplied. . How speed adjusted? is the What curve? one 10. What the rating of is the its measurement What "hot ? hot spot temperature may a engine? steam Give reasons temperatures insulatingmaterials can A upon turbine? steam in each case. . m.8 amp. 10 by error 372 is 1.000 lines per pole. similar 10-kw.4 amp. loss in this motor? to Fig. when watts 1. is the torque what amp.200r. the flux What 800 r. What is the stray power of each machine resistance of 0.000 r.2 ohm. the loss is 1. loss of the machine under is the stray power 370. (a) What the speed is raised to 1. its armature resistance is 0.200 watts. Xm flux of a loss when the eddy current CHAPTER is loss is is its efldciency at what this load? 367.800 watts. 220 at stray is the horsepower input to the generator? is its efficiency? (c)If the generator speed is 400 r. Why are 374. ? To same delivers 100 amp. is the loss at flux what are motor 180 ohms. loss in the the stray power measure of generator values should the of connections in 220-volt generators are connected shown as When 366. 368. It is desired and Its armature motor. in each same takes is maining re- flux a of case. 220 at resistance is 0.3 ohm The losses total Its field resistance its stray power and is its output in horsepower and What running 1..m.m. at this load. The 800 at eddy r.. be and terminal volts a adjusted? Make diagram speed and of instruments methods the adjustment.p. ohm The (a) What generator is running lightas A shunt 369. volts..p.p. field current armature and after the machine field resistances of had been a 550-volt standingidle for this at problem and the efficiency of each machine the stray power in the the fieldcurrents different two machines? The the generator fieldcurrent is 2. What is its efficiency? 1.m. a 372. 330. / is found is motor a taking its rated The to be 75 of 48 amp. for the purpose of having their losses measured.m. If the hysteresisloss in what is the loss when The 1. amp.035 armature appliedto A running light takes motor and shunt field resistance is 12 ohms What is the stray power 371. shunt A it is is the loss at 800 generator in the machine 366. current the 373.8 amp.000r. Assiune per cent. A the stray power loss of problem 366 is in does this introduce into the efficiency ? that What error shunt generator delivers 250 field current is 5 amp. of each machine at this load? What is the efficiency load? and Its ohm.p.000 r.? shimt A 366.p. is 1.000 lines? (c) With this 364.200.m. its armature 400 watts. measured the is now in the current (half load) field current Determine field current the 2.08 ohm.p. power (b) What resistance 0. showing problem shunt the its shaft? The armature from 220-volt mains. Each machine has an armature amp. resistance is 0.2 line amp.p. of generator armature current and the / is motor 5 The amp. loss in current and ON with generator is 300 a unchanged? (") 1. at 115 volts. 24 motor When amp. 35 amp.m. volts.? is 600 a generator watts with a speed of the speed is increased to 1. 25 amp.000. page the machine operating as line current Ih What from 110-volt mains.476 DIRECT CURRENTS PROBLEMS 363.m.016 368 Two takes these conditions? To what by running it lightas a motor.p. flux is the with r. shunt generator some time is generator in an are engine . rating Two a straightline of 100 kw.. operating in parallel. How doubled how would the weight of copper be If the transmission voltagewere affected the other factors remaining unchanged? 4. What is the general scheme for conductor? Why is 110 volts most convenient is a highervoltageundesirable ? What are of a lower voltage for this purpose? 6. It is desired to operate a 100-kw. What five conditions in general determine the size of conductor to be For what conditions does the question of heatingparticularly used ? apply ? size of the the How determine conductor? economics the of problem may Too small a What is the disadvantage of having too large a conductor? 2. no aggregate load on the system is 360 straightline in each a 2 amp. its rated load is applied.21 ohm. How current operating in parallel.8 amp. 377. for incandescent the lighting? Why advantages and disadvantages . What is the temperature rise of each? temperatures safe for untreated cotton insulation? maximum 60-kw. of the rheostat is found resistance Xhe armature ixients is found load for these marked two After the machine measurements same commutator seg- been running under had repeated. In generator generators adjusted to 230 volts at no 1 the voltagedrops 8 volts from 12 volts.They load and are then paralleled.002 1.whose room temperature is 30" C. an Repeat problem aggregate load of 400 amp. voltage is these volts and the field wmding volts and the fieldcurrent 420 between to be 0. What the voltage drop of the second generator in order that each may its proportionate share of the load at all times? Assume that the be voltage drops each for ON should The has a resistance of the be the resistance of the division of load? CHAPTER XIV the ordinary direct-current voltagesbe used for transmitting amounts commonly of power utilized? over What Where is direct long distances? these its advantages under are conditions? of power transmittinglarge amounts the consumers' premises? What station to from a remotely situated power of transmission voltages? Of distribution voltages? What the ranges are part does the sub-station play in the system? does the weight of conductor vary with the transmission voltage? 3.? are ohm.The voltage of the first drops 8 kw. Two both are No.8 amp. and generators the other series fieldof the second machine cannot considerable current most case. 376. What for proper QUESTIONS Why in each the system demand compound series field of the first is 0. 220-volt shunt generator and a 60220-volt shunt generator in parallel. were The now 460 resistance is now 0. drops 220-volt the clusive ex- 4. 375 volts from should take a no-load voltage of 230 when follow deliver when 378. hours 2 voltage across The to be 477 PROBLEMS AND QUESTIONS case. 376. it what field current the Assume Are load to full load and in No. One ratingof 75 kw. a much does is 700 amp. kilowatt load does each What voltagedrops in that the field armature are generator deliver? does each current deliver? When The 4.225 ohm. Upon does the balancer set operate? What what principle As a generator? What which machine shall operate as a motor? 16. What Where by distributed loads? of uniform conductors are Where do loads occur? such cross-section throughout most commonly used? 8. How What are the are the objections to relations existing among the series-parallel system overcome? the voltages of the Edison 3- wire system? If the 13. What advantage is gained by connecting llQ-volt loads in series and utilizing 22("-volt supply? What the disadvantages are groups of two of so grouping the loads? 12. What the voltage on that side of the system? of a 3-wire system upon Upon the voltage on the other side of the system? method 18. other conditions being the same? the 14. what are in the 3-wire system with 220 volts across relative weights of copper outers and in the simple llQ-volt system. State two brieflythe (6) unbalanced and methods 21. 11. What the are CURRENTS trolleyvoltages? Why common are these voltages so chosen? is meant 7. How a storage battery be used for obtaining a neutral? may generalhow does the current in the neutral wire divide when it reaches the center of the battery? mines deter20. What Make system sketch and a stillmore the disadvantage of the return overeomes show this system may how be further loop system? modified to form a efficientsystem. Upon are what effect of loads. distributed loads? is most of conductor type is the What economical practicalcondition nearly approaches this theoretical condition? 9. used to accentuate principledoes does the alternatingcurrent flow? neutral? is the direct current How the motor the 3-wire and the generator actions? generator operate? Where returning direct current from able to pass so readilyback into The the the armature? 22. what Theoretically. Sketch of obtaining a neutral by the use of two shunt a generators? What is the principal disadvantage of this method? In 19. Why is the "return loop" system of distribution used? for uniformly that most is its What disadvantage? one 10. In what negativeload? is the greater? The bear this condition how Under to the in the current outer wires? What is the commercial What used in the neutral? What should be type of ammeter limit of unbalancing? opening the neutral with (a)balanced loads Why is the neutral usually grounded? in general is the effect of putting too heavy a load on one side 17. neutral wire be of the size same the two as outers. What loads? by balanced is meant much flows through the neutral? direction does the neutral current current flow if the positiveload relation does the neutral current 16. How in general is power congested districts? What supplied to direct-current loads is the function of the feeders? in the The more mains? .478 DIRECT 6. QUESTIONS Where junctionboxes? The AND are 479 PROBLEMS the house services connected? How are voltagesat feedingpointsgenerallydetermined? 23. What is meant by a "floating" battery? What is the purpose of is it often necessary to install auxiliarymeans for such a battery? Why and load ? of the with Sketch discharge change accentuating battery charge the connections of one simple method for accomplishingthis purpose. Why is such a a community load curve load curve undesirable than a uniform far more having the same the total kilowatt-hours? is meant 29. What by which electrolysis may of of idea the measurements give a good magnitude stray currents between pipes and track? Show how the habits of 28.Why are storage batteries not more generallyused for this purpose? to carry the load 31. What is met when an difficulty attempt is made to operate storage be batteries in conjunctionwith a power plant? What simplemethod may is the objectionto this method? What used to control the battery load? force cells 33. Sketch a typicalcentral station load curve. Name two methods be reduced. occurs at the point where the current enters a pipe? Where it leaves the pipe? 27. if any. What for type of generator is most conmionly used to supply power to the system? railways? How are such generators connected 24. Why will a battery placed at the end of a long feeder tend to equalize the station load without auxiliaryapparatus for charging and discharging? Under what conditions does such a battery "float? 34. Under what conditions are What is multiple feeders employed? How be the disadvantage of their use? this overcome? disadvantage may 26. Under what conditions does a singletrolleysuffice for transmitting If a singletrolley the power to the car? of the ordinary size is of insufficient what means be taken to assist it in supplying the required can cross-section. What Is by load factor? a high or low a sirable? load factor de- Why? 30. Where can storage batteries be used efficiently should For in off-peaktimes? Where stations? central what are purposes they commonty now Under should they be located? what used by conditions battery very useful to a central station? 32. determine the generalshape of such a curve. the of is size power? Why trolleynot increased? 26. What In what is meant by is the connection manner " 37. How a may storage battery smooth out a station load curve? When the battery be charged? Discharged? . What is the system parallel essential difference of distribution? between the series system In the series system what and the is the effect of . Upon what simple principledo the counter-electromotive of of chief this is the method control over the advantage operate? What is a resistance method? end cell control? How is such a battery charged? changed from one cellto the next without opening the circuit or dead-short circuitingthe batteries? 36. Why does the return from current a trolleycar leave the track? What determines the paths which it follows? What damage. 36. assuming that a (h)What is the weight mil-foot of copper has a resistance of 10 ohms? of copper if a"subic inch weighs 0.motor is 86 per cent.what will be the weight of the a switchboard voltageof 230 and the same per a switchboard voltage of 550 and the same per certain street is 2.480 attemptingto out in a remove CURRENTS load by opening the circuit? is a load cut How series system 7 devices is By what 38. from 600-volt bus-bars. at switchboard terminals when (a) Of and the motor switchboard the bus-bars of which is located at a it is desired to have the motor copper are distance of 500 ft. from runs to the first load. long.? 880. but with 550 volts at the with the respective How do the weights of copper compare load. 884. A 4/0 annealed copper feeder amp. Name the XIV CHAPTER distance of 1. the same distance and the same percentage line drop. 20O- A 882. from voltage of 110 at the motor is carryingits fullload of 10 hp.G. over a cable of such potentialdifference of 215 volts at the load with bus-bars. in. transmitted are size that there is a distribution..32 lb. If the lamps of problem 382 are fed by the anti-parallel system (see Fig. the switchboard? of efficiency the motor (c) Repeat (a)and (h)for cent. cu. The voltage at the feedingend of each two adjacent is the voltagedrop between the street is 120 volts. It is illuminated by eleven multiple-connectedlamps placed 200 ft. 883. What used to lamps? What is the voltage at the last lamp? Assume that each lamp takes 2. What must be wire used temperature a The a a (mils)? the diameter Assume is fed from 10-hp. a DIRECT a of the series system ? the advanseries system supplied? What tages are Where does itsfieldof applicationlie? Sketch the layout of two different systems of series advantagesof each. drop to the motor. per ductors con- are supplythis system.000 ft. 140 kw. is located.page 386). 4 wire stillbeing used. load. (d) Repeat (a)and (6)for cent. A maintained the 115 volts. 1 wires run from is the voltage at each the 100 load? . (a) What is the weight of copper used? load (6)What the bus-bars to the No. A load of 100 amps. No. 343 (a). 65 amp. No. Compare their absolute voltageand their difference of voltagewith the results of problem 382.000 ft. issituated 800 ft. watt lb.000 ft. 4 A. = to The 746 watts. voltages cases? in the two 881. determine the voltage the two at the lamps on ends of the street. 1.32 (6) copper wire in (a)? the motor to connect of 50" C. If weighs 0. 1 hp. Repeat problem 379 with the same the same loss. drop to the motor. apart. volts at the a arc (a)What 225 size of feeder is used.W. ON PROBLEMS 879.farther on a second load of 65 amps. power.0 amp. 388. Fig.problem 391.AND QUESTIONS (a) Determine 386. the current and its direction at each of the pointsa-k inclusive. z: jg-0. weight a uniform feeder which will have the same feeders of problem 384. (c)Under which condition is the copper the two as with load the size of 481 PROBLEMS utilized? effectively most It is desired to operate 40 75-watt 386.388A. Repeat problem 393 with the motor and the negative conductor. Owing to the fact that the voltageis halved the motor take must now approximately200 amp. If the neutral is cut at point X. 393 A. Find the voltage across if the neutral each load. Fig. 391. lamps on one circuit.lO FlQ. find the voltagesacross sides of the system. Repeat problem 387. loads A and B. each of the loads AB voltage across the motor. assuming that the load resistances do the two an change. Find the voltagesacross each 40 amp. Edison 3-wire system with various loads. " 7?=0. Fig. 31 the . 388 a. the neutral is the 386 size same shows for as an Edison the outer 3-wire system. Determine power. assuming that wires. are cate Indi- if loads A and B 1 5 v. page 410.) 8a5 ii" V. Neglect the drop in the mains themselves. not 390.388A 389.390 A. *lBa ^-^ 1:5 v. Fig.2 n llfiV. and also the voltageacross the neutral connected between 394. and load B is 20 amp. and BCj Fig. across (Use Table Appendix D. 892. Repeat problem 390 when load A is 60 amp. which would occur opened. 390 A. to develop its former were 393. (6)Determine the voltageat each this uniform feeder. Compare the sizes of wire necessary to feed these lamps when all are connected in volts and when 110 the connected in series groups lamps are parallelacross of two 220 volts. 395^ There ia is 80 per machine generator deliver? I -3000 ttr- "-300ftr"- "h 500.163 resistance trolleywire runs from 600-volt bus-bais copper For 4 miles it is paralleled feeder by a 350.-N^ ^aoo.482 DIRECT 895.26 ohm of 0. 357(6). connected negative main and there is no load on the positive problem 395 the neutral and when side. 393A. feeds it every which wire has a is 0.0000. Motor 121 100a: 500. 395 a.000 CM.000 CM. Find the voltage at a car 5 miles out and is the voltage at the end of the line? resistance of 0. Z 2BO.00OO. 399A shows a 5-mile length of hard-drawn This is fed by three 300. the Find equivalentresistance of the trolleyand feeders to the end of the line.000 CM. Fig.ooo Fig.M.000P. V. (a) Find the voltage at the car in the problem 397. 896. The a car. The resistance of the track and ground per mile. when car is 4 the car is 2 miles from the station. Find the current indicate which machine volts each 110 across How cent.05 return taking 60 quarter mile. ohm amp. when it is at the end station voltage is 600 resistance is 0. (See Fig. 897.M. from amp. voltage at the station and taking 100 the Fig.399A. 400. Find the voltage at and taking and track 401. M. Solve between there is a total load of 100 amp. much in each CURRENTS machine is the motor machine and and does current of the balancer the which set of is the generator. mile.) The 4/0 feeder has a per mile and the 350. A to a 4/0 hard-drawn station 6 miles out. 898.page 397. (b)When 4/0 copper trolley 899. per car volts and of problem 400 when amp. of each efficiency the main and Fig.M. ohm per What c. wire. the power station. la 150a.04 ohm Find the 100 of the line the ground mile. the car is 3 mile? . multiplefeeders each feedingat miles from points l}^ miles apart. ~ Fig. . . of.89 in multipolar machines.355 losses due to. 89 Daniell cell. definition of.274 laminated pole cores.275 method.271 components of.48 Ampere-turn.). 3 Battery.90 grouping.257.76 275 a of motor armature. 316 Ammeter. Co. definition of. cells. 129 Ampere. 128 Bar Weston. 391 for quick action.94 cell. definition of.136 Back shunts.INDEX startingbox. effect of breaking a.resistance of.43 B conductors.68 403 floating.86 - dry cell. gravitycell. definition of. 239 hot-wire tjrpe. voltage of. 335 Cutler-Hammer. 335 Electric Controller and Mfg.85 feeder system. 111 Clark 93 cell. electromotive force of.definition of. 85 electrolyte. 7 3 series. 131 Balancer solenoid type. 316 paths through. 384 Anti-parallel 300 Armature.for best economy. 168 485 87 .251 electromotive force of. 176 Annealed Copper Standard. characteristic.W. charging. 75 series-parallel. 170 determination of. 45 Anode. Edison-Lalande for maximum 76 current.270 compensation of.88 polarization remedies for. 222 Astatic watt-hour set.47 Wire Gage (A. 274 slotted pole faces.85 73 in parallel.44 Aluminum American Back electromotive pitch of windings. definition of.225.85 cathode.68 97 lead cell. Thompson-Ryan magnet. 336 Ayrton shunt.76 internal. Automatic Absolute potential.85 electrodes. 319 355 resistance.91 definition of. 272 motor. 128 96 Alloys. 230 reaction. 225 coils.52 Accumulator (seeStorage Battery).84 anode.. measurement of. construction of. definition of. 69. 355 windings (seeWindings). definition of. 128 of force meter. 91 115 nickel-iron-alkaline.71.267 calculations of.G. Le Clanch^ cell. 309 compoimd. 403 series generators as.253 . Characteristics of generators. 281 undercut mica. primary cell. 111 constant potentialmethod. 360 effect of speed on. 405 Brush.181 Coils. 276 high mica. dynamic. 211 galvanometer method. 321 poles.in a dynamo.definition of. 283 with commutating poles.211 parallelplates.256 Building up of generator.195 Closed Coercive force. of a motor. British Thermal shimt 347 (B. definition of.).92 tery of storage batBoosters.86 of. 319 Characteristics of motors. 213 for loop ground. 324 series. (see Shimt Generator). 328 shunt. 211 bridge method. 213 of parallel condensers. saturation series Prony. Capacitance. 111 booster method. Unit 258 (see Series Generator).377 Circular mil.285 Commutation.255 position. 301 rope. 348 Braking.486 INDEX Capacitiesof storage batteries.u. electrostatic. 257 electromotive armature force. 385 Coefficient of coupling.38 foot. Brush curve. cradle dynamometer.285 (Commutator construction.t. Cable testing.calculation of.68 Cell.267 commutation.147 Murray loop for 116 locating a ground.location of.228.84 principles 86 secondary cell. 39 Clark cell.115 Cathode.dummy.71. 257 96 terminal voltagedrop armature in. 93 loop feeder system.of lead cell. 225 Commutating. construction. 62.68 Standard Weston reaction. Gen- 295 Arc 244 in a generator. 283 sparking due to. Wire 44 Sharpe machine. 242 formed.206 159 Circuit breakers. 148 Varley Calibration locating of ammeter. 264 method. 303.209 curve of co-axial of cylinders.293 407 and Gage.99 constant current of nickel-iron-alkaline battery. 351 Browne erator).321 198 Charge.85 Battery. 264 total. definition of.205 of series condensers. Charging of storage batteries. 147 total disconnecion.regulation discharge with. 112 Chemical reaction. 304 Brakes. 221. 112 rocker ring for holding. 281 in a motor. storage (see Storage Battery). 276 compound (seeCompound voltageof.202 measurement ballistic of.209 definition of. 305 292 regulation. 328 of 394 *Doubly re-entrant winding.227 Dielectric. D'Arsonval galvanometer. Standaid Annealed.19 Coiona. definition of. Dynamo construction. 297 over under speed compounding.374 parallel series field diverter for. Daniell cell.206 Conductance.396 405 series.. Counter current.144 Development of a winding.202 Differential compound 36 specific. 46 field around. 328 Compound Damping of galvanometers.123 Decade bridge. Duplex winding. 242 Dummy coil.223 94 Dry cell.36 parallelconnection strength. 46 aluminum. 299 compounding. 53 with potentiometer. 36 feeder motor. 8 Compensation of amature dynamometer.202 definition of. 17 112 system. storage battery.190 per cent.243 Cradle Critical field resistance. 316 of. 296 motor.205 202 materials. 384 Copper.318 Coupling.36 Conductivity. 201 45 Coulomb. 380 298 Diverter. 195 demonstration voltage. Corkscrew rule. characteristics of. long for.204 table of. 47 Distribution copper. characteristics of.265 274 motor.168 rise in inductive circuit. Direct Conductors.125 89. braking. 383 electromotive systems. battery chargpotential.series field.charge of. connection measurement. Creeping in winding.47 46 silver. productionof.298 short compound Cumulative generator. 295 Compound automatic starter.48 Cutler-Hammer operation of.5 Constant ing. constants. 380 constant iron. Condensers.487 INDEX Compass. Dobrowolsky method.208 energy of. definition of.7 Consequent poles.48 force.328 cumulative.249 220 . definition of.202 stored in. Thury System of. magnetic.235 Drop-wire.328 328 differential.decay in inductive circuit.303.coefficient of. connection of.32. 187 unit 296 shunt.220 Disc dynamo. 328 Current. 335 for. 360 reaction.157 Drum winding.399 385 three-wire. 305 Discharge switch. 4 steel.235 Dynamic.383 electric railway. 297 shunt.296 efifect of 189 on.347 198 electricity. motor. definition of. distribution system.205 series connection of. 58 watt-second. of.85.68 of self induction. 48 farad. series field.179 rating of. 115 applicationsof.59 60 kilowatt-hour.250 losses 359 in.plunger type. 105 Electromagnet. 251 Edison-Lalande cell.361 magnetic calculations in. 184 joule. Controller automatic shoes.48 generated in armature.336 coulomb. 355 355 shunt field.186 calculation magnetism.210 61 condenser. 249 Electrical in.198 field. 316 battery. Mfg. 385 121 Electrotyping.390 three-wire generator.369 copper. 184 in motor 257 armature. starter.390 balancer CJo.356 eddy currents. 253 commutator. . 391 storage battery.60.48 of E and units. efficiency of. ohm. definition ampere.255 84 batteries. 16 Eddy current losses. induced. efficiencyof conversion.360 Earth's .222 Dynamometer. 117 chemical reaction of. Electrostatic.355 355 armature. 118 charging of. 254 Electric cores. 359 stray power.definition of. 387 effect of open methods of obtaining neutral Energy. cores. Edison advantages of.17 Electromotive force.200 induction. defintion Electrolyte. 402 neutral on. 394 two-generator.135 windings. 390 Toltage unbalancing of stored in for.359 heating of. 32 volt.356 357 hysteresis. 355 determination of. cradle. construction.365 358 friction. 15 of.199 200 lines. 407 kilowatt. 191 three-wire system. 23 Electromagnetism. charges. set.368 windings (seeWindings).388 Equalizingconnections in 236 Exide Vehicle battery. 250 frame. End cells.190 intensityof.356 Edison battery.91 Efficiencyof dynamos. 407 Electrode. 109 Extension coils. 249 396 field coils. of magnetic field. 116 120 Electroplating. 358 pole face. measurement of. armature. iron.204 henry.208 60 units of electrical. Electric brushes. Electric railway distribution system.60. 48 48 watt. 215. 375 force. of.85 397 Electrolysis.488 INDEX 249 Dynamo. 216 in Heat. 305 regulationof.).90 H of electrostatic lines. 222 definition of. 309 coercive.261 field resistance line. 276 compound (seeCompound Faraday disc dynamo. 384 Field. 260 183 coefficients.368 Henry. 17 coil construction.19 armature. Gen- 295 shunt (see Shunt Generator). definition of.181.257 homopolar.130 Gauss.254 control of speed by.267 armature Induced electromotive force.7 intensity. 126 Weston Generated electromotive 171 force. rule.7. 171 Force.67 power systems of. 44 Gage.292 saturation of. 357 Hot-wire portable. 305 Farad.63 loss in. losses due to. armature of.226. around a conductor. definition of. American 123 Galvanometer. 305 Horseshoe. 283 Homopolar generator. 65 potentialdiop in.190 unit of. 332 Four-pointstarting Fractional pitchwinding. 136 Hydrometer. 218 Floating battery.262 301 Fleming's Left Hand Rule.W.243 box.G. 215 . Gould ploughed plates.100 Gradient.128 damping of. 184 High mica. 305 Feeders.181 lines of. Forced unipolar. Ayrton shunt for.258 of. 13 solenoid. 105 Hysteresis. mechanical equivalentof. 124 methods shunts. acting on a conductor. 407 Gramme-ring winding. 123 of reading. 5 winding.300 reaction of. 239 Front G Wire (A. 182.magnet. 215. resistance definition of.403 Flux erator). characteristics of. 311 Right Hand Rule. 222 Gravity cell.202 Gram-calorie. 171 o f electromagnetic lines. curve determination line.62.6 magnetic. 125 D'Arsonval.215 electromotive force of. definition of.262 260 hysteresis. Hand pitch.potential.257 effect of speed on.184 in generator armature. 293 density. 170 Gilbert.489 INDEX Generator.7.24 instruments. Fringing. 62 of Heating dynamos.218 characteristic Generator. 395 estimation of. 224 358 Friction losses. 342 discharge switch. 369 measurement of. 257 lighthand rule for.210 .370 Standardization Rules for. series (see Series Generator).215 equationof.305 windings (seeWindings). 264 total characteristic of.204 commutation. 246 Lead cell. 145 resistance low potentiometer. magnets.60 Lenz's motor. curve. 407 Joule's Law.Fleming's. 99 Leakage. 226 uses of. artificial. 193 self.Exide battery.356 eddy current. 343 armature. 49 Linkages.150 rule. definition of. 161 volt. 11 186 Inductive circuit. 155 Left hand Insulation testing. 171.definition of. M 1 Magnet.22 Jagabi tachoscope. 102 solenoid. 187 Instruments. iron. 27 LeClanch6 cell. 69 Kilowatt-hour. dial bridge. 236 number of paths in. 122 ammeters (seeAmmeter). 356 hysteresis.186 calculation of. 183 Load. 274 224 winding. 355 wattmeter. 183 mutual.218 Inductance. .365 Kilowatt.136 voltmeters. 26 Insulators. 2 3 electro-.97 chemical reaction of. 82 of. 356 357 hysteresis.228 simplex.134 128 396 sjrstem of distribution. of current decay !n. Laminated.285 Iron. 355 of.91 Leeds " Northrup.358 356 series field. in armature.357 pole face. 316 rule for direction applicationsof. 77 Ladder force of self. 359 of. definition of. 200 magnetic.dynamo. 62 Junction boxes. shunt 356 field.coil. 190 199 electrostatic. 358 pole face.123 damping of.490 INDEX Induced electromotive motor force.60.183 Induction. 186 Liftingmagnet.126 hot-wire. 189 rise of current in.233 requirementsof.399 Lodestone.353 Joule. 256 losses. galvanometers. 125 shunts for. stray power. Lap development of.227 equalizingconnections in. magnetic. 250.311 Law.48 Interpoles. 1 Losses.78. 14 pole cores. 399 factor.356 eddy current. 395 K Kapp oppositiontest.196 electromotive Kirchhoff's Laws.32 Lincoln International ohm.as a conductor. explorationof field around a 6.2. lines of.361 measurement 182 hysteresis.365 determination 358 friction. Iron-clad. . conductivity. 399 electrical imit of. 157 Power.173 definition of. 381 weight of conductor 381 Permittivity. 92 Production of direct current.406 parallel return loop. 384 384 anti-parallel. 53 Open loop series distribution. 5 -face losses.63 measurement of.32 Ohm's Law. distribution systems.in dynamos.384 385 series-parallel. . 147 Mutual inductance.definition of.365 voltage measurement with.385 open loop.86 requirements of. 51 in drop feeders.86 Weston. 116 O Pole. 171 of iron and Permeance. closed loop. 226.226. due to. definition of. 303.396 feeder systems.67 measurement. 406 operation. fielii loop feeder system. 239 front. 225. 117 chemical reaction of. loop.374 generators.52 difference. steel.36 for cast steel. 380 constant Edison 383 potential.341 Murray loop. 384 Open Oppositiontest. 380 voltage of. 155 88 Polarization. 170 405 series. 19 conductors.358 interpole.205 Pilot 106 cell. 157 157 wire. 55 circuits. 285. size of conductor three-wire. 239 Plants plate. Pitch of winding. Parallel.382 storage battery.101 Per cent. 73 batteries.23 Poggendorf method.INDEX 492 MuUi-voltage speed control.385 Thury. drop volt box. curve shunt 174 definition of. 58 loss. 158 " Northrup low resistLeeds ance. 158 standard resistances.385 electric railway.372 compound generators. 321 magnetic. three-wire.406 384 open spiral. 225 back. 193 coefficient of coupling. 220 winding. 321 consequent. 53 Potentiometer.commutating. 153 current measurement with.195 effect of iion on.89 for.372 Pasted plate. 48. 115 applicationsof.definition of.absolute. 118 charging of.5 Potential. Pfeogressive 239 for. remedies for. Permeability.406 spiral feeder system. 196 N Neutral of magnets. in feeders. 2 strength. 285. 155 Oersted. 3 zone Nickei-iron-alkaline battery. definition of.100 Plunger electromagnet. 170 Ohm. 355 160 Primary cell. line.351 Prony brake. 139 voltmeter-ammeter method.99. 170 405 distribution. 40 units for startingboxes.334 torque of.256 Rope brake. field.302 Thompson-Houston. 40 volume.328 speed equation of. chemical. 37 standard. 35 Retrogressivewinding. 116 Regulation. Rating. determination of. 325 railway. Rocker ring. 186 calculation of. 27 Series. of storage battery. table of.190 319 104 Separator. Railway 345 multipleunit control. telegraph. 49 method. Q Saturation Quantity of definition of.armature. 385 37 resistances.304 motor. 240 Return loop feeder system.325 startingboxes for. 110 force of. 96 electromotive Self-induction. International Standard of. (magnetic induction) ^^ of turns 300 .in batteries. 303 characteristics of. 261 effect of hysteresison. 345 speed control.31. ^ condensers.magnetic. 73 54 circuits.334 no load 334 release. definition of.calculation of.323 voltage. 37 relation to direction of current. Shunt.32.300 turns. .Fleming's. 303 Thury system. 267. 137 Wheatstone Bridge. 141 parallelconnection of. 350 197 Pull due to magnetic field. 384 Arc machine.298 181 loss in. definition of. of 368 dynamos.262 14 86 Secondary cell. 303 used as booster.493 INDEX 218 Right hand rule. 324 uses of.295 generator. motors. 222 Ring winding. 40 150 insulation. (seeStorage Battery). 128 no for. 131 Ayrton.206 Reluctance. 348 coolingof. 260 R unit 258 curve. 32 series connection of. Tirrill. 48 determination field resistance Screens. 350 of. 137 measurement voltmeter uses of. 324 characteristics of. 326 parallelsystem. 356 Resistance. 301 Brush of.batteries in. electricity.227. 43 unit of.158 temperature coefiicient of. diverter for. 41 table of.338 34 Resistivity. 328 Reaction.171 Remanence of. voltage release. 350 power zero reading of.292 306 Regulator. 239. ammeter. 24 Relay.speed. magnetic. 324 Silver conductors. 103 Steel conductors. 334 no 128 voltage release.334 speed adjustment. 22 definition of.204 table of.46 Simplex winding.21 horseshoe.408 capacity. 36 Specific. 322 Solenoid. 111 no iron-clad.ammeter.341 ' * 219 Sparking at commutator. resistance line. 353 commutation Slide wire method.353 magneto and voltmeter. 343 tachometer. 334 load release. 324 uses of. 22 Spark coil.331 Static electricity.22 magnetic field of. 111 potential method. 47 Storage battery. field.106 booster method. Mfg. armature " magnetic blowouts for. 266 paralleloperation. Electric bridge. 265 failure to build up. control of motors. 321 Weston regulation. 341 Startingboxes. 333 three-point. 338 resistance units for. 399 electromotive counter of. 114 . 96 capacity of. 353 regulation..353 generator. 329 automatic.265 characteristics of. floatingbattery. railway.323 startingtorque.372 regulation. 45 Clark cell.345 126 reaction of. constant current constant 112 method.494 INDEX loss in. 403 resistance control. 335 speed.192 281 positionon. characteristics of. Speed. Co. Annealed Copper.276 critical field resistance. 205 force. control of.288 oi. 264 armature Stow method.100 installation. system. 401 34 resistance. Slotted pole faces. Ward equation for determining. 283 conductance. control of motors.275 inductive 92 cell. 20 plunger.267 buildingup of.323 Standard. Leonard revolution counter.338 commercial.401 Edison. 115 118 efficiency. 198 Stationary battery. 226 Cutler-Hammer. 353 Jagabi tachoscope. 112 distribution systems. 93 158 resistances. undercut mica. Gould ploughed plates. Lincoln method. 262 for galvanometer.24 table 335 Controller 332 four-point. 107. gravity. .292 motor. 343 multi-voltage. Speed. 105 electrolytes. 116 charging. 336 series motor. 366 Shunt.319 measurement of. 323 Sine wave. 282 283 high mica.144 effect of brush 339 resistance 339 342 field. 100 watthour Thomson 115 nickel-iron-alkaline. 102 Thermal 97 lead cell.24 Tanks Temperature coefficient of 41 table of. Edison.394 -wire system. 103 Telegraphrelay. 167 Thury system. plate. 114 vehicle. 44 wires. chemical Manchester reaction of. Syringe hydrometer. 99 405 -Ryan method. 385 series-parallel. Types of generators. 283 Unipolar generator. 104 gravity. 380 Time constant. 407 Thompson-Houston generator.407 sistance.106 meter. parallelloop. Wire characteristic 293 loop. 312 190 Switch.495 INDEX units. 187 Tirrill voltage regulator. resist- Varley loop.406 384 open spiral. 385 Plants plate. pasted plate. American meter. definition of. 410 U 40 resistivity.353 for batteries.106 specific stationary.43 of generator. 103 390 balancer set.384 anti-parallel. 313 series motor.Jagabi.385 loop. 343 Stray power. 303.406 open return Total current capacity of layer windings. 305 Units.109 177 .103 tanks. 353 Tachoscope. 390 voltage unbalancing. Storagebattery. Undercut 408 specific gravities.312 developed by motor. 303.409 relations of units. separators. re- 43 Tachometer. closed loop. imits of. 106 Systems of feeders.380 three-wire generator. 163 Three-pointstartingbox.301 shunt. 263 compound.discharge. 306 Torque. 324 shunt motor 324 starting.385 three-wire.Iron-clad Exide. temperature coefficients of mica.388 of. 295 series.361 measurement 276 ance. 369 curves of.100 rating.386 effect of open neutral on.62.384 Edison " generator. 148 Vehicle battery. 384 Tables.407 Gage.108 Exide.108 Stow motor.110 advantages. 264 Typical magnetization curves.391 storage battery.magnetic. 387 methods of obtainingneutral. 170 relations of. 363 two -wire watt-hour .101 pilotcell. 394 temperature.332 -wire generator. table.227 drum. 238 brushes for.235 duplex.226 Watt.225 226 progressive. gradient. 135 multipliers. closed circuit.Tirrill.227 306 regulator.236 233 multiplex. 60 Weber's theory of magnets. 246 Wire gage.168 Thomson.244 requiried paths through armature.235 singlyre-entrant. 94 secondary. ammeter.228 meter. 130 Standard Cell.167 numbering slots for.141 method of using.236 meter. 223 219 242 dummy coil. doubly re-entrant. equalizerconnection. wave. 222 lap. 239 progressive. requirement for.224 development of.48 wave. 129 portablegalvanometer. 162 astatic.generatedby rotatingcoil. 143 223 Winding.226 221 circuit. American. 165 three-wire.definition of.225 fractional regulationof generator. 3 Weston. lap and 245 creeping.box. W Ward-Leonard paths through armature.202 measurement. 157 definition Winding.228 system.496 INDEX Volt.246 233 multiplex.157 coils for. open pitch of. 44 A N X.58 -hour 230 uses of. comparisons of. 244 . Voltage. 341 simplex. uses. of 52 formed with potentiometer. Voltmeter. 48 International. 243 forced. 161 -second.243 development of.224 Gramme-dng. 94 Wheatstone bridge.134 135 extension coils.92 normal. 239 retrogressive. 163 adjustments of. 202 pitch. definition of.