Question 1

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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Question 2

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?

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Question 3

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

Accepted Answer

The power factor (PF) is the cosine of the angle between the voltage and current in an AC circuit. In an LRC circuit, we need to consider the reactance due to both capacitance and inductance. The total impedance (Z) of the circuit is given by:

Z = sqrt((R^2) + ((Xc - Xl)^2))

where R is the resistance, Xc is the capacitive reactance, and Xl is the inductive reactance.

Substituting the given values, we get:

Z = sqrt((28000^2) + ((17000 - 9000)^2)) = 33541.02 Ω

The phase angle (θ) between voltage and current is given by:

θ = arctan((Xc - Xl)/R)

Substituting the given values, we get:

θ = arctan((17000 - 9000)/28000) = 38.66°

The power factor (PF) is the cosine of this angle, i.e., cos(θ). Substituting the value of θ, we get:

PF = cos(38.66°) = 0.96

Therefore, the best choice is A.

Question 4

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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Question 5

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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Question 6

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

Accepted Answer

The impedance of the circuit is given by:

$$Z=\sqrt{R^2+(X_L-X_C)^2}$$

where $R$ is the resistance of the resistor, $X_L=\omega L$ is the inductive reactance, and $X_C=\frac{1}{\omega C}$ is the capacitive reactance. At 1000 Hz, we have:

$$X_L=2\pi f L=2\pi (1000	ext{ Hz})(25.0	imes 10^{-3}	ext{ H})=157.1	ext{ }\Omega$$

and

$$X_C=\frac{1}{2\pi fC}=\frac{1}{2\pi (1000	ext{ Hz})(2.00	imes 10^{-6}	ext{ F})}=79.58	ext{ }\Omega$$

Substituting into the impedance equation and solving for $R$, we get:

$$200	ext{ }\Omega=\sqrt{R^2+(157.1	ext{ }\Omega-79.58	ext{ }\Omega)^2}$$

$$R=\sqrt{(200	ext{ }\Omega)^2-(77.52	ext{ }\Omega)^2}\approx\boxed{184	ext{ }\Omega}$$

Question 7

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

Accepted Answer

To find the power factor of the circuit, we need to calculate the impedance and the phase angle of the circuit.

The impedance of the circuit is given by:

Z = sqrt(R^2 + (XL - XC)^2)
where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance.

Using the given values, we get:

Z = sqrt(40^2 + (2π*50*0.30 - 1/(2π*50*60*10^-6))^2)
   = 51.76 Ω

The phase angle of the circuit is given by:

θ = tan^-1((XL - XC)/R)

Using the given values, we get:

θ = tan^-1((2π*50*0.30 - 1/(2π*50*60*10^-6))/40)
   = 42.58°

The power factor of the circuit is cos(θ), which is:

cos(42.58°) = 0.70

Therefore, the best choice is A) 0.70.

Question 8

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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Question 9

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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Question 10

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

Accepted Answer

We can use the equation tan(Φ) = (X_L - X_C)/R where Φ is the phase angle, X_L is the inductive reactance, X_C is the capacitive reactance, and R is the resistance. Substituting the given values, we get tan(40°) = (200 Ω - 100 Ω)/R. Solving for R, we get R = (200 Ω - 100 Ω)/tan(40°) = 119 Ω. Therefore, the answer is choice B.

Question 11

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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Question 12

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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Question 13

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?

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Question 14

An ac series circuit consists of a voltage source of frequency 60 Hz and voltage amplitude V, a  resistor, and a capacitor of capacitance  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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Question 15

For an LRC series circuit containing a resistance of  a capacitance of  and an inductance of  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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Question 16

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?

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Question 17

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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Question 18

A series LRC ac circuit has a peak voltage of  and a peak current of  If the current lags the voltage by  what is the average power of the circuit?
A) 91 W
B) 182 W
C) 78 W
D) 156 W

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Question 19

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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Question 20

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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Quiz 32: Ac Circuits

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.

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?

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 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 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 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 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?

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?

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?

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?

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 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?

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?

An ac series circuit consists of a voltage source of frequency 60 Hz and voltage amplitude V, a resistor, and a capacitor of capacitance 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.

For an LRC series circuit containing a resistance of a capacitance of and an inductance of what frequency is needed to minimize the impedance?

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 series LRC ac circuit has a peak voltage of and a peak current of If the current lags the voltage by what is the average power of the circuit?

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?

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.