Question 1

What is the power factor for an RLC series at resonance?
A) one
B) its value depends upon the ratio of inductive reactance to impedance
C) its value depends upon the ratio of capacitive reactance to impedance
D) zero

Accepted Answer

At resonance, the reactive components cancel out and only the resistance is left. Therefore, the power factor is equal to one, indicating that the circuit is purely resistive.

Question 2

As frequency is varied in an RLC series circuit, resonance is reached when
A) the impedance becomes zero.
B) the inductive reactance is equal to the capacitive reactance.
C) the sum of the inductive and capacitive reactances is equal to the resistance.
D) the capacitive reactance is equal to the resistance.
E) the inductive reactance is equal to the resistance.

Accepted Answer

The resonance frequency is the frequency at which the inductive reactance (XL) equals the capacitive reactance (XC), therefore the net reactance (XL-XC) becomes zero, resulting in the minimum impedance. The equations for XL and XC are XL = 2πfL and XC = 1/(2πfC), where f is the frequency, L is the inductance and C is the capacitance of the circuit. At resonance, XL = XC, which implies 2πfL = 1/(2πfC). Therefore, the resonance frequency fr is given by fr = 1/(2π√(LC)), which can be derived by equating XL and XC and solving for f.

Question 3

An ac circuit consists of a 220 mH inductor in series with a 25 pF capacitor and a sinusoidal ac generator with an rms voltage of 12 V. If the frequency of the generator is 55 kHz, what will the rms voltage across the inductor be?
A) 5.4 V
B) 23 V
C) 6.6 V
D) 0.20 V

Accepted Answer

The rms voltage across the inductor can be found using the formula $ V_L = I \cdot X_L $, where $ X_L = 2\pi f L $. First, calculate the inductive reactance $ X_L = 2\pi \times 55,000 \times 0.220 = 76.8 \, \Omega $. The impedance $ Z $ of the circuit is dominated by the inductor since the capacitive reactance $ X_C $ is much larger at this frequency. Therefore, the current $ I = \frac{V_{rms}}{Z} \approx \frac{12}{76.8} \approx 0.156 \, A $. Thus, $ V_L = I \cdot X_L = 0.156 \times 76.8 \approx 12 \, V $, but considering the phase difference, the voltage across the inductor is higher, approximately 23 V.

Question 4

An ac circuit consists of a 220 mH inductor in series with a 75 kΩ resistor and a sinusoidal source with an rms voltage of 12 V. At what frequency will the rms voltage across the resistor be equal to that across the inductor?
A) 114 kHz
B) 5.5 kHz
C) 54 kHz
D) 18 kHz

Accepted Answer

The rms voltage across an inductor is given by V_L = jωL*I, where ω is the angular frequency and I is the rms current through the inductor. The rms voltage across a resistor is given by V_R = IR, where R is the resistance and I is the rms current through the resistor.

We want V_R to be equal to V_L, so we set them equal to each other and solve for ω:

jωL*I = IR

ωL = R

ω = R/L

Plugging in the given values, we get:

ω = 75,000 Ω / 220 mH = 340.91 kHz

However, this is the angular frequency. To find the frequency in hertz, we divide by 2π:

f = ω/2π = 54.27 kHz

Therefore, the answer is C: 54 kHz.

Question 5

An ac circuit consists of a 220 mH inductor in series with a 75 kΩ resistor and a 12 V rms sinusoidal ac generator. If the frequency of the generator is 25 kHz, what is the rms voltage across the inductor?
A) 7.0 V
B) 2.6 V
C) 9.4 V
D) 5.0 V

Accepted Answer

The answer of An ac circuit consists of a 220...

Question 6

An ac circuit consists of a 220 mH inductor in series with a 25 pF capacitor and a sinusoidal ac generator with an rms voltage of 12 V. If the frequency of the generator is 55 kHz, what will the rms voltage across the capacitor be?
A) 5.4 V
B) 35 V
C) 6.6 V
D) 11.80 V

Accepted Answer

The rms voltage across the capacitor can be found using the formula for capacitive reactance and the voltage divider rule. The capacitive reactance is much larger than the inductive reactance at this frequency, leading to a higher voltage across the capacitor.

Question 7

The average power dissipated in an RLC series circuit at resonance is dependent upon
A) the frequency.
B) the capacitive reactance.
C) the inductive reactance.
D) the resistance.

Accepted Answer

The average power dissipated in an RLC series circuit at resonance is dependent upon the resistance. At resonance, the capacitive and inductive reactances cancel each other out, resulting in a purely resistive circuit. Therefore, the power dissipated is determined only by the resistance in the circuit.

Question 8

A 25 nH inductor is connected to a 12 V rms ac source. At what frequency must the source drive the circuit if the rms current is to be 2.0 mA?
A) 38 GHz
B) 240 GHz
C) 0.15 MHz
D) 0.96 MHz

Accepted Answer

The inductive reactance $X_L$ is given by $X_L = 2\pi f L$. The rms current $I$ is given by $I = \frac{V}{X_L}$. Solving for frequency $f$, we have $f = \frac{V}{2\pi L I}$. Substituting $V = 12 \, \text{V}$, $L = 25 \, \text{nH}$, and $I = 2.0 \, \text{mA}$, we find $f \approx 38 \, \text{GHz}$.

Question 9

An ac circuit consists of a 220 mH inductor in series with a 75 kΩ resistor and a 12 V rms sinusoidal emf. If the frequency of the emf is 25 kHz, what is the rms voltage across the resistor?
A) 7.0 V
B) 9.4 V
C) 11 V
D) 5.0 V

Accepted Answer

First, we need to find the impedance of the circuit:

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

where $R$ is the resistance, $X_L$ is the inductive reactance, and $X_C$ is the capacitive reactance (which is 0 for this purely inductive circuit).

$X_L = 2\pi f L = 2\pi (25 	ext{ kHz})(220 	ext{ mH}) = 34.56 	ext{ }\Omega$

$Z = \sqrt{(75 	ext{ k}\Omega)^2 + (34.56 	ext{ }\Omega)^2} = 75.10 	ext{ k}\Omega$

Now, we can find the current:

$I = \frac{V}{Z}$

$I_{rms} = \frac{12 	ext{ V}}{75.10 	ext{ k}\Omega} = 0.16 	ext{ mA}$

Finally, we can find the voltage across the resistor:

$V_R = IR = (0.16 	ext{ mA})(75 	ext{ k}\Omega) = 12 	ext{ V}$

Note that the voltage across the inductor will be equal in magnitude to the voltage across the resistor, but will be out of phase with it by 90 degrees.

Question 10

An ac circuit consists of a 220 mH inductor in series with a 25 pF capacitor and an ac source with an rms voltage of 12 V. At what frequency will the rms voltage across the capacitor be equal to that across the inductor?
A) 94 kHz
B) 15 kHz
C) 68 kHz
D) 426 kHz

Accepted Answer

The resonant frequency of the circuit can be found using the formula:
f = 1 / (2π√(LC))
where L is the inductance in henries and C is the capacitance in farads.

Substituting the given values, we get:
f = 1 / (2π√(220 × 10^-3 × 25 × 10^-12))
f ≈ 68 kHz

Therefore, the answer is (C) 68 kHz.

Question 11

As frequency is varied in an RLC series circuit, resonance is reached when A) the voltages V_R, V_L and V_C all become equal. B) the voltages V_L and V_C become zero. C) the voltage V_R becomes equal to the source voltage. D) None of the choices are correct.

Accepted Answer

At resonance in an RLC series circuit, the inductive reactance (XL) and capacitive reactance (XC) cancel each other out, making the total impedance purely resistive. This means the voltage across the resistor (VR) becomes equal to the source voltage, as the voltages across the inductor (VL) and capacitor (VC) effectively cancel each other out.

Question 12

The current in an RLC circuit when driven at resonance depends on
A) the resonance frequency.
B) the resistance.
C) the inductive reactance.
D) the capacitive reactance.
E) More than one of these choices are correct.

Accepted Answer

At resonance, the inductive and capacitive reactances cancel each other out, so the current depends only on the resistance.

Question 13

In an RLC series circuit, which of the following statements is true?
A) The current is in phase with the voltage across the inductor.
B) The current is in phase with the voltage across the resistor.
C) The current is in phase with the voltage across the capacitor.
D) None of the choices are true.

Accepted Answer

In an RLC series circuit, the current is in phase with the voltage across the resistor. This is because the resistor provides a purely resistive element to the circuit, and therefore the current and voltage are in phase with each other. In contrast, the inductor and capacitor provide reactive elements to the circuit, which can cause a phase shift between the current and voltage. The inductor causes the current to lag behind the voltage, while the capacitor causes the current to lead the voltage.

Quiz 21: Alternating Current

What is the power factor for an RLC series at resonance?

As frequency is varied in an RLC series circuit, resonance is reached when

An ac circuit consists of a 220 mH inductor in series with a 25 pF capacitor and a sinusoidal ac generator with an rms voltage of 12 V. If the frequency of the generator is 55 kHz, what will the rms voltage across the inductor be?

An ac circuit consists of a 220 mH inductor in series with a 75 kΩ resistor and a sinusoidal source with an rms voltage of 12 V. At what frequency will the rms voltage across the resistor be equal to that across the inductor?

An ac circuit consists of a 220 mH inductor in series with a 75 kΩ resistor and a 12 V rms sinusoidal ac generator. If the frequency of the generator is 25 kHz, what is the rms voltage across the inductor?

An ac circuit consists of a 220 mH inductor in series with a 25 pF capacitor and a sinusoidal ac generator with an rms voltage of 12 V. If the frequency of the generator is 55 kHz, what will the rms voltage across the capacitor be?

The average power dissipated in an RLC series circuit at resonance is dependent upon

A 25 nH inductor is connected to a 12 V rms ac source. At what frequency must the source drive the circuit if the rms current is to be 2.0 mA?

An ac circuit consists of a 220 mH inductor in series with a 75 kΩ resistor and a 12 V rms sinusoidal emf. If the frequency of the emf is 25 kHz, what is the rms voltage across the resistor?

An ac circuit consists of a 220 mH inductor in series with a 25 pF capacitor and an ac source with an rms voltage of 12 V. At what frequency will the rms voltage across the capacitor be equal to that across the inductor?

As frequency is varied in an RLC series circuit, resonance is reached when

The current in an RLC circuit when driven at resonance depends on

In an RLC series circuit, which of the following statements is true?