# Quiz 35: Ac Circuits

Physics & Astronomy

Q 1Q 1

An ac source of period T and maximum voltage V is connected to a single unknown ideal element that is either a resistor, and inductor, or a capacitor. At time t = 0 the voltage is zero. At time t = T/4 the current in the unknown element is equal to zero, and at time t = T/2 the current is I = -I

_{max}, where I_{max}is the current amplitude. What is the unknown element? A) a resistor B) an inductor C) a capacitor D) an inductor or a capacitorFree

Multiple Choice

C

Q 2Q 2

A resistor is connected to an ideal ac power supply.
(a) The phase angle between the current and voltage is
A) 0
B) π/2 radians.
C) -π/2 radians.
D) π radians.
E) 3π/4 radians.
(b) The current in the resistor
A) leads the voltage across the resistor by 90°.
B) lags the voltage across the resistor by 90°.
C) is in phase with the voltage across the resistor.
D) the voltage across the resistor by 45°.
E) lags the voltage across the resistor by 45°.
(c) How does the average power dissipated in the resistor change as the frequency in the ac power supply decreases?
A) It decreases.
B) It increases.
C) It does not change.
D) It increases or decreases depending on the sign of the phase angle.

Free

Short Answer

(a) A (b) C (c)C

Q 3Q 3

When an LRC series circuit is at resonance, which one of the following statements about that circuit is accurate? (There may be more than one correct choice.)
A) The impedance has its maximum value.
B) The reactance of the inductor is zero.
C) The reactance of the capacitor is zero.
D) The reactance due to the inductor and capacitor has its maximum value.
E) The current amplitude is a maximum.

Free

Multiple Choice

E

Q 4Q 4

In a series LRC circuit, the frequency at which the circuit is at resonance is f

_{0}. If you double the resistance, the inductance, the capacitance, and the voltage amplitude of the ac source, what is the new resonance frequency? A) 4 f_{0}B) 2 f_{0}C) f_{0}D) f_{0}/2 E) f_{0}/4Free

Multiple Choice

Q 5Q 5

Which one of the phasor diagrams shown below best represents a series LRC circuit driven at resonance?
A) 1
B) 2
C) 3
D) 4
E) 5

Free

Multiple Choice

Q 6Q 6

When an LRC series circuit is driven at resonance, which of the following statements about the circuit are correct? (There may be more than one correct choice.)
A) The impedance of the circuit is zero.
B) The impedance of the circuit has its maximum value.
C) The impedance of the circuit has its minimum value.
D) The inductive reactance and the capacitive reactance are both zero.
E) The inductive reactance and the capacitive reactance are exactly equal to each other.

Free

Multiple Choice

Q 7Q 7

(a) In an ac circuit, if the peak value of the voltage is 100 V, what is the rms value of the voltage?
A) 141 V
B) 100 V
C) 210 V
D) 71 V
E) 120 V
(b) In an ac circuit, if the rms value of the current is 100 mA, what is the peak value of the current?
A) 141 mA
B) 100 mA
C) 210 mA
D) 71 mA
E) 120 mA

Free

Short Answer

Q 8Q 8

An alternating current is supplied to an electronic component with a warning that the voltage across it should never exceed 12 V. What is the highest rms voltage that can be supplied to this component while staying below the voltage limit in the warning?
A) 6 V
B) 12 V
C) 144 V
D) 6 V

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Multiple Choice

Q 9Q 9

The inductor in a radio receiver carries a current of amplitude 200 mA when a voltage of amplitude 2.40 V is across it at a frequency of 1400 kHz. What is the value of the inductance?
A) 1.43 µH
B) 1.36 µH
C) 9.20 µH
D) 4.42 µH
E) 1.97 µH

Free

Multiple Choice

Q 10Q 10

The 60-Hz ac source of the series circuit shown in the figure has a voltage amplitude of 120 V. The capacitive reactance is 790 Ω, the inductive reactance is 270 Ω, and the resistance is 500Ω.
(a) What is the capacitance of the capacitor?
(b) What is the inductance of the inductor?

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Essay

Q 11Q 11

If the voltage amplitude across an 8.50-nF capacitor is equal to 12.0 V when the current amplitude through it is 3.33 mA, the frequency is closest to:
A) 32.6 MHz
B) 5.20 MHz
C) 32.6 kHz
D) 5.20 kHz
E) 32.6 Hz

Free

Multiple Choice

Q 12Q 12

An ac series circuit consists of a voltage source, an 880-Ω resistor, and an inductance L. (There is no capacitance in the circuit.) The current amplitude is 0.60 A, and the phase angle between the source voltage and the current has a magnitude of 41°
(a) Does the source voltage lag or lead the current?
(b) What is the voltage amplitude of the source?

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Essay

Q 13Q 13

An LRC series circuit has R = 15.0 Ω, L = 25.0 mH, and C = 30.0 μF. The circuit is connected to a 120-V (rms) ac source with frequency 200 Hz.
(a) What is the impedance of the circuit?
(b) What is the rms current in the circuit?
(c) What is the rms voltage across the resistor?
(d) What is the rms voltage across the inductor?
(e) What is the rms voltage across the capacitor?

Free

Essay

Q 14Q 14

An ac circuit is shown in the figure. The rms current in the circuit is measured to be 1.8 A. What is the capacitance of the capacitor?
A) 23 μF
B) 24 μF
C) 21 μF
D) 19 μF
E) 18 μF

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Multiple Choice

Q 15Q 15

The 60-Hz ac source of a series circuit has a voltage amplitude of 120 V. The resistance, capacitive reactance, and inductive reactance are as shown in the figure. What is the rms current in the circuit?
A) 0.097 A
B) 0.11 A
C) 0.12 A
D) 0.14 A
E) 0.17 A

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Multiple Choice

Q 16Q 16

A series ac circuit consists of an inductor having a reactance of 80 Ω and an inductance of 190 mH, a 40-Ω resistor, a capacitor whose reactance is 100 Ω, and an ac source. The rms current in the circuit is measured to be 2.2 A. What is the rms voltage of the source?
A) 98 V
B) 96 V
C) 93 V
D) 91 V
E) 88 V

Free

Multiple Choice

Q 17Q 17

A 120-V rms voltage at 1000 Hz is applied to an inductor, a 2.00-μF capacitor and a 100-Ω resistor, all in series. If the rms value of the current in this circuit is 0.680 A, what is the inductance of the inductor?
A) 34.2 mH
B) 35.8 mH
C) 11.4 mH
D) 17.9 mH
E) 22.8 mH

Free

Multiple Choice

Q 18Q 18

A series LRC circuit has a sinusoidal voltage supplied to it at 197 kHz with a peak voltage of 270 V, a 41-Ω resistance, a 14- μF capacitor, and a 64-H inductance. What is the peak current for this circuit?
A) 3.5 μA
B) 2.3 μA
C) 4.2 μA
D) 6.6 μA

Free

Multiple Choice

Q 19Q 19

A series circuit consists of a 50-Hz ac source, a 50-Ω resistor, a 0.50-H inductor, and a 60-μF capacitor. The rms current in the circuit is measured to be 3.1 A. What is the voltage amplitude of the source?
A) 510 V
B) 270 V
C) 220 V
D) 180 V
E) 160 V

Free

Multiple Choice

Q 20Q 20

A series circuit consists of ac source, a 90-Ω resistor, a 0.80-H inductor, and an 80-μF capacitor. The frequency of the source is adjusted so that the capacitive reactance is equal to twice the inductive reactance. What is the frequency of the source?
A) 14 Hz
B) 13 Hz
C) 16 Hz
D) 17 Hz
E) 19 Hz

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Multiple Choice

Q 21Q 21

An LRC series circuit consists of an 85.0-Ω resistor, a 14.0-μF capacitor, a 1.50-mH inductor, and a variable frequency ac source of voltage amplitude 13.25 V. At what angular frequency will the inductive reactance be 4.00 times as large as the capacitive reactance?
A) 1.38 × 10

^{4}rad/s B) 6.90 × 10^{3}rad/s C) 3.45 × 10^{4}rad/s D) 2.20 × 10^{4}rad/s E) 1.10 × 10^{4}rad/sFree

Multiple Choice

Q 22Q 22

A series ac circuit consists of a voltage source of frequency 60 Hz and source voltage amplitude 345 volts, a 701-Ω resistor, a 1.6-μF capacitor, and an inductor of inductance L.
(a) What must be the value of L for the phase angle to be zero?
(b) When L has the value calculated in part (a), what is the current amplitude in the circuit?

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Essay

Q 23Q 23

A series LRC circuit consists of an ac voltage source of amplitude 75.0 V and variable frequency, a 12.5-µF capacitor, a 5.00-mH inductor, and a 35.0-Ω resistor.
(a) To what angular frequency should the ac source be set so that the current amplitude has its largest value?
(b) Under the conditions of part (a), what is the maximum current amplitude?
(c) Suppose that the voltage source is set to twice the angular frequency needed in part (a). What will be the current amplitude in this case?

Free

Essay

Q 24Q 24

An ac circuit is shown in the figure. The rms current in the circuit is 1.3 A. What is the peak magnetic energy in the inductance?
A) 0.32 J
B) 0.16 J
C) 0.48 J
D) 0.64 J
E) 0.80 J

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Multiple Choice

Q 25Q 25

A 120-V rms voltage at 60.0 Hz is applied across an inductor, a capacitor, and a resistor in series. If the peak current in this circuit is 0.8484 A, what is the impedance of this circuit?
A) 200 Ω
B) 141 Ω
C) 20.4 Ω
D) 120 Ω
E) 100 Ω

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Multiple Choice

Q 26Q 26

A 25.0-mH inductor, a 2.00-μF capacitor, and a certain resistor are connected in series across an ac voltage source at 1000 Hz. If the impedance of this circuit is 200 Ω, what is the resistance of the resistor?
A) 100 Ω
B) 184 Ω
C) 200 Ω
D) 552 Ω
E) 579 Ω

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Multiple Choice

Q 27Q 27

A series circuit has a resistance of 4.0 Ω, a reactance (due to the capacitance) of 21.0 Ω, and a reactance (due to the inductance) of 17.0 Ω. Find the impedance of the circuit.
A) 5.7 Ω
B) 27 Ω
C) 8.0 Ω
D) 42 Ω

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Multiple Choice

Q 28Q 28

The phase angle of an LRC series circuit with an inductive reactance of 200 Ω and a capacitive reactance of 100 Ω is 40.0°. What is the value of the resistor in this circuit?
A) 100 Ω
B) 119 Ω
C) 156 Ω
D) 200 Ω
E) 265 Ω

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Multiple Choice

Q 29Q 29

The phase angle of an LRC series circuit with an inductive reactance of 200 Ω, a resistor of 200 Ω and a certain capacitor at 1000 Hz is 40.0°. What is the value of the capacitance in this circuit?
A) 1.95 µF
B) 2.95 µF
C) 3.95 µF
D) 4.95 µF
E) 5.95 µF

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Multiple Choice

Q 30Q 30

The phase angle of an LRC series circuit with a capacitive reactance of 40 Ω, a resistor of 100 Ω and a certain inductor at 1000 Hz is 40.0°. What is the value of the inductance in this circuit?
A) 11.8 mH
B) 124 mH
C) 212 mH
D) 61.9 mH
E) 19.7 mH

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Multiple Choice

Q 31Q 31

An LRC series circuit has voltage supplied to it at a frequency of 13.0 kHz with a phase difference between the current and the voltage of magnitude 0.20 rad. If the circuit has a capacitance of 5.0 μF and an inductance of 0.050 H find the resistance of the circuit.
A) 20 kΩ
B) 0.99 kΩ
C) 9.0 kΩ
D) 0.32 kΩ

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Multiple Choice

Q 32Q 32

A series LRC ac circuit has a resistance of 4.0 kΩ, a capacitance of 33.0 μF, and an inductance of 23.0 H. If the frequency of the alternating current is 2.0/π kHz, what is the phase angle between the voltage and the current?
A) 1.5 rad
B) -1.6 rad
C) 23 rad
D) 3.1 rad

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Multiple Choice

Q 33Q 33

An LRC ac series circuit has R = 15 Ω, L = 25 mH, and C = 30 μF. The circuit is connected to a 120-V (rms) ac source with frequency 200 Hz.
(a) What is the average power dissipated by the circuit?
(b) What is the power factor for the circuit?

Free

Essay

Q 34Q 34

An LRC ac series circuit with R = 15 Ω, L = 25 mH, and C = 30 μF, is attached to a 100-V (rms) ac power supply. The frequency of the power supply is adjusted so that the circuit is in resonance.
(a) What is the rms current in the circuit?
(b) What is the power dissipated by the circuit?

Free

Essay

Q 35Q 35

What is the average power dissipated by a 25-Ω resistor in an LRC series ac circuit for which the power factor is equal to 0.25 and the maximum voltage of the ac source is 8.0 V?
A) 0.040 W
B) 0.32 W
C) 0.16 W
D) 0.62 W
E) 0.080 W

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Multiple Choice

Q 36Q 36

A series LRC ac circuit has a peak voltage of 111 V and a peak current of 2.00 A. If the current lags the voltage by 35.0

^{∘}, what is the average power of the circuit? A) 91 W B) 182 W C) 78 W D) 156 WFree

Multiple Choice

Q 37Q 37

An LRC ac circuit has a reactance (due to its capacitance) of 17 kΩ, a reactance (due to its inductance) of 9.0 kΩ, and a resistance of 28 kΩ. What is the power factor of the circuit?
A) 0.96
B) 0.28
C) 1.04
D) 0.48

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Multiple Choice

Q 38Q 38

For an RLC ac circuit, the rms current is 10 A. If the impedance is 12 kΩ when the voltage leads the current by 39°, find the average power of the circuit.
A) 930 kW
B) 47 kW
C) 93 kW
D) 190 kW

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Multiple Choice

Q 39Q 39

A series LRC ac circuit has a peak current of 1.0 A with a frequency of 54 kHz. If the resistance of the circuit is 51 kΩ, the capacitance of the circuit is 19 μF, and the inductance of the circuit is 25 μH, determine the average power of the circuit.
A) 26 kW
B) 77 kW
C) 7.7 kW
D) 4.1 kW

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Multiple Choice

Q 40Q 40

A series circuit consists of a 50-Hz ac source, a 40-Ω resistor, a 0.30-H inductor, and a 60-μF capacitor. The rms current in the circuit is measured to be 1.6 A. What is the power factor of the circuit?
A) 0.70
B) 0.66
C) 0.63
D) 0.59
E) 0.56

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Multiple Choice

Q 41Q 41

An ac series circuit consists of a voltage source of frequency 60 Hz and voltage amplitude V, a 533-Ω resistor, and a capacitor of capacitance 6.4-μF. What must be the source voltage amplitude V for the average electrical power consumed in the resistor to be 989 W? There is no inductance in the circuit.

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Short Answer

Q 42Q 42

For an LRC series circuit containing a resistance of 11.0-Ω, a capacitance of 2.0-μF, and an inductance of 24.0 H, what frequency is needed to minimize the impedance?
A) 0.023 kHz
B) 0.14 kHz
C) 10 kHz
D) 1.7 kHz

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Multiple Choice

Q 43Q 43

A series LRC circuit consists of a 100-Ω resistor, a 0.100-μF capacitor and a 2.00-mH inductor connected across a 120-V rms ac voltage source operating at . At what frequency will this circuit be in resonance?
A) 70.7 kHz
B) 17.9 kHz
C) 22.5 kHz
D) 35.3 kHz
E) 11.3 kHz

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Multiple Choice

Q 44Q 44

An ac source having a maximum voltage output of 30 V is connected in series with a 50-Ω resistor, a 0.60-H inductor, and a 20-µF capacitor. What is the maximum charge on the capacitor when the frequency of the source is adjusted so that the circuit is in resonance?
A) 1.0 mC
B) 0.00 mC
C) 2.1 mC
D) 4.2 mC
E) 8.4 mC

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Multiple Choice

Q 45Q 45

A series LRC circuit consists of a 5.00-pF capacitor, a 7.25-mH inductor, a 75.0-Ω resistor, and a 50.0-V ac power source of variable frequency. At what frequency will the impedance of this circuit be equal to 75.0 Ω?

Free

Short Answer

Q 46Q 46

A series LRC circuit consists of a 12.0-mH inductor, a 15.0-µF capacitor, a resistor, and a 110-V (rms) ac voltage source. If the impedance of this circuit is 45.0 Ω at resonance, what is its impedance at a frequency twice the resonance frequency?

Free

Short Answer