Question 1

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 2

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 3

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 4

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

Accepted Answer

The capacitive reactance (Xc) is given by 1/(2πfC) and the inductive reactance (Xl) is given by 2πfL. Given that Xc = 2Xl, we can set up the equation 1/(2πfC) = 2(2πfL). Solving for f with L = 0.80 H and C = 80 μF gives f ≈ 14 Hz.

Question 5

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

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Question 6

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

Accepted Answer

The phase angle is given by:$$\phi = \arctan\left(\frac{XL - XC}{R}\right)$$where:* XL is the inductive reactance* XC is the capacitive reactance* R is the resistanceIn this case, we have:$$XL = 2\pi f L = 2\pi (2.0/π kHz)(23.0 H) = 29.9 kΩ$$$$XC = \frac{1}{2\pi f C} = \frac{1}{2\pi (2.0/π kHz)(33.0 μF)} = 12.0 kΩ$$Therefore, the phase angle is:$$\phi = \arctan\left(\frac{29.9 kΩ - 12.0 kΩ}{4.0 kΩ}\right) = 1.5 rad$$

Question 7

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

Accepted Answer

The voltage amplitude of the source can be found by first calculating the impedance (Z) of the circuit and then using Ohm's law (V = IZ) in its AC form, where V is the voltage amplitude, I is the rms current, and Z is the impedance. The impedance of a series RLC circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$, where $X_L = 2\pi fL$ is the inductive reactance and $X_C = \frac{1}{2\pi fC}$ is the capacitive reactance. Given $f = 50\,Hz$, $L = 0.50\,H$, and $C = 60\,\mu F = 60 \times 10^{-6}\,F$, we calculate $X_L$ and $X_C$, then find $Z$, and finally use $V = IZ$ to find the voltage amplitude.1. Calculate $X_L = 2\pi(50)(0.50) = 157\,\Omega$.2. Calculate $X_C = \frac{1}{2\pi(50)(60 \times 10^{-6})} \approx 53.05\,\Omega$.3. Calculate $Z = \sqrt{50^2 + (157 - 53.05)^2} \approx 164.9\,\Omega$.4. Calculate $V = 3.1 \times 164.9 \approx 510\,V$.Therefore, the voltage amplitude of the source is approximately 510 V.

Question 8

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 9

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 = √(R^2+(ωL-1/(ωC))^2)

where 
R is the resistance of the resistor
L is the inductance of the inductor 
C is the capacitance of the capacitor
ω = 2πƒ is the angular frequency

Substituting the given values, we get:

200 = √(R^2+(2π×1000×25×10^-3-1/(2π×1000×2×10^-6))^2)

Simplifying and solving for R, we get:

R = 184 Ω

Therefore, the option B is correct.

Question 10

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

Accepted Answer

The impedance of a series circuit is given by the formula Z = sqrt(R^2 + (XL - XC)^2), where R is the resistance, XL is the inductive reactance, and XC is the capacitive reactance. In this problem, we are given the peak current and the voltage, so we can use Ohm's law to find the impedance: Z = V/I = 120 V / 0.8484 A = 141 Ω.

Question 11

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 12

A series ac circuit consists of a voltage source of frequency 60 Hz and source voltage amplitude 345 volts,a  resistor,a  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 13

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 for an LRC series circuit can be calculated using the following formula:

tan θ = (XL - XC)/R

where XL is the inductive reactance, XC is the capacitive reactance, and R is the resistance.

Substituting the given values, we have:

tan 40.0° = (200 Ω - 100 Ω)/R

tan 40.0° = 100 Ω/R

R = 100 Ω/tan 40.0°

R = 119 Ω (rounded to the nearest whole number)

Therefore, the value of the resistor in this circuit is 119 Ω, which corresponds to choice B.

Question 14

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 15

A series LRC circuit has a sinusoidal voltage supplied to it at  with a peak voltage of  a  resistance,a  capacitor,and a  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

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Question 16

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 17

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

Accepted Answer

The phase difference between the current and the voltage in an LRC series circuit is given by:$$	an \phi = \frac{XL - XC}{R}$$where XL is the inductive reactance, XC is the capacitive reactance, and R is the resistance.We are given that the frequency of the voltage is 13.0 kHz, the capacitance is 5.0 μF, and the inductance is 0.050 H. We can use these values to calculate XL and XC:$$XL = 2\pi fL = 2\pi (13.0 kHz)(0.050 H) = 4.10 k\Omega$$$$XC = \frac{1}{2\pi fC} = \frac{1}{2\pi (13.0 kHz)(5.0 \mu F)} = 2.44 k\Omega$$We are also given that the phase difference between the current and the voltage is 0.20 rad. We can use this value to solve for R:$$	an 0.20 rad = \frac{4.10 k\Omega - 2.44 k\Omega}{R}$$$$R = \frac{4.10 k\Omega - 2.44 k\Omega}{	an 0.20 rad} = 9.9 k\Omega$$Therefore, the resistance of the circuit is 9.9 kΩ, which is closest to choice A, 20 kΩ.

Question 18

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

Accepted Answer

The impedance of a series circuit is calculated using the formula Z = √(R² + (X_L - X_C)²), where R is resistance, X_L is inductive reactance, and X_C is capacitive reactance. Here, Z = √(4.0² + (17.0 - 21.0)²) = √(16 + (-4)²) = √(16 + 16) = √32 = 5.7 Ω.

Question 19

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 20

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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Quiz 31: Alternating Current

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?

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?

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?

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 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 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 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?

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 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 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 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?

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?

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 circuit has a sinusoidal voltage supplied to it at with a peak voltage of a resistance,a capacitor,and a inductance.What is the peak current for 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?

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 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 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?