Physics 72: Chapter 31 Problem Set
Summer 2010
Name: Lecturer: Mr Carlos Baldo III
Score: Section: X7-7
Encircle the letter of the correct answer. Solve each problem clearly and completely for full credit. For the next two numbers, consider a 2 â„Ś resistor connected in series to an ac source. The voltage measured by an ac multimeter across the resistor is VRMS = 4V. 1.
Maximum current. What is the peak value of the current through the resistor? A. B. C.
2.
2A 2 2A
2A
1 E.
A.
8W
B.
8 2W
C.
A
2 2
D. E.
4 2W 4 W 2
W
2
RMS. What is the voltage amplitude of an ac source if its RMS voltage is 10 2 V? A. 25 V B. 20 V C. 15 V D. 10 V E. 5 V
For the next two numbers, consider a sinusoidal current through a resistor with R = 10 ohms. 4.
D.
Power. What is the average power dissipated in the resistor?
8
3.
1 A 2
i ( t ) = Icosωt
has an rms value of Irms = 2 A and passes
RMS. What is the current amplitude of the given ac circuit? A. B. C.
2 2A 2A 1A
D. E.
1/ 2A 2 / 2A
5.
Resistor in AC. What is the value of the rms voltage across the resistor? A. 1 V B. 2 V C. 5 V D. 10 V E. 20 V
6.
Frequency. As the frequency in the AC circuit shown increases, the rms current through the resistor _______. A. Increases B. Decreases C. Does not change D. May increase or decrease depending on the magnitude of the original frequency E. May increase or decrease depending on the magnitude of the resistance
Physics 72: Chapter 31 Problem Set 7.
Summer 2010
Instantaneous I and V. A capacitor is connected in series to an ac source ε(t) = 10 cos(ωt) V. What is the instantaneous current across a capacitor at the instant its instantaneous voltage is 10 V? A. 0 A B. 5 A C. 10 2 A D. −10 2 A E. 10 A
For the next two numbers, consider the circuit shown at the right. The given reactances are for a certain nonzero finite source frequency 8.
9.
Impedance. What is the impedance of the circuit? A.
75 Ω
B.
125 Ω
C.
925 Ω
D.
35 Ω
E.
15 Ω
Power. Which of the following statements is false? A. The average power of a resistor connected to an ac source is zero B. The average power of a capacitor connected to an ac source is zero C. The average power of an inductor connected to an ac source is zero D. The instantaneous power of an inductor connected to an ac source can be nonzero E. The instantaneous power of a capacitor connected to an ac source can be nonzero
For the next two numbers, consider the circuit shown at the right. Let ε1 = (20 V) cos(2πft), f = 100/π Hz, ε2 = 10 V. 10. Resistor with ac source. If R = 1 kΩ, what are the maximum and minimum currents through the resistor. A. 0 mA; 0 mA B. 10 mA; -10 mA C. 10 mA; -30 mA D. 30 mA; -10 mA E. 30 mA; -30 mA 11. Capacitor with ac source. If the resistor is replaced with a capacitor of capacitance C = 1 µF, what is the average current through the capacitor. A. 0 mA B. 6 mA C. 12 mA D. -12 mA E. -6 mA 12. RLC circuit Consider a series RLC circuit with R = 270 Ω, L = 18 mH and C = 100 µF connected to an ac source VRMS = 2 V. Shown at the right is the superimposed labeled W, X, Y and Z as a function of source frequency. Based on the graph, W, X, Y and Z are the ___________ respectively? A. Current, resistance, capacitive reactance and inductive reactance B. Resistance, impedance, inductive reactance and capacitive reactance C. Resistance, impedance, capacitive reactance and inductive reactance D. Impedance, resistance, inductive reactance and capacitive reactance E. Impedance, resistance, capacitive reactance and inductive reactance
Physics 72: Chapter 31 Problem Set
Summer 2010
13. AC Current-voltage. Consider an inductor in series with an ac battery. If the maxiimum voltage is doubled, the RMS current through the inductor ___________. A. Increases by a factor of 2 B. Decreases by a factor of 2 C. Increases by a factor of 2 D. Decreases by a factor of 2 E. Remains the same 14. Impedance. What is the impedance of an LRC series circuit with L = 3 H, R = 3 Ω, C = 0.25 F, and ω = 2 rad/s? A. 2 Ω B. 4 Ω C. 5 Ω D. 10 Ω E. 15 Ω 15. Impedance at High Frequency. What happens to the impedance of the circuit as the source voltage frequency approaches infinity (i.e. very large)? A. approaches infinity B. approaches zero C. decreases D. increases E. not enough information is given 16. Phasor. The current phasor of an inductor in an L-R-C series circuit is shown below. Which of the following statements is definitely TRUE? I. The instantaneous current of the inductor is positive. II. The voltage phasor of the capacitor is in the second quadrant. III. The current phasor of the resistor is parallel to the phasor shown. A. B. C. D. E.
I only I and II only II and III only I and III only I, II and III
17. Resonance. Which of the following statements are TRUE for an LRC series circuit? I. Increasing the inductance will increase the resonance frequency. II. Decreasing the inductance will increase the resonance frequency. III. Increasing the capacitance will increase the resonance frequency. IV. Decreasing the capacitance will increase the resonance frequency. A. B. C. D. E.
I only I and III I and IV II and III II and IV
18. Resonance 1. In an LRC series circuit, the current becomes ___________ and the impedance becomes _________ at an angular frequency A. B. C. D. E.
maximum, minimum minimum, minimum minimum, maximum maximum, maximum zero, maximum
ω0 = 1/ LC called the resonance angular frequency.
Physics 72: Chapter 31 Problem Set
Summer 2010
19. Resonance 2. For a series LRC ac circuit at resonance, all of the following statements are TRUE except that A. the voltage across the resistor is maximum B. the voltage across the series connection of the inductor and capacitor is zero. C. the voltage across the capacitor is zero D. the current through the resistor is maximum E. the current through the inductor is maximum 20. Capacitive reactance. A series LRC circuit is tuned to its resonance angular frequency of 3.0 x 106 rad/s. If the inductor in the circuit has inductance of 1.0 x10-6 H, what is the capacitive reactance of the circuit at this frequency? A. 0 Ω B. 1.5 Ω C. 3.0 Ω D. 6.0 Ω E. 12.0 Ω 21. Power up. The phase difference of the current and the voltage in an ac circuit is 60 degrees. If the current amplitude is 2.0 A and the voltage is 100 V, what is the average power input to the circuit? A. 200 W B. 100 W C. 50 W D. 25 W E. 12.5 W 22. Tuned. A. B. C. D. E.
At resonance, the current and the voltage _________. are out of phase. are in-phase. Has a phase difference of 45 degrees. Has a phase difference of 30 degrees. Has a phase difference of 60 degrees.
i = (3.0 x10−3 A) cos(2π (60 Hz )t )
flowing through a 23. Capacitor in AC circuit. Consider a current given by 1.0 x10-6 F capacitor. What happens to the maximum voltage VC across the capacitor if the frequency is increased to 120 Hz? A. Decreases by a factor of 4 B. Decreases by a factor of 2 C. Remains the same D. Increases by a factor of 4 E. Increases by a factor of 2 24. RLC AC Circuit. For an RLC circuit connected to an AC source, the instantaneous voltage of the source is equal to ________? A. the sum of the maximum voltages across the elements B. the sum of the instantaneous voltages across the elements C. the sum of the rms voltages across the elements D. they are not related to the instantaneous voltage of the source E. zero
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