Alternating Current

29 NEET-UG practice questions on Alternating Current, part of Physics. The first 25 are below; the first 5 with answers and explanations (tap Show answer after you have chosen), the rest in Learn with a free account.

1. 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.

2. 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.

3. 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.

4. 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.

5. 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.

6. 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

7. 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?

   

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   1. AGraph D
   2. BGraph C
   3. CGraph B
   4. DGraph A

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8. 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?

   

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   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

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9. Question 9 · Easy

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

   

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   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

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10. Question 10 · Medium

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

    

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    1. A333 W
    2. B200 W
    3. C160 W
    4. D120 W

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11. Question 11 · Easy

    Household mains supply in India is 220 V (rms). What is the peak value of this voltage?

    1. AAbout 156 V
    2. B220 V
    3. C440 V
    4. DAbout 311 V

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12. Question 12 · Hard

    In a series LCR circuit, ac voltmeters read 40 V across the resistor, 80 V across the inductor and 50 V across the capacitor. Find the rms voltage of the source and the power factor of the circuit.

    1. A50 V and 0.6
    2. B170 V and 0.24
    3. C50 V and 0.8
    4. D70 V and 0.57

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13. Question 13 · Medium

    Consider the following statements about transformers: A. In an ideal transformer, V_s/V_p = N_s/N_p. B. A step-up transformer increases both voltage and current. C. A laminated core reduces energy loss due to eddy currents. D. A transformer works equally well with a steady dc supply. Which of these are correct?

    1. AC and D only
    2. BA, B and C only
    3. CA only
    4. DA and C only

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14. Question 14 · Medium

    Match List-I with List-II. List-I (Circuit across an ac source) A. Pure resistor B. Pure inductor C. Pure capacitor D. Series LR circuit with X_L = R List-II (Phase of current relative to voltage) I. Lags by π/4 II. Leads by π/2 III. In phase IV. Lags by π/2 Choose the correct answer.

    1. AA-I, B-IV, C-II, D-III
    2. BA-III, B-IV, C-I, D-II
    3. CA-III, B-II, C-IV, D-I
    4. DA-III, B-IV, C-II, D-I

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15. Question 15 · Medium

    A series LCR circuit is driven by an ac source at exactly its resonant frequency. Which of these is true?

    1. AThe impedance of the circuit is at its maximum
    2. BThe voltages across L and C are each zero
    3. CThe current is in phase with the source voltage
    4. DThe current lags the source voltage by π/2

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16. Question 16 · Hard

    A series LCR circuit has L = (1/π) H, C = (1/π) µF and R = 100 Ω, and is connected to a variable-frequency source of rms voltage 10 V. When the source is tuned to resonance, what are the resonant frequency and the rms voltage across the inductor?

    1. A500 Hz and 0 V
    2. B1000π Hz and 100 V
    3. C500 Hz and 10 V
    4. D500 Hz and 100 V

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17. Question 17 · Medium

    Assertion A: In a circuit, a capacitor allows an alternating current to flow but blocks a steady direct current. Reason R: The reactance of a capacitor increases as the frequency of the applied voltage increases. Choose the correct answer.

    1. ABoth A and R are correct and R is the correct explanation of A
    2. BBoth A and R are correct but R is not the correct explanation of A
    3. CA is not correct but R is correct
    4. DA is correct but R is not correct

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18. Question 18 · Medium

    In a series LCR circuit driven by an ac source, R = 30 Ω, X_L = 80 Ω and X_C = 40 Ω. Taking tan 53° = 4/3, how is the current related in phase to the source voltage?

    1. AIt lags the voltage by 53°
    2. BIt lags the voltage by 37°
    3. CIt leads the voltage by 53°
    4. DIt leads the voltage by 37°

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19. Question 19 · Medium

    A step-down transformer takes 5 A from a 220 V ac line and supplies a load at 110 V. If its efficiency is 90%, what current flows in the secondary?

    1. A11.1 A
    2. B10 A
    3. C9 A
    4. D2.5 A

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20. Question 20 · Easy

    A capacitor of capacitance (100/π) µF is connected to a 50 Hz ac supply. What is its reactance?

    1. A200 Ω
    2. B0.01 Ω
    3. C100 Ω
    4. D628 Ω

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21. Question 21 · Medium

    Why does a transformer give no output voltage when its primary is connected to a steady dc source?

    1. ADirect current cannot flow through the copper windings of the primary
    2. BThe secondary has too few turns to respond to a steady current
    3. CA steady current gives no change of flux, so no emf is induced in the secondary
    4. DDirect current permanently demagnetises the iron core

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22. Question 22 · Easy

    In an ac circuit containing only an ideal capacitor, what is the average power consumed over a complete cycle?

    1. AV_rms I_rms
    2. BV_rms I_rms/2
    3. CV₀I₀
    4. DZero

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23. Question 23 · Medium

    Match List-I with List-II. List-I (quantity in an ac circuit) A. Inductive reactance B. Capacitive reactance C. Resonant angular frequency of a series LCR circuit D. Impedance of a series LCR circuit List-II (expression) I. √(R² + (X_L − X_C)²) II. 1/√(LC) III. 1/(ωC) IV. ωL Choose the correct answer.

    1. AA-IV, B-III, C-II, D-I
    2. BA-IV, B-II, C-III, D-I
    3. CA-III, B-IV, C-II, D-I
    4. DA-IV, B-III, C-I, D-II

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24. Question 24 · Medium

    A coil of resistance 5 Ω and inductive reactance 12 Ω is connected to a 130 V (rms) ac supply. What average power does it consume?

    1. A1200 W
    2. B1300 W
    3. C3380 W
    4. D500 W

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25. Question 25 · Hard

    For a series LCR circuit driven by an ac source of variable frequency, consider the following statements: A. At resonance the impedance is least and equals R. B. Below the resonant frequency, the current leads the source voltage. C. At resonance the power factor is zero. D. At resonance the voltages across L and C are equal in magnitude and in phase. Which of these are correct?

    1. AB and D only
    2. BA, B and D only
    3. CA and B only
    4. DA and C only

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