A capacitor is connected across an a.c. source of 230\ V . Which one…

The correct answer is Option (4) → The average electrical power delivered to the capacitor over one full cycle is zero.

In a purely capacitive a.c. circuit the current leads the voltage by \( \pi/2 \), and a.c. meters and ratings quote rms values, so 230 V is the rms voltage.

Option (1) The current and voltage attain their peak value at the same instant. — Incorrect. With a phase difference of \( \pi/2 \), the current is at its peak when the voltage is zero.

Option (2) The potential difference across the capacitor reaches a maximum value of \( 230\ \mathrm{V} \). — Incorrect. 230 V is the rms value. The peak value is \( \sqrt{2}\times230 \approx 325\,\mathrm{V} \).

Option (3) The current through the capacitor lags the voltage in phase. — Incorrect. The current leads; it lags in an inductor.

Option (4) The average electrical power delivered to the capacitor over one full cycle is zero. — Correct.

    \( P_{\mathrm{av}} = V_{\mathrm{rms}}I_{\mathrm{rms}}\cos\phi = V_{\mathrm{rms}}I_{\mathrm{rms}}\cos 90^{\circ} = 0 \)

The capacitor stores energy in one quarter-cycle and returns it to the source in the next.

NCERT (2026-27):
Summary – “… The current through the capacitor is \( \pi/2 \) ahead of the applied voltage. As in the case of inductor, the average power supplied to a capacitor over one complete cycle is zero.”