The average power dissipated in a pure capacitor in an ac circuit is

The correct answer is Option (4) → zero

The current in a pure capacitor leads the voltage by \( \pi/2 \). The instantaneous power \( p=\frac{1}{2}i_mv_m\sin(2\omega t) \) is positive while the capacitor charges and negative while it discharges. So the energy taken from the source in one quarter cycle is returned in the next. The average power over a complete cycle is zero.

With the phase angle \( \phi=90^\circ \), the average power is:

    \( \begin{aligned} P &= VI\cos\phi \\ &= VI\cos90^\circ \\ &= 0 \end{aligned} \)

NCERT (2026-27):
Power in AC Circuit: the Power Factor – “Case (ii) Purely inductive or capacitive circuit: If the circuit contains only an inductor or capacitor, we know that the phase difference between voltage and current is π/2. Therefore, cos φ = 0, and no power is dissipated even though a current is flowing in the circuit.”