JEE Physics Alternating Current MCQs Set 22

Multiple Choice Questions (MCQs) for JEE Physics: Alternating Current

Review structured MCQ sets for JEE Physics Alternating Current. Built according to official JEE guidelines, these downloadable questions support daily revision and core concept reinforcement.

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Multiple Choice Questions

Question 1: A transformer connected to 220 V mains is used to light a lamp of rating 100 W and 110 V. If the primary current is 0.5 A, the efficiency of the transformer is approximately
(a) 60%
(b) 35%
(c) 50%
(d) 90%
Show Answer & Explanation

Answer: (d) 90%

Explanation:
1. Input power = 220 × 0.5 = 110 W.
2. Efficiency = 100/110, about 90%.

Teacher's Note:
1. Recall the basic relation.

Question 2: For minimum dissipation of energy in the circuit, the power factor should be
(a) large
(b) moderate
(c) small
(d) cannot say
Show Answer & Explanation

Answer: (c) small

Explanation:
1. P = V I cos φ, so a small power factor gives the minimum power dissipation.

Teacher's Note:
1. Recall the basic relation.

Question 3: A parallel L-C combination is connected across an a.c. source. The current through the inductor is 0.9 A and through the capacitor is 0.4 A. The current drawn from the source is
(a) 1.3 A
(b) 0.5 A
(c) 0.6 A
(d) 0.36 A
Show Answer & Explanation

Answer: (b) 0.5 A

Explanation:
1. The currents in L and C are 180° out of phase.
2. I = 0.9 - 0.4 = 0.5 A.

Teacher's Note:
1. Recall the basic relation.

Question 4: A charged 30 microfarad capacitor is connected to a 27 mH inductor. The angular frequency of free oscillations of the circuit is
(a) \( 1.1\times10^3\ \text{rad s}^{-1} \)
(b) \( 2.1\times10^3\ \text{rad s}^{-1} \)
(c) \( 3.1\times10^3\ \text{rad s}^{-1} \)
(d) \( 4.1\times10^3\ \text{rad s}^{-1} \)
Show Answer & Explanation

Answer: (a) \( 1.1\times10^3\ \text{rad s}^{-1} \)

Explanation:
1. ω = 1/√(LC) = 1/√(27 × 10⁻³ × 30 × 10⁻⁶) = 1/√(8.1 × 10⁻⁷) = 1.1 × 10³ rad/s.

Teacher's Note:
1. Recall the basic relation.

Question 5: In tuning, we vary the capacitance of a capacitor in the tuning circuit so that the resonant frequency of the circuit becomes nearly equal to the frequency of the radio signal received. When this happens, the ____ A ____ in the circuit for that station is maximum. A refers to
(a) resonant frequency
(b) impedance
(c) amplitude of the current
(d) reactance
Show Answer & Explanation

Answer: (c) amplitude of the current

Explanation:
1. At resonance the impedance is minimum, so the current amplitude is maximum.

Teacher's Note:
1. Recall the basic relation.

Question 6: In which of the following circuits is the maximum power dissipation observed?
(a) pure capacitive circuit
(b) pure inductive circuit
(c) pure resistive circuit
(d) none of these
Show Answer & Explanation

Answer: (c) pure resistive circuit

Explanation:
1. Power factor is 1 for a pure resistor, so the average power is maximum.

Teacher's Note:
1. Recall the basic relation.

Question 7: A sinusoidal a.c. current flows through a resistor of resistance R. If the peak current is I_p, then the average power dissipated is
(a) I_p² R cos θ
(b) \( \tfrac12I_p^2R \)
(c) \( \tfrac4\pi I_p^2R \)
(d) \( \tfrac1{\pi^2}I_p^2R \)
Show Answer & Explanation

Answer: (b) \( \tfrac12I_p^2R \)

Explanation:
1. I_rms² R = (I_p²/2) R.

Teacher's Note:
1. Recall the basic relation.

Question 8: An inductance L having a resistance R is connected to an alternating source of angular frequency ω. The quality factor Q of the inductor is
(a) \( R/\omega L \)
(b) \( (\omega L/R)^2 \)
(c) \( (R/\omega L)^{1/2} \)
(d) \( \omega L/R \)
Show Answer & Explanation

Answer: (d) \( \omega L/R \)

Explanation:
1. Q = ωL/R.

Teacher's Note:
1. Recall the basic relation.

Question 9:
Assertion (A): In the purely resistive element of a series LCR a.c. circuit, the maximum value of the rms current increases with an increase in the angular frequency of the applied emf.
Reason (R): I_max = ε_max/Z, where Z = √[R² + (ωL - 1/ωC)²].
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (d) A is false, but R is true.

Explanation:
1. The current increases with frequency only until resonance and then decreases, so the assertion is false.
2. The expression for I_max is correct.

Teacher's Note:
1. Current peaks at resonance.

Question 10: A fully charged capacitor C with initial charge Q0 is connected to a coil of self-inductance L at t = 0. The time at which the energy is stored equally between the electric and the magnetic field is
(a) \( \frac\pi4\sqrt{LC} \)
(b) \( 2\pi\sqrt{LC} \)
(c) \( \sqrt{LC} \)
(d) \( \pi\sqrt{LC} \)
Show Answer & Explanation

Answer: (a) \( \frac\pi4\sqrt{LC} \)

Explanation:
1. q = Q0 cos(ωt) with ω = 1/√(LC).
2. Equal energies need q² = Q0²/2, i.e. ωt = π/4, so t = (π/4)√(LC).

Teacher's Note:
1. Recall the basic relation.

Question 11: In a transformer, the number of turns in the primary coil is 140 and in the secondary coil 280. If the current in the primary coil is 4 A, then that in the secondary coil is
(a) 4 A
(b) 2 A
(c) 6 A
(d) 10 A
Show Answer & Explanation

Answer: (b) 2 A

Explanation:
1. For an ideal transformer I_s = I_p N_p/N_s = 4 × 140/280 = 2 A.

Teacher's Note:
1. Recall the basic relation.

Question 12: Which of the following correctly describes the variation of inductive reactance X_L with frequency?
(a) X_L is independent of frequency
(b) X_L is directly proportional to frequency (a straight line through the origin)
(c) X_L is infinite at one particular frequency and zero elsewhere
(d) X_L decreases linearly with frequency
Show Answer & Explanation

Answer: (b) X_L is directly proportional to frequency (a straight line through the origin)

Explanation:
1. X_L = 2πfL.

Teacher's Note:
1. Recall the basic relation.

Question 13: Which of the following statements are correct? I. If the resonance is less sharp, not only is the maximum current less, but the circuit is close to resonance for a larger range of frequencies and the tuning will not be good. II. The less sharp the resonance, the less the selectivity of the circuit and vice versa. III. If the quality factor is large, i.e. R is low or L is large, the circuit is more selective.
(a) I and II
(b) II and III
(c) I and III only
(d) I, II and III
Show Answer & Explanation

Answer: (d) I, II and III

Explanation:
1. All three statements are true statements about sharpness of resonance and quality factor.

Teacher's Note:
1. Recall the basic relation.

Question 14:
Assertion (A): Power is produced when a transformer steps up the voltage.
Reason (R): In an ideal transformer V I = constant.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is not the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Show Answer & Explanation

Answer: (d) A is false, but R is true.

Explanation:
1. A transformer does not produce power; it transfers it, so the assertion is false.
2. In an ideal transformer V_p I_p = V_s I_s, so the reason is true.

Teacher's Note:
1. Power in = power out.

Question 15: A.C. power is transmitted from a power house at a high voltage because
(a) the rate of transmission is faster at high voltages
(b) it is more economical due to less power loss
(c) power cannot be transmitted at low voltages
(d) it is a precaution against theft of transmission lines
Show Answer & Explanation

Answer: (b) it is more economical due to less power loss

Explanation:
1. For a given power the current is smaller at high voltage, so the I²R loss in the lines is less.

Teacher's Note:
1. Recall the basic relation.

Question 16: A capacitor acts as an infinite resistance for
(a) DC
(b) AC
(c) DC as well as AC
(d) neither AC nor DC
Show Answer & Explanation

Answer: (a) DC

Explanation:
1. X_C = 1/(ωC) tends to infinity as ω tends to zero (d.c.).

Teacher's Note:
1. Recall the basic relation.

Question 17: The power factor of an a.c. circuit having resistance R and inductance L connected in series, with angular frequency ω, is
(a) \( R/\omega L \)
(b) \( R/(R^2\omega^2L^2) \)
(c) \( \omega L/R \)
(d) \( R/(R^2+\omega^2L^2)^{1/2} \)
Show Answer & Explanation

Answer: (d) \( R/(R^2+\omega^2L^2)^{1/2} \)

Explanation:
1. cos φ = R/Z = R/√(R² + ω²L²).

Teacher's Note:
1. Recall the basic relation.

Question 18: The average power dissipated in an a.c. circuit containing a resistance alone is
(a) e_rms I_rms
(b) e_rms I_rms cos φ
(c) 0
(d) none of these
Show Answer & Explanation

Answer: (a) e_rms I_rms

Explanation:
1. For a resistor φ = 0, so P = e_rms I_rms.

Teacher's Note:
1. Recall the basic relation.

Question 19: The electric mains supply in our homes and offices is a voltage that varies like a sine function with time. Such a voltage is called ____ A ____ and the current driven by it in a circuit is called ____ B ____. A and B refer to
(a) DC voltage, AC current
(b) AC voltage, DC current
(c) AC voltage, AC voltage
(d) AC voltage, AC current
Show Answer & Explanation

Answer: (d) AC voltage, AC current

Explanation:
1. A sinusoidally varying voltage is an a.c. voltage and it drives an a.c. current.

Teacher's Note:
1. Recall the basic relation.

Question 20: In a series R-C circuit the current leads the voltage by an angle φ given by
(a) \( \tan^{-1}\left(\frac1{\omega CR}\right) \)
(b) \( \tan^{-1}(\omega CR) \)
(c) \( \tan^{-1}\left(\frac{\omega C}{R}\right) \)
(d) \( \tan^{-1}\left(\frac R{\omega C}\right) \)
Show Answer & Explanation

Answer: (a) \( \tan^{-1}\left(\frac1{\omega CR}\right) \)

Explanation:
1. tan φ = X_C/R = 1/(ωCR).

Teacher's Note:
1. Recall the basic relation.

Question 21: An alternating voltage e = 200√2 sin(100t) volt is connected to a capacitor of capacity 1 microfarad. The r.m.s. value of the current in the circuit is
(a) 10 mA
(b) 100 mA
(c) 200 mA
(d) 20 mA
Show Answer & Explanation

Answer: (d) 20 mA

Explanation:
1. X_C = 1/(100 × 10⁻⁶) = 10⁴ ohm.
2. I_rms = 200/10⁴ = 0.02 A = 20 mA.

Teacher's Note:
1. Recall the basic relation.

Question 22: An inductive coil has a resistance of 100 ohm. When an a.c. signal of frequency 1000 Hz is fed to the coil, the applied voltage leads the current by 45°. What is the inductance of the coil?
(a) 10 mH
(b) 12 mH
(c) 16 mH
(d) 20 mH
Show Answer & Explanation

Answer: (c) 16 mH

Explanation:
1. tan 45° = X_L/R, so X_L = 100 ohm.
2. L = 100/(2π × 1000) = 15.9 mH, about 16 mH.

Teacher's Note:
1. Recall the basic relation.

Question 23: A step up transformer operates on a 230 V line and supplies a current of 2 ampere. The ratio of primary and secondary windings is 1 : 25. The current in the primary is
(a) 25 A
(b) 50 A
(c) 15 A
(d) 12.5 A
Show Answer & Explanation

Answer: (b) 50 A

Explanation:
1. I_p/I_s = N_s/N_p = 25.
2. I_p = 25 × 2 = 50 A.

Teacher's Note:
1. Recall the basic relation.

Question 24: In an alternating current circuit, in general,
(a) the average value of current over a cycle is zero
(b) the average value of the square of the current is zero
(c) the average power dissipation is zero
(d) the phase difference between voltage and current is zero
Show Answer & Explanation

Answer: (a) the average value of current over a cycle is zero

Explanation:
1. For a sinusoidal current the positive and negative half cycles cancel, so the average over a cycle is zero.
2. The average of i² and the average power in a resistor are not zero.

Teacher's Note:
1. Recall the basic relation.

Question 25: The frequency of a.c. mains in India is
(a) 30 c/s
(b) 50 c/s
(c) 60 c/s
(d) 120 c/s
Show Answer & Explanation

Answer: (b) 50 c/s

Explanation:
1. The mains frequency in India is 50 Hz.

Teacher's Note:
1. Recall the basic relation.

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Alternating Current Objective Questions & Solutions for JEE Physics

About Alternating Current MCQs for JEE Physics

Review structured objective questions for JEE Physics Alternating Current. Built according to official JEE guidelines, these MCQ sets support daily revision and core concept reinforcement.

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FAQs

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