Question 1

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

Accepted Answer

The rms voltage of the source can be calculated using the formula $V = IZ$, where $V$ is the rms voltage, $I$ is the rms current, and $Z$ is the impedance of the circuit. The impedance $Z$ of a series RLC circuit is given by $Z = \sqrt{R^2 + (X_L - X_C)^2}$, where $R$ is the resistance, $X_L$ is the inductive reactance, and $X_C$ is the capacitive reactance. Substituting the given values, $Z = \sqrt{40^2 + (80 - (-100))^2} = \sqrt{1600 + 180^2} = \sqrt{1600 + 32400} = \sqrt{34000} = 184.39 \Omega$. Therefore, the rms voltage $V = 2.2 A \times 184.39 \Omega = 405.658 V$. However, this calculation seems to have an error in interpretation of the correct answer options provided, indicating a mistake in the calculation process. Correctly calculating, the impedance should be considered with the correct subtraction for reactances, and the final voltage calculation should align with the provided options. Correcting the calculation: $Z = \sqrt{40^2 + (80 - 100)^2} = \sqrt{1600 + 400} = \sqrt{2000} = 44.72 \Omega$. Then, $V = IZ = 2.2 \times 44.72 = 98.384 V$, which rounds to approximately 98 V, matching option A. The initial calculation provided was incorrect; the correct approach gives us the answer as 98 V, aligning with option A.

Question 2

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

Accepted Answer

A

Question 3

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

Accepted Answer

B

Question 4

An alternating current is supplied to an electronic component with a warning that the voltage across it should never exceed  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

Accepted Answer

The answer of An alternating current is supplied to an...

Question 5

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

Accepted Answer

The answer of An ac circuit is shown in the...

Question 6

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.

Accepted Answer

The answer of When an LRC series circuit is at...

Question 7

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

Accepted Answer

The answer of The 60-Hz ac source of a series...

Question 8

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.

Accepted Answer

We can use the formula for capacitive reactance (Xc) to find the frequency:

Xc = 1/(2πfC)

Rearranging this formula gives:

f = 1/(2πXcC)

We know the capacitance (C) and the voltage amplitude (V), and we can use Ohm's Law to find the current amplitude (I):

I = V/Xc (since Xc = V/I)

So:

I = V/(1/(2πfC))
I = 2πfCV

Solving for f:

f = I/(2πVC)
f = (3.33 mA)/(2π)(8.50 nF)(12.0 V)
f = 5.20 MHz

Therefore, the answer is B: 5.20 MHz.

Question 9

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?

Accepted Answer

The answer of The 60-Hz ac source of the series...

Question 10

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 answer of A series circuit consists of ac source,...

Question 11

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 12

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

Accepted Answer

The answer of In a series LRC circuit, the frequency...

Question 13

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.

Accepted Answer

At resonance in an LRC series circuit, the inductive reactance (XL) and capacitive reactance (XC) are equal and cancel each other out, leading to the circuit having its minimum impedance, which is primarily resistive.

Question 14

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?

Accepted Answer

The answer of An LRC series circuit has R =...

Question 15

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

Accepted Answer

The answer of Which one of the phasor diagrams shown...

Question 16

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 capacitor

Accepted Answer

The unknown element is a capacitor because the current leads the voltage by 90 degrees in a capacitive circuit. At t = 0, the voltage is zero and the current is at its maximum (positive or negative), but since the current is zero at t = T/4, this indicates the current is lagging behind the voltage by a quarter period, characteristic of a capacitive circuit. At t = T/2, the voltage would be at its maximum negative value, aligning with the described current behavior.

Question 17

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 18

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?

Accepted Answer

The answer of An ac series circuit consists of a...

Question 19

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

Accepted Answer

The answer of A 120-V rms voltage at 1000 Hz...

Question 20

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?

Accepted Answer

The answer of A series ac circuit consists of a...

Quiz 32: Ac Circuits

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 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?

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?

An alternating current is supplied to an electronic component with a warning that the voltage across it should never exceed What is the highest rms voltage that can be supplied to this component while staying below the voltage limit in the warning?

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?

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.)

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?

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

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?

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 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?

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?

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.)

Which one of the phasor diagrams shown below best represents a series LRC circuit driven at resonance?

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 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?

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?