Choose the correct statements from the following:
A. Induced emf opposes any change in the current in a circuit
B. Induced emf in a closed coil can be increased by increasing the number of turns in the coil
C. Varying current in a coil can not induce emf in a neighbouring coil.
D. An LCR circuit has zero impedance at resonant frequency
E. Average power supplied to an inductor over one complete cycle is zero
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A, B and E only
The statements test Lenz's law, Faraday's law, mutual induction, resonance and the power in an ac circuit.
(A) Induced emf opposes any change in the current in a circuit — Correct. By Lenz's law the induced emf always acts to oppose the change that produces it.
(B) Induced emf in a closed coil can be increased by increasing the number of turns in the coil — Correct. By Faraday's law the emf is \( \varepsilon = -N\,d\Phi/dt \), so it is proportional to the number of turns \( N \).
(C) Varying current in a coil can not induce emf in a neighbouring coil. — Incorrect. A varying current changes the flux linked with a nearby coil, so it does induce an emf there. This is mutual induction, \( \varepsilon_2 = -M\,dI_1/dt \).
(D) An LCR circuit has zero impedance at resonant frequency — Incorrect. At resonance \( X_L = X_C \), so \( Z = \sqrt{R^2 + (X_L - X_C)^2} = R \). The impedance is minimum and equal to R, not zero.
(E) Average power supplied to an inductor over one complete cycle is zero — Correct. In a pure inductor the current lags the voltage by \( \pi/2 \), so \( P_{\mathrm{av}} = V_{\mathrm{rms}} I_{\mathrm{rms}} \cos 90^\circ = 0 \).
NCERT (2026-27):
Lenz’s Law and Conservation of Energy – “… The statement of the law is: The polarity of induced emf is such that it tends to produce a current which opposes the change in magnetic flux that produced it.”
Faraday’s Law of Induction – “… The induced emf can be increased by increasing the number of turns N of a closed coil.”
AC Voltage Applied to an Inductor – “… Thus, the average power supplied to an inductor over one complete cycle is zero.”