MasteringPhysics: Assignment Print Viewhttp://session.masteringphysics.com/myct/assignmentPrintView?assignme... Test 5 Due: 11:59pm on Sunday, April 10, 2011 Note: You will receive no credit for late submissions. To learn more, read your instructor's Grading Policy [Switch to Standard Assignment View] Exercise 24.49 A parallel-plate capacitor has the volume between its plates filled with plastic with dielectric constant magnitude of the charge on each plate is . Part A Use Gauss's law to calculate the magnitude of the electric field in the dielectric. Express your answer in terms of the given quantities and appropriate constants. ANSWER: = Correct . Each plate has area . The , and the distance between the plates is Part B Use the electric field determined in part A to calculate the potential difference between the two plates. Express your answer in terms of the given quantities and appropriate constants. ANSWER: = Correct Part C Use the result of part B to determine the capacitance of the capacitor. Express your answer in terms of the given quantities and appropriate constants. ANSWER: = Correct Problem 24.73 Capacitors in networks cannot always be grouped into simple series or parallel combinations. As an example, the figure (a) shows three capacitors , and in a delta network, so called because of its triangular 1 of 17 5/12/2011 8:11 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... shape. This network has three terminals a, b, and c and hence cannot be transformed into a single equivalent capacitor. It can be shown that as far as any effect on the external circuit is concerned, a delta network is equivalent to what is called a Y network. For example, the delta network of the figure (a) can be replaced by the Y network of the figure (b). (The name "Y network" also refers to the shape of the network.) The transformation equations that give , , and in terms of , and , and are . Part A For the network shown in the figure (c), determine the equivalent capacitance between the terminals at the left end of the network. (Hint: Use the delta-Y transformation derived in the introduction. Use points a, b, and c to form the delta, and transform the delta into a Y. The capacitors can then be combined using the relationships for series and parallel combinations of capacitors.) ANSWER: = 14.0 Correct Part B Determine the charges of, and the potential differences across, each capacitor in the figure (c). ANSWER: −4 = 5.04×10 Correct Part C ANSWER: = 7.00 Correct Part D ANSWER: −4 = 2.30×10 Correct Part E 2 of 17 5/12/2011 8:11 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... ANSWER: = 13.0 All attempts used; correct answer displayed Part F ANSWER: −4 = 2.80×10 Correct Part G ANSWER: = 10.0 Correct Part H ANSWER: −4 = 2.60×10 Correct Part I ANSWER: = 9.00 Correct Part J ANSWER: −4 = 2.50×10 Correct Part K ANSWER: = 12.0 Correct Part L 3 of 17 5/12/2011 8:11 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... ANSWER: −5 = 1.50×10 Correct Part M ANSWER: = 2.50 Correct Problem 24.75 Two square conducting plates with sides of length constant with dimensions are separated by a distance . A dielectric slab with is inserted a distance into the space between the plates, as shown in the figure . Part A Find the capacitance C of this system . Express your answer in terms of the given quantities and appropriate constants. ANSWER: = Correct Part B Suppose that the capacitor is connected to a battery that maintains a constant potential difference between the plates. If the dielectric slab is inserted an additional distance plates, show that the change in stored energy is into the space between the 4 of 17 5/12/2011 8:11 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... Essay answers are limited to about 500 words (3800 characters maximum, including spaces). ANSWER: My Answer: Part C Suppose that before the slab is moved by , the plates are disconnected from the battery, so that the charges on the plates remain constant. Determine the magnitude of the charge on each plate. Express your answer in terms of the given quantities and appropriate constants. ANSWER: = Correct Part D Show that when the slab is moved farther into the space between the plates, the stored energy changes given in part B. by an amount that is the negative of the expression for Essay answers are limited to about 500 words (3800 characters maximum, including spaces). ANSWER: My Answer: Part E If is the force exerted on the slab by the charges on the plates, then . Thus should equal the work done against this force to move the slab a distance . Show that applying this expression to the result of part B suggests that the electric force on the slab pushes it out of the capacitor, while the result of part D suggests that the force pulls the slab into the capacitor. Essay answers are limited to about 500 words (3800 characters maximum, including spaces). ANSWER: My Answer: Part F Figure24.16 in the textbook shows that the force in fact pulls the slab into the capacitor. Explain why the result of part B gives an incorrect answer for the direction of this force. Essay answers are limited to about 500 words (3800 characters maximum, including spaces). ANSWER: My Answer: Part G 5 of 17 5/12/2011 8:11 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... Calculate the magnitude of the force. (This method does not require knowledge of the nature of the fringing field.) Express your answer in terms of the given quantities and appropriate constants. ANSWER: = Correct Exercise 24.11 A cylindrical capacitor has an inner conductor with a radius of 1.3 3.3 Part A What is the capacitance per unit length? Express your answer using two significant figures. ANSWER: −11 = 6.0×10 Correct and an outer conductor with a radius of . . The two conductors are separated by vacuum, and the entire capacitor has a length of 3.0 Part B The potential of the inner conductor relative to that of the outer conductor is 350 (magnitude and sign) on both conductors. Enter your answers numerically separated by a comma. Express your answers using two significant figures. ANSWER: −11 −11 = 6.3×10 ,−6.3×10 Correct . Find the charge Exercise 24.13 A spherical capacitor contains a charge of 3.50 when connected to a potential difference of 230 . . If its plates are separated by vacuum and the inner radius of the outer shell is 5.00 Part A Calculate the capacitance. ANSWER: = 15.2 Correct 6 of 17 5/12/2011 8:11 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... Part B Calculate the radius of the inner sphere. ANSWER: = 3.66 All attempts used; correct answer displayed Part C Calculate the electric field just outside the surface of the inner sphere. ANSWER: 4 = 2.35×10 Correct Exercise 24.23 Suppose the 3 capacitor in Figure 24.10a in the textbook were removed and replaced by a different one, and to 8 . and that this changed the equivalent capacitance between points Part A What would be the capacitance of the replacement capacitor? ANSWER: = 57.0 Correct Exercise 24.30 A parallel-plate vacuum capacitor has 8.10 2.90 Part A what is the energy now stored if the capacitor was disconnected from the potential source before the separation of the plates was changed? ANSWER: = 5.17 Correct of energy stored in it. The separation between the plates is , . If the separation is decreased to 1.85 Part B What is the energy now stored if the capacitor remained connected to the potential source while the separation of the plates was changed? 7 of 17 5/12/2011 8:11 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... ANSWER: = 12.7 All attempts used; correct answer displayed Problem 24.56 Two capacitors are connected parallel to each other and connected to the battery with voltage 28 = 9.1 , = 4.9 . Let be their capacitances. Suppose the charged capacitors are disconnected from the source and from each other, and then reconnected to each other with plates of opposite sign together. Part A By how much does the energy of the system decrease? Express your answer using two significant figures. ANSWER: −3 = 5.0×10 Correct Problem 26.86 An Part A If the circuit is discharging, how long will it take for its stored energy to be reduced to value? Express your answer in terms of the variables ANSWER: = Correct , , and constant . of its initial circuit has a time constant . Part B If it is charging, how long will it take for the stored energy to reach Express your answer in terms of the variables ANSWER: = Correct , of its maximum value? , and constant . 8 of 17 5/12/2011 8:11 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... Problem 26.88 Part A Using the equation instantaneous power for the current in a discharging capacitor, derive an expression for the dissipated in the resistor. , , and . Express your answer in terms of the variables ANSWER: = Correct Part B Integrate the expression for to find the total energy dissipated in the resistor. , , and . Express your answer in terms of the variables ANSWER: = Correct Part C Show that the total energy dissipated in the resistor is equal to the total energy initially stored in the capacitor. Essay answers are limited to about 500 words (3800 characters maximum, including spaces). ANSWER: My Answer: Problem 26.90: A Capacitor Burglar Alarm The capacitance of a capacitor can be affected by dielectric material that, although not inside the capacitor, is near enough to the capacitor to be polarized by the fringing electric field that exists near a charged capacitor. This effect is usually of the order of picofarads ( ), but it can be used with appropriate electronic circuitry to detect a change in the dielectric material surrounding the capacitor. Such a dielectric material might be the human body, and the effect described above might be used in the design of a burglar alarm. Consider the simplified circuit shown in the figure . The voltage source has emf = 1000 , and the capacitor has capacitance 10.0 . The electronic circuitry for detecting the current, represented as an ammeter in the diagram, has negligible resistance and is capable of detecting a current that persists at a level of at least 1.00 for at least 200 after the capacitance has 9 of 17 5/12/2011 8:11 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... changed abruptly from to . The burglar alarm is designed to be activated if the capacitance changes by 10%. Part A Determine the charge on the 10.0capacitor when it is fully charged. ANSWER: −8 = 1.00×10 Correct Part B If the capacitor is fully charged before the intruder is detected, assuming that the time taken for the capacitance to change by 10% is short enough to be ignored, derive an equation that expresses the current through the resistor as a function of the time since the capacitance has changed. Express your answer in terms of the variables ANSWER: = All attempts used; correct answer displayed , , , ( ) and . Part C Determine the range of values of the resistance that will meet the design specifications of the burglar alarm. (Hint: You will not be able to solve this part analytically but must use numerical methods. Express as a logarithmic function of plus known quantities. Use a trial value of and calculate from the agree to within three expression a new value. Continue to do this until the input and output values of significant figures.) Enter your answers numerically separated by a comma. ANSWER: , 6 7 = 7.15×10 ,7.01×10 Correct Part D What happens if is too small? Too large? Essay answers are limited to about 500 words (3800 characters maximum, including spaces). ANSWER: My Answer: 10 of 17 5/12/2011 8:11 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... Exercise 26.40 A 12.8 . Part A Compute the charge on the capacitor at the following times after the connections are made: 0, 5.0 , 10.0 , 20.0 , and 100.0 . Express your answers using two significant figures. Enter your answers numerically separated by commas. ANSWER: , , , , −4 −4 −4 −4 = 0,2.7×10 ,4.5×10 ,6.4×10 ,7.7×10 Correct capacitor is connected through a 0.890 resistor to a constant potential difference of 60.0 Part B Compute the charging currents at the same instants. Express your answers using two significant figures. Enter your answers numerically separated by commas. ANSWER: , , , , −5 −5 −5 −5 −8 = 6.7×10 ,4.3×10 ,2.8×10 ,1.2×10 ,1.0×10 Correct Exercise 26.41 In the circuit shown in the figure both capacitors are initially charged to 50.0 . Part A How long after closing the switch S will the potential across each capacitor be reduced to 10.0 ? ANSWER: = 4.51 Correct 11 of 17 5/12/2011 8:11 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... Part B What will be the current at that time? ANSWER: = 0.125 Correct Exercise 26.45 In the circuit shown in the figure each capacitor initially has a charge of magnitude 3.20 on its plates. Part A After the switch is closed, what will be the current in the circuit at the instant that the capacitors have lost 80.0% of their initial stored energy? ANSWER: = 12.4 Correct Exercise 31.7 In each circuit described next, an ac voltage source producing a current additional circuit element. Part A The ac source is connected across a resistor . Sketch graphs of the current in the circuit and the is connected to an potential difference across the resistor as functions of time, covering one cycle of oscillation. Put both graphs on the same set of axes so you can compare them. ANSWER: 12 of 17 5/12/2011 8:11 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... View Answer Requested Part B Do the same as in part A, except suppose the resistor is replaced by an inductor graphs as in part A, but this time across the inductor instead of the resistor. ANSWER: . Sketch the same View Answer Requested Part C Do the same as in part A, except suppose the resistor is replaced by an capacitor graphs as in part A, but this time across the capacitor instead of the resistor. ANSWER: . Sketch the same View Answer Requested Part D Sketch phasor diagram for resistor. Draw the phasors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded. 13 of 17 5/12/2011 8:11 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... ANSWER: View Correct Part E Sketch phasor diagram for inductor. Draw the phasors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded. ANSWER: View Correct Part F Sketch phasor diagram for capacitor. Draw the phasors with their tails at the dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded. ANSWER: View Correct Exercise 31.18 You have a 200resistor and a 6.00capacitor. Suppose you take the resistor and capacitor and make and an angular frequency of 250 a series circuit with a voltage source that has a voltage amplitude of 30.0 14 of 17 5/12/2011 8:11 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... . The current is given by Part A Graph , versus for 0 to 27.0 , so . . ANSWER: View Answer Requested Part B Graph , versus for 0 to 27.0 . ANSWER: View Answer Requested Part C Graph , versus for 0 to 27.0 . ANSWER: View Answer Requested Part D 15 of 17 5/12/2011 8:11 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... What is at ? ANSWER: = -25.1 Correct Part E What is at ? ANSWER: = 2.45 Correct Part F What is at ? ANSWER: = -27.5 Correct Part G What is at ? ANSWER: = -22.9 Correct Part H What is at ? ANSWER: = -7.23 Correct Part I What is at ? ANSWER: = -15.6 Correct 16 of 17 5/12/2011 8:11 PM MasteringPhysics: Assignment Print View http://session.masteringphysics.com/myct/assignmentPrintView?assignme... Score Summary: Your score on this assignment is 82%. You received 81.97 out of a possible total of 100 points. 17 of 17 5/12/2011 8:11 PM