When an ac source drives a purely inductive circuit, how is the current related in phase to the source voltage?

It is in phase with the voltage

Given below are two statements: Statement I: In a series LCR circuit driven below its resonant frequency, the current leads the applied voltage. Statement II: The average power consumed over a complete cycle by an ideal inductor is (1/2)LI₀². Choose the correct answer.

Statement I is correct but Statement II is incorrect

Statement I is incorrect but Statement II is correct

Both Statement I and Statement II are correct

Both Statement I and Statement II are incorrect

Alternating Current

10 NEET-UG practice questions on Alternating Current, part of Physics. The first 10 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

Question 1 · Medium
A series LCR circuit has R = 30 Ω, inductive reactance 80 Ω and capacitive reactance 40 Ω. It is connected to a 100 V (rms) ac source. Find the average power it consumes.
1. A120 W
2. B200 W
3. C72 W
4. D160 W
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Answer: A · 120 W
Z = √(30² + (80 - 40)²) = 50 Ω, so I = 100/50 = 2 A. Average power is I²R = 4 × 30 = 120 W, the same as VI cosφ = 100 × 2 × 0.6.
- B: This is the apparent power VI, without the power factor.
- C: The power factor was applied a second time to I²R.
- D: The net reactance 40 Ω was used in place of R.
Remember this
Only the resistance consumes average power: P = I²R = V I cosφ with cosφ = R/Z.
Question 2 · Hard
A series circuit has L = 0.5 H, C = 8 μF and R = 25 Ω, with an ideal inductor. It is driven at its resonant frequency by a source of 20 V (rms). What does an ac voltmeter read when connected across the inductor alone?
1. A400 V
2. B200 V
3. C0 V
4. D20 V
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Answer: B · 200 V
Resonance is at ω = 1/√(LC) = 1/√(4 × 10⁻⁶) = 500 rad/s, where X_L = 500 × 0.5 = 250 Ω. The impedance is R alone, so I = 20/25 = 0.8 A. Then V_L = 0.8 × 250 = 200 V, ten times the source.
- A: V_L and V_C were added, though they are opposite in phase.
- C: This is the combined voltage across L and C together.
- D: This is the source voltage, which appears across R at resonance.
Remember this
At resonance V_L and V_C cancel in the circuit, but each alone can far exceed the source voltage.
Question 3 · Easy
When an ac source drives a purely inductive circuit, how is the current related in phase to the source voltage?
1. AIt leads the voltage by π/2
2. BIt lags the voltage by π
3. CIt lags the voltage by π/2
4. DIt is in phase with the voltage
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Answer: C · It lags the voltage by π/2
The source voltage balances L di/dt, so i is a sine shifted back by π/2 relative to v. The current therefore reaches its peak a quarter-cycle after the voltage.
- A: This is the behaviour of a pure capacitor.
- B: The phase difference in an inductor is π/2, not π.
- D: This is the behaviour of a pure resistor.
Remember this
Current lags voltage by π/2 in a pure inductor and leads it by π/2 in a pure capacitor.
Question 4 · Medium
A transformer with a turns ratio of 10:1 (primary to secondary) steps 200 V down and supplies a 10 Ω load. Its efficiency is 80%. What current does the primary draw?
1. A0.25 A
2. B0.16 A
3. C2.5 A
4. D0.20 A
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Answer: A · 0.25 A
The secondary voltage is 20 V, so the load takes 2 A and 40 W. With 80% efficiency the input is 40/0.8 = 50 W. So I₁ = 50/200 = 0.25 A.
- B: The efficiency was multiplied instead of divided.
- C: The secondary current was divided by 0.8 and the turns ratio ignored.
- D: This assumes an ideal transformer and ignores the 80% efficiency.
Remember this
Efficiency is output power over input power; the input power, not the turns ratio alone, fixes a real transformer's primary current.
Question 5 · Medium
Given below are two statements: Statement I: In a series LCR circuit driven below its resonant frequency, the current leads the applied voltage. Statement II: The average power consumed over a complete cycle by an ideal inductor is (1/2)LI₀². Choose the correct answer.
1. AStatement I is incorrect but Statement II is correct
2. BBoth Statement I and Statement II are correct
3. CBoth Statement I and Statement II are incorrect
4. DStatement I is correct but Statement II is incorrect
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Answer: D · Statement I is correct but Statement II is incorrect
Below resonance, X_C exceeds X_L, so the circuit acts capacitively and the current leads; I is correct. An ideal inductor takes energy in one quarter-cycle and returns it in the next, so its average power is zero and II is incorrect.
- A: I is correct, and II confuses energy with power.
- B: (1/2)LI₀² is stored energy, while the average power is zero.
- C: The current does lead below resonance, so I is correct.
Remember this
Average power in an ideal L or C is zero; (1/2)LI₀² is the peak stored energy, not power.
Question 6 · Easy
The current in a circuit is i = 5√2 sin(100πt) ampere, with t in seconds. Identify its rms value and frequency.
1. A5√2 A and 100 Hz
2. B5 A and 100 Hz
3. C5√2 A and 50 Hz
4. D5 A and 50 Hz
Answer and explanation in LearnFree account
Question 7 · Medium
A series LCR circuit has resistance R and resonant frequency f₀. Which graph shows its impedance Z against the source frequency f?
Figure: MedExams
1. AGraph D
2. BGraph C
3. CGraph B
4. DGraph A
Answer and explanation in LearnFree account
Question 8 · Hard
Ideal meters in this series circuit, with a pure inductor, give the readings shown at 100 Hz. The source voltage is held at its rms value while its frequency is changed until resonance occurs. What are the resonant frequency and the new current?
Figure: MedExams
1. A200 Hz and 2.5 A
2. B50 Hz and 4.5 A
3. C25 Hz and 2.5 A
4. D50 Hz and 2.5 A
Answer and explanation in LearnFree account
Question 9 · Easy
For the alternating voltage plotted here, what are the rms value and the frequency?
Figure: MedExams
1. A200√2 V and 50 Hz
2. B400 V and 50 Hz
3. C200 V and 50 Hz
4. D200 V and 100 Hz
Answer and explanation in LearnFree account
Question 10 · Medium
The series circuit drawn here runs on the rms voltage marked. What is the average power it draws from the source?
Figure: MedExams
1. A333 W
2. B200 W
3. C160 W
4. D120 W
Answer and explanation in LearnFree account

Alternating Current

A series LCR circuit has R = 30 Ω, inductive reactance 80 Ω and capacitive reactance 40 Ω. It is connected to a 100 V (rms) ac source. Find the average power it consumes.

A series circuit has L = 0.5 H, C = 8 μF and R = 25 Ω, with an ideal inductor. It is driven at its resonant frequency by a source of 20 V (rms). What does an ac voltmeter read when connected across the inductor alone?

When an ac source drives a purely inductive circuit, how is the current related in phase to the source voltage?

A transformer with a turns ratio of 10:1 (primary to secondary) steps 200 V down and supplies a 10 Ω load. Its efficiency is 80%. What current does the primary draw?

Given below are two statements: Statement I: In a series LCR circuit driven below its resonant frequency, the current leads the applied voltage. Statement II: The average power consumed over a complete cycle by an ideal inductor is (1/2)LI₀². Choose the correct answer.

The current in a circuit is i = 5√2 sin(100πt) ampere, with t in seconds. Identify its rms value and frequency.

A series LCR circuit has resistance R and resonant frequency f₀. Which graph shows its impedance Z against the source frequency f?

Ideal meters in this series circuit, with a pure inductor, give the readings shown at 100 Hz. The source voltage is held at its rms value while its frequency is changed until resonance occurs. What are the resonant frequency and the new current?

For the alternating voltage plotted here, what are the rms value and the frequency?

The series circuit drawn here runs on the rms voltage marked. What is the average power it draws from the source?