HW35Due: 11:59pm on Thursday, December 3, 2009 Note: To understand how points are awarded, read your instructor's Grading Policy. [Return to Standard Assignment View] Graphical Analysis of AC Voltage Source Conceptual Question The figure shows a graph of the output from an AC voltage source. Part A What is the maximum voltage Hint A.1 AC voltage Hint not displayed ANSWER: =3 of the source? Correct Part B What is the average voltage Hint B.1 Average voltage of the source? The AC voltage source illustrated symmetrically alternates between positive and negative voltages. Mathematically, it can be described by . ANSWER: =0 Correct Part C What is the root-mean-square voltage Hint C.1 Root-mean-square voltage or has an average value of zero when averaged over a complete of the source? Any physical quantity described by cycle. However, if the quantity is first squared and averaged and then the square root taken, the value is positive and gives information about the magnitude of the physical quantity. This is referred to as the quantity's root-mean-square (rms) value. The rms value of any quantity described by or is equal to the maximum value of the quantity divided by . Express your answer to three significant figures. ANSWER: = 2.12 Correct Part D What is the period Hint D.1 Period Hint not displayed Express your answer in seconds to two significant figures. ANSWER: = 0.08 Correct of the source? Part E What is the frequency of the source? that is. a sinusoidal current will flow through the inductor. At one extreme. = Correct Part B What is the reactance Hint B. The frequency of the source is the inverse of the period of the source. What is across this inductor? Voltage and current for an inductor Hint not displayed Express your answer in terms of ANSWER: . imagine that a current .5 Correct Part F What is the angular frequency Hint F.5 Correct Inductive Reactance Learning Goal: To understand the concept of reactance (of an inductor) and its frequency dependence. where the subscript L indicates that this formula applies to an inductor. so the amplitude of the current will be proportional to the amplitude of the voltage.1 Frequency The frequency of the AC voltage source is the number of cycles of the source per second. However. Express your answer in hertz to three significant figures. and relationship between voltage and current is summarized by the reactance. This is the essence of AC (alternating current) circuits used in radio. capacitors. . its magnitude depending on the frequency.1 of the source? Angular frequency Hint not displayed Express your answer in radians per second to three significant figures.1 of an inductor? The definition of reactance Hint not displayed Express your answer in terms of ANSWER: and the inductance . The voltage source has EMF the inductor is Part A . and the inductance . like a resistor with large resistance so that essentially no current will flow no matter what the applied voltage. is flowing through the inductor. and resistors are linear devices. Circuit elements like inductors. the current and voltage may not be in phase with each other. ANSWER: = 12. . TV. = Correct Part C In thinking of an inductor as a circuit element.Hint E. : Part A To find the reactance the voltage Hint A. like a resistor with almost no resistance (an ideal wire) having essentially no voltage drop across it no matter what the current. and stereos.1 of an inductor. the inductor might behave like a short circuit. and frequency . ANSWER: = 78. that is. the ratio of voltage and current amplitudes. This new . it is helpful to consider its limiting behavior at high and low frequencies. Based on the formula you obtained for the reactance. how does an inductor behave at high and low frequencies? ANSWER: like a short circuit at both high frequencies and low frequencies like an open circuit at both high frequencies and low frequencies like an open circuit at high frequencies and a short circuit at low frequencies like an open circuit at low frequencies and a short circuit at high frequencies Correct Determining Inductance from Voltage and Current An inductor is hooked up to an AC voltage source. The current amplitude in . the inductor might behave like an open circuit. When an inductor is connected to a voltage source that varies sinusoidally. Alternatively. Correct were doubled? Note that. .1 of the total current in the circuit? How to approach the problem Hint not displayed Hint A. and . in "A Resistor and a Capacitor in a Series AC Circuit" you do NOT know the amplitude of the driving EMF. The amplitude of the current would be quadrupled. You will find the answer in the "Answers to Homework Problems" link on our course webpage. and . .What is the reactance Hint A. . .3 The reactance of a capacitor Hint not displayed Express your answer in terms of any or all of ANSWER: . Reactance in terms of Part C What would happen to the amplitude of the current in the inductor if the inductance Hint C. GBA A Resistor and a Capacitor in a Series AC Circuit A resistor with resistance and a capacitor with capacitance are connected in series to an AC voltage source. = Correct Part B What is the amplitude Hint B. Part B What is the inductance Hint B. dependent voltage across the capacitor is given by Part A What is the amplitude Hint A.2 Applying Ohm's law to a capacitor Hint not displayed Hint A. The amplitude of the current would be halved.1 Relating of the voltage across the resistor? to Hint not displayed Express your answer in terms of ANSWER: . . and .1 of the inductor? Definition of reactance Hint not displayed Express your answer in terms of ANSWER: = Correct and .1 How to approach the problem Hint not displayed ANSWER: There would be no change in the amplitude of the current.1 of the inductor? and Hint not displayed Express your answer in terms of ANSWER: = Correct . It is instructive to calculate that driving amplitude once you have successfully completed the problem. The amplitude of the current would be doubled. The time. . 5 Correct if 200 ? Part E What is the reading of the voltmeter ANSWER: = 21. to the nearest integer. are connected as shown in figure . Express your answer numerically.ANSWER: = Correct Part C If Hint C.8 Correct if 1000 ? Part G What is the reading of the voltmeter if 1000 ? .0 . Part A What is the reading of the voltmeter ANSWER: = 5. calibrated to read rms values. and .1 . ANSWER: =3 mV Correct Five Voltmeters in an AC Circuit Five infinite-impedance voltmeters.7 Correct if 200 ? Part D What is the reading of the voltmeter ANSWER: = 20.2 Correct if 200 ? Part F What is the reading of the voltmeter ANSWER: = 13. . . 6. what is ? Calculating the answer Use the equation obtained in Part B to work out the answer. in millivolts. Let 0. 200 .400 .18 Correct if 200 ? Part C What is the reading of the voltmeter ANSWER: = 22. and 30.44 Correct if 200 ? Part B What is the reading of the voltmeter ANSWER: = 2.00 . Be careful of powers of ten in your calculation. e. these designs frequently appear in audio circuits.5 Correct if 1000 ? Part I What is the reading of the voltmeter ANSWER: = 16. just think about adding the three curves for the resistor. Hint A. . an inductor of inductance . the audio "signals" consist of current of a mixture of frequencies. and inductor voltages). from 20 Hz up to 20 kHz. and .ANSWER: = 27. Define . and .1 Find Hint not displayed Hint A.1 Correct if 1000 ? Part J What is the reading of the voltmeter ANSWER: = 21.2 Find Hint not displayed Express your answer in terms of either . In "High-Pass Filter".6 Correct Part H What is the reading of the voltmeter ANSWER: = 11. capacitor. The alternating current in audio circuits is not current of a single frequency. instead. I suggest that you ignore MP's comment following a correct answer to Part A. GBA A High-Pass Filter A series L-R-C circuit consisting of a voltage source. Parts B and C are much easier to answer by considering the answer to A in the form sqrt(R^2+X_L^2)/Z (i. Part A Find the ratio . The following two circuit designs are used to suppress the low frequencies (high-pass filter) or to suppress the high frequencies (low-pass filter). . or . and a resistor to be the amplitude of the voltage across the resistor and the inductor. ANSWER: = Correct For the following questions it will be useful to write the voltage ratio in the following form: . a capacitor of capacitance of resistance is driven with an AC voltage of amplitude and frequency . In my opinion.2 Correct if 1000 ? The following two problems are a reminder that AC circuits have a wide range of applications beyond the 60-Hz circuits we use to deliver power to our homes. capacitor. I suggest that you ignore MP's comment following a correct answer to Part A. . and when is small.1 Implications of large Hint not displayed ANSWER: is proportional to is proportional to is proportional to is close to 1.e.1 Implications of small Hint not displayed ANSWER: is proportional to is proportional to is proportional to is close to 1. while the amplitude of the high-frequency inputs will pass through relatively unchanged. . and inductor voltages). . Parts B and C are much easier to answer by considering the answer to A in the form X_C/Z (i. Define to be the amplitude of the . the capacitance of the capacitor is Part A What is the ratio ? . In "Constructing a Low-Pass Filter". . just think about adding the three curves for the resistor. and frequency . Therefore. Part B Which of the following statements is true in the limit of large ( )? Hint B. . . and the inductance of the . GBA Constructing a Low-Pass Filter A series L-R-C circuit is driven with AC voltage of amplitude voltage across the capacitor. . Correct Part C Which of the following statements is true in the limit of small ( )? Hint C. The resistance of the resistor is inductor is . In my opinion. This is why such a circuit is called a high-pass filter. . Correct When is large. this circuit has the property that only the amplitude of the low-frequency inputs will be attenuated (reduced in value) at the output.. . . Correct Part C Which of the following statements is true in the small limit (that is.6%. and . . the circuit of this problem has the property that only the high-frequency inputs will be attenuated (reduced in value) at the output. .1 In the large ANSWER: Implications of large limit. That is why such a circuit is called a low-pass filter. .1 Find Hint not displayed Hint A. Score Summary: Your score on this assignment is 99. .2 Find Hint not displayed Express your answer in terms of either . . so all terms in the denominator involving can be neglected. Therefore.1 In the small ANSWER: Implications of small limit. Correct When omega is large. . Part B Which of the following statements is true in the large limit (that is. ANSWER: = Correct For the following questions it will be useful to write the voltage ratio in the following form: . and .Hint A. is proportional to is proportional to is proportional to is close to 1. while low-frequency inputs will pass through relatively unchanged. . . and . for )? Hint B. is proportional to is proportional to is proportional to is close to 1.8 out of a possible total of 50 points. . so becomes the only significant term in the denominator. for )? Hint C. . You received 49. and or . and when omega is small. .