Choose the correct phase relationship between the current and the applied voltage in an a.c. circuit.
(A) In a pure resistive circuit, the current is in phase with the applied voltage.
(B) In a pure inductive circuit, the current lags behind the voltage by a phase angle of 90°.
(C) In a pure inductive circuit, the current leads the voltage by a phase angle of 90°.
(D) In a pure resistive circuit, the current is not in phase with the applied voltage.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A) and (B) only
(A) In a pure resistive circuit, the current is in phase with the applied voltage. — Correct. For \( V = V_0\sin\omega t \) across a resistor, \( I = V/R \) rises and falls with \( V \), so the phase difference is zero.
(B) In a pure inductive circuit, the current lags behind the voltage by a phase angle of 90°. — Correct. The induced emf opposes the change of current, so the voltage leads the current by \( \pi/2 \).
\( \displaystyle V = L\frac{dI}{dt}, \qquad I = I_0\sin\omega t \;\Rightarrow\; V = \omega L\,I_0\cos\omega t \)
(C) In a pure inductive circuit, the current leads the voltage by a phase angle of 90°. — Incorrect. It is the other way round; the current leads the voltage by \( 90^\circ \) only in a pure capacitive circuit.
(D) In a pure resistive circuit, the current is not in phase with the applied voltage. — Incorrect. This contradicts (A).
NCERT (2026-27):
Summary – “1. An alternating voltage \( v = v_m \sin\omega t \) applied to a resistor R drives a current \( i = i_m \sin\omega t \) in the resistor, \( i_m = v_m/R \). The current is in phase with the applied voltage.”
AC Voltage Applied to a Capacitor – “… Thus, we see that in the case of an inductor, the current lags the voltage by π/2 and in the case of a capacitor, the current leads the voltage by π/2.”