Question 1

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

(a) The source voltage leads the current.
(b) 700 volts

Question 2

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

At resonant frequency, capacitive reactance Xc = 1/ωC = 1/(2ωL) = inductive reactance Xl
Thus, 1/ωC= 2ωL
Solving for ω: ω = 1/(sqrt(LC)) = 1/(sqrt(0.8H x 80μF)) = 5 rad/s
Frequency, f = ω/2π = 5/(2π) = 0.795 Hz
Since capacitive reactance is inversely proportional to frequency, we need to double the frequency to halve the reactance, which gives us a frequency of 2 x 0.795 Hz ≈ 1.59 Hz
Therefore, the correct answer is option A) 14 Hz, which is the closest frequency to 1.59 Hz.

Question 3

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 4

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

Accepted Answer

The highest rms voltage that can be supplied to the component while staying below the voltage limit is half of the peak-to-peak voltage, which is equal to 12 V. Therefore, the highest rms voltage is 6 V.

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

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 7

(a) In an ac circuit, if the peak value of the voltage is 100 V, what is the rms value of the voltage?
 A) 141 V
 B) 100 V
 C) 210 V
 D) 71 V
 E) 120 V
(b) In an ac circuit, if the rms value of the current is 100 mA, what is the peak value of the current?
 A) 141 mA
 B) 100 mA
 C) 210 mA
 D) 71 mA
 E) 120 mA

Accepted Answer

The answer of (a) In an ac circuit, if the...

Question 8

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

The answer of The inductor in a radio receiver carries...

Question 9

A series LRC circuit has a sinusoidal voltage supplied to it at 197 kHz with a peak voltage of 270 V, a 41-Ω resistance, a 14- μF capacitor, and a 64-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

Accepted Answer

The peak current in an LRC circuit is given by I_peak = V_peak / Z, where Z is the impedance. The impedance Z is calculated using Z = sqrt(R^2 + (X_L - X_C)^2), where X_L = 2πfL and X_C = 1/(2πfC). For the given values, calculate X_L and X_C, then Z, and finally I_peak.

Question 10

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

At t = T/4, the voltage is maximum and the current is zero. This suggests that the element is either a capacitor or an inductor, as in a resistor the voltage and current would both be non-zero. At t = T/2, the current is given as I = -I_max, where I_max is the current amplitude. This indicates that the element is a capacitor, as in an inductor the current would be maximum and nonzero at t = T/2. Therefore, the unknown element is most likely a capacitor.

Question 11

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 know that the voltage amplitude across a capacitor and the current amplitude through it are related by the following equation:

$$V = IXC$$

Where V is the voltage amplitude (in volts), I is the current amplitude (in amperes), X is the capacitive reactance (in ohms), and C is the capacitance (in farads). We can rearrange this equation to solve for X:

$$X = \frac{V}{I C}$$

Substituting the given values, we get:

$$X = \frac{12.0	ext{ V}}{3.33	imes 10^{-3}	ext{ A} 	imes 8.50	imes 10^{-9}	ext{ F}} = 4.00	imes 10^5	ext{ }\Omega$$

We also know that capacitive reactance is related to frequency and capacitance by the following equation:

$$X = \frac{1}{2\pi fC}$$

where f is the frequency (in hertz). Rearranging this equation, we get:

$$f = \frac{1}{2\pi XC}$$

Substituting the value we calculated for X, and the given value for C, we get:

$$f = \frac{1}{2\pi 	imes 4.00	imes 10^5	ext{ }\Omega 	imes 8.50	imes 10^{-9}	ext{ F}} = 5.20	ext{ MHz}$$

Therefore, the closest frequency is 5.20 MHz, which corresponds to answer choice B.

Question 12

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 13

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 14

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 15

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 16

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 17

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 18

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 19

A resistor is connected to an ideal ac power supply. 
(a) The phase angle between the current and voltage is
 A) 0
 B) π/2 radians.
 C) -π/2 radians.
 D) π radians.
 E) 3π/4 radians.
(b) The current in the resistor
 A) leads the voltage across the resistor by 90°.
 B) lags the voltage across the resistor by 90°.
 C) is in phase with the voltage across the resistor.
 D) the voltage across the resistor by 45°.
 E) lags the voltage across the resistor by 45°.
(c) How does the average power dissipated in the resistor change as the frequency in the ac power supply decreases?
 A) It decreases.
 B) It increases.
 C) It does not change.
 D) It increases or decreases depending on the sign of the phase angle.

Accepted Answer

The answer of A resistor is connected to an ideal...

Question 20

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...

Quiz 35: Ac Circuits

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 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?

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?

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?

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) In an ac circuit, if the peak value of the voltage is 100 V, what is the rms value of the voltage? A) 141 V B) 100 V C) 210 V D) 71 V E) 120 V (b) In an ac circuit, if the rms value of the current is 100 mA, what is the peak value of the current? A) 141 mA B) 100 mA C) 210 mA D) 71 mA E) 120 mA

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 series LRC circuit has a sinusoidal voltage supplied to it at 197 kHz with a peak voltage of 270 V, a 41-Ω resistance, a 14- μF capacitor, and a 64-H inductance. What is the peak current for this 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 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?

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 at resonance, which one of the following statements about that circuit is accurate? (There may be more than one correct choice.)

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?

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 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?

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

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?