Question 1

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 2

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 3

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 4

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 5

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 6

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 7

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:
$$Z=\sqrt{R^2+(\omega L-\frac{1}{\omega C})^2}$$
where $\omega =2\pi f$ is the angular frequency.
Substituting the given values:
$$200=\sqrt{R^2+(2\pi\cdot 1000\cdot 25	imes 10^{-3}-\frac{1}{2\pi\cdot 1000\cdot 2	imes 10^{-6}})^2}$$
Solving for $R$, we get:
$$R=184\ \Omega$$
Therefore, the answer is B.

Question 8

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 9

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 10

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 11

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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Question 12

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 13

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

Accepted Answer

The average power in an AC circuit is given by P_avg = V_peak * I_peak * cos(φ) / 2, where φ is the phase angle. Here, V_peak = 111 V, I_peak = 2.00 A, and φ = 35°. So, P_avg = 111 * 2 * cos(35°) / 2 = 91 W.

Question 14

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 15

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 16

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

Accepted Answer

The inductive reactance $X_L = \omega L$ and the capacitive reactance $X_C = \frac{1}{\omega C}$, where $\omega$ is the angular frequency, $L$ is the inductance, and $C$ is the capacitance. Given that $X_L = 4X_C$, we can set up the equation $\omega L = 4 \left(\frac{1}{\omega C}\right)$. Solving for $\omega$ gives $\omega = \sqrt{\frac{4}{LC}}$. Substituting $L = 1.50 \times 10^{-3}$ H and $C = 14.0 \times 10^{-6}$ F into the equation yields $\omega \approx 1.38 \times 10^{4}$ rad/s.

Question 17

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 18

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 19

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

The phase angle in an LRC series circuit can be calculated using the formula: tan φ = (XL − XC)/R
where φ is the phase angle, XL is the inductive reactance, XC is the capacitive reactance, and R is the resistance of the circuit.
Substituting the given values, we get: tan 40° = (200 − 100)/R
Solving for R, we get R = 119 Ω. Therefore, the answer is choice B: 119 Ω.

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 35: Ac Circuits

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 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 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 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.

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 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?

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 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.

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?

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 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 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 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?

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?

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 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?

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?

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 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?