Alternating Currents Chapter-Wise Test 1

Correct answer Carries: 4.

Wrong Answer Carries: -1.

A transformer steps up \( 220 \, \text{V} \) to \( 440 \, \text{V} \). If the primary current is \( 10 \, \text{A} \), what is the secondary current?

Power input = Power output: \( V_p I_p = V_s I_s \).

\( I_s = \frac{V_p I_p}{V_s} = \frac{220 \times 10}{440} = 5 \, \text{A} \).

4 A
5 A
6 A
7 A
2

What is the behavior of the impedance in a series LCR circuit at very high frequencies?

At very high frequencies, \( X_L = \omega L \) becomes very large, while \( X_C = \frac{1}{\omega C} \) becomes very small. The impedance \( Z = \sqrt{R^2 + (X_L - X_C)^2} \) is dominated by \( X_L \), making the circuit behave as predominantly inductive.

It behaves as predominantly inductive
It behaves as predominantly capacitive
It becomes purely resistive
It approaches zero
1

In an AC circuit with only an inductor, what is the instantaneous power when the current is at its maximum?

In a purely inductive circuit, current lags voltage by 90°. When the current is at its maximum, the voltage is zero (since voltage leads by 90°), making the instantaneous power (\( P = V I \)) zero at that instant.

Zero
Maximum
Half the peak power
Negative maximum
1

A transformer has \( N_p = 550 \), \( N_s = 1100 \). If \( V_p = 110 \, \text{V} \) (rms), what is the secondary voltage?

\( \frac{V_s}{V_p} = \frac{N_s}{N_p} \).

\( V_s = V_p \times \frac{N_s}{N_p} = 110 \times \frac{1100}{550} = 220 \, \text{V} \).

200 V
220 V
240 V
260 V
2

A series LCR circuit with \( R = 100 \, \Omega \), \( X_L = 130 \, \Omega \), \( X_C = 70 \, \Omega \) has a \( 300 \, \text{V} \) (rms) source. What is the power dissipated?

\( Z = \sqrt{R^2 + (X_L - X_C)^2} = \sqrt{100^2 + (130 - 70)^2} = \sqrt{10000 + 3600} = \sqrt{13600} \approx 116.62 \, \Omega \).

RMS current: \( I = \frac{V}{Z} = \frac{300}{116.62} \approx 2.573 \, \text{A} \).

Power: \( P = I^2 R = (2.573)^2 \times 100 \approx 661.8 \, \text{W} \).

640 W
650 W
670 W
661.8 W
4

A \( 85 \, \text{mH} \) inductor is connected to a \( 230 \, \text{V} \), \( 50 \, \text{Hz} \) source. What is the peak current?

\( X_L = \omega L \), \( \omega = 2\pi \times 50 = 314 \, \text{rad/s} \).

\( L = 85 \times 10^{-3} \, \text{H} \).

\( X_L = 314 \times 0.085 = 26.69 \, \Omega \).

RMS current: \( I = \frac{V}{X_L} = \frac{230}{26.69} \approx 8.62 \, \text{A} \).

Peak current: \( i_m = \sqrt{2} I = 1.414 \times 8.62 \approx 12.19 \, \text{A} \).

12 A
12.1 A
12.19 A
12.5 A
3

In a series LCR circuit, under what condition does the circuit behave as if it has only resistance?

In a series LCR circuit, the circuit behaves as purely resistive at resonance, where the inductive reactance equals the capacitive reactance (\( X_L = X_C \)). This cancels the reactive components, leaving only the resistance to determine the impedance.

When frequency is zero
When inductive and capacitive reactances are equal
When resistance is zero
When capacitance is infinite
2

A \( 254.6 \, \text{V} \) (peak) AC source is connected to a \( 90 \, \Omega \) resistor. What is the average power consumed?

RMS voltage: \( V = \frac{v_m}{\sqrt{2}} = \frac{254.6}{1.414} \approx 180 \, \text{V} \).

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

Average power: \( P = I^2 R = 2^2 \times 90 = 360 \, \text{W} \).

360 W
380 W
400 W
420 W
1

A \( 60 \, \text{mH} \) inductor is connected to a \( 220 \, \text{V} \), \( 50 \, \text{Hz} \) AC source. What is the rms current?

\( X_L = \omega L \), \( \omega = 2\pi \times 50 = 314 \, \text{rad/s} \).

\( L = 60 \times 10^{-3} \, \text{H} \).

\( X_L = 314 \times 0.06 = 18.84 \, \Omega \).

RMS current: \( I = \frac{V}{X_L} = \frac{220}{18.84} \approx 11.68 \, \text{A} \).

11 A
11.68 A
12 A
12.5 A
2

In a series LCR circuit at resonance, what is the relationship between the inductive and capacitive reactances?

At resonance in a series LCR circuit, the inductive reactance (\( X_L \)) equals the capacitive reactance (\( X_C \)). This balance cancels out the reactive components, making the impedance purely resistive and maximizing the current.

They are equal
Inductive reactance is greater
Capacitive reactance is greater
They are inversely proportional
1

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