Deck 30: Alternating Current

Question 1

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?

Answer 1

(a) 3.4 µF
(b) 720 mH

Question 2

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?

Answer 2

(a) 15.8 Ω
(b) 7.61 A
(c) 114 V (d) 239 V
(e) 202 V

Question 3

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

Answer 3

6 V

Question 4

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

Question 5

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

Question 6

A transformer changes the 10,000 V power line to 120 V. If the primary coil contains 750 turns, how many turns are on the secondary?

A) 3
B) 6
C) 9
D) 63,000
E) 21,000

Question 7

The primary coil of a transformer has 100 turns and its secondary coil has 400 turns. If the ac voltage applied to the primary coil is 120 V, what voltage is present in its secondary coil?

A) 100 V
B) 30 V
C) 70 V
D) 480 V
E) 400 V

Question 8

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.

Question 9

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.

Question 10

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?

Question 11

In a series LRC circuit, the frequency at which the circuit is at resonance is f0. 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 f0
B) 2 f0
C) f0
D) f0/2
E) f0/4

Question 12

When a current of 2.0 A flows in the 100-turn primary of an ideal transformer, this causes 14 A to flow in the secondary. How many turns are in the secondary?

A) 700
B) 356
C) 114
D) 14
E) 4

Question 13

In a transformer, how many turns are necessary in a 110-V primary if the 24-V secondary has 100 turns?

A) 458
B) 240
C) 110
D) 22
E) 4

Question 14

An ideal transformer consists of a 500-turn primary coil and a 2000-turn secondary coil. If the current in the secondary is 3.0 A, what is the current in the primary?

A) 0.75 A
B) 1.3 A
C) 12 A
D) 24 A
E) 48 A

Question 15

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

Question 16

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

Question 17

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

Question 18

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

Question 19

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 = -Imax, where Imax is the current amplitude. What is the unknown element?

A) a resistor
B) an inductor
C) a capacitor
D) an inductor or a capacitor

Question 20

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

Question 21

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

Question 22

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?

Question 23

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

Question 24

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 × 10⁴ rad/s
B) 6.90 × 10³ rad/s
C) 3.45 × 10⁴ rad/s
D) 2.20 × 10⁴ rad/s
E) 1.10 × 10⁴ rad/s

Question 25

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

Question 26

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

Question 27

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

Question 28

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?

Question 29

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

Question 30

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

Question 31

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

Question 32

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

Question 33

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

Question 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?

Question 35

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

Question 36

A series LRC circuit has a sinusoidal voltage supplied to it at 197 kHz with a peak voltage of 270 V, a 41-kΩ resistance, a 14-μF capacitor, and a 63-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

Question 37

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

Question 38

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?

Question 39

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 W

Question 40

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

Question 41

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?

Question 42

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

Question 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

Question 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

Question 45

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

Question 46

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.

Question 47

For an LRC series circuit containing a resistance of 11.0 kΩ, 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

Question 48

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?

Question 49

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