Alternating Currents Chapter-Wise Test 13

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A \( 50 \, \mu\text{F} \) capacitor is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the peak current?

\( X_C = \frac{1}{\omega C} \), \( \omega = 2\pi \times 50 = 314 \, \text{rad/s} \).

\( C = 50 \times 10^{-6} \, \text{F} \).

\( X_C = \frac{1}{314 \times 50 \times 10^{-6}} \approx 63.7 \, \Omega \).

RMS current: \( I = \frac{V}{X_C} = \frac{220}{63.7} \approx 3.45 \, \text{A} \).

Peak current: \( i_m = \sqrt{2} I = 1.414 \times 3.45 \approx 4.88 \, \text{A} \).

4.5 A
4.88 A
5.2 A
5.5 A
2

A series LCR circuit has \( R = 20 \, \Omega \), \( X_L = 40 \, \Omega \), \( X_C = 60 \, \Omega \). What is the phase angle?

\( \tan \phi = \frac{X_C - X_L}{R} = \frac{60 - 40}{20} = 1 \).

\( \phi = \tan^{-1}(1) = 45^\circ \).

Since \( X_C > X_L \), current leads voltage.

40°
42°
45°
50°
3

A series LCR circuit has \( R = 50 \, \Omega \), \( X_L = 80 \, \Omega \), \( X_C = 60 \, \Omega \). What is the power factor?

\( Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{50^2 + (80 - 60)^2} = \sqrt{2500 + 400} = \sqrt{2900} \approx 53.85 \, \Omega \).

Power factor: \( \cos \phi = \frac{R}{Z} = \frac{50}{53.85} \approx 0.928 \).

0.9
0.91
0.928
0.95
3

A \( 20 \, \mu\text{F} \) capacitor is connected to a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the peak current?

\( X_C = \frac{1}{\omega C} \), \( \omega = 2\pi \times 50 = 314 \, \text{rad/s} \).

\( C = 20 \times 10^{-6} \, \text{F} \).

\( X_C = \frac{1}{314 \times 20 \times 10^{-6}} \approx 159.2 \, \Omega \).

RMS current: \( I = \frac{V}{X_C} = \frac{230}{159.2} \approx 1.445 \, \text{A} \).

Peak current: \( i_m = \sqrt{2} I = 1.414 \times 1.445 \approx 2.04 \, \text{A} \).

1.8 A
2.04 A
2.2 A
2.5 A
2

What is the role of resonance in the operation of a radio receiver?

In a radio receiver, resonance in an LCR circuit is used to tune to a specific frequency. By adjusting the capacitance or inductance, the circuit’s resonant frequency matches the desired station’s signal, amplifying it while filtering out others.

It increases resistance
It reduces current
It amplifies all frequencies
It selects a specific frequency
4

A series LCR circuit has \( L = 5 \, \text{H} \), \( C = 20 \, \mu\text{F} \). What is the resonant angular frequency?

\( \omega_0 = \frac{1}{\sqrt{L C}} \).

\( L = 5 \, \text{H} \), \( C = 20 \times 10^{-6} \, \text{F} \).

\( \omega_0 = \frac{1}{\sqrt{5 \times 20 \times 10^{-6}}} = \frac{1}{\sqrt{10^{-4}}} = 100 \, \text{rad/s} \).

100 rad/s
120 rad/s
140 rad/s
160 rad/s
1

A \( 180 \, \text{V} \) (rms) source supplies a \( 90 \, \Omega \) resistor. What is the peak current?

RMS current: \( I = \frac{V}{R} = \frac{180}{90} = 2 \, \text{A} \).

Peak current: \( i_m = \sqrt{2} I = 1.414 \times 2 \approx 2.828 \, \text{A} \).

2.5 A
2.7 A
3 A
2.828 A
4

Why does a purely capacitive AC circuit not dissipate power despite having current flow?

In a purely capacitive circuit, the current leads the voltage by 90°. The instantaneous power oscillates, but the average power over a cycle is zero because the energy is stored during one half-cycle and returned during the other, with no net dissipation.

Because capacitance is infinite
Because energy is stored and returned without loss
Because resistance is high
Because current is zero
2

A series LCR circuit with \( R = 50 \, \Omega \) is at resonance with a \( 230 \, \text{V} \) (rms) source. What is the rms current?

At resonance, \( Z = R = 50 \, \Omega \).

RMS current: \( I = \frac{V}{R} = \frac{230}{50} = 4.6 \, \text{A} \).

4 A
4.2 A
4.6 A
5 A
3

In an AC circuit with only a capacitor, what is the nature of the current when the voltage is at its peak?

In a purely capacitive circuit, the current leads the voltage by 90°. When the voltage is at its peak (maximum positive or negative), the current is zero because it reaches its peak 90° earlier and crosses zero at the voltage peak.

It is zero
It is at its maximum
It is in phase with the voltage
It lags the voltage
1

Performance Summary

Score:

Category Details
Total Attempts:
Total Skipped:
Total Wrong Answers:
Total Correct Answers:
Time Taken:
Average Time Taken per Question:
Accuracy:
0