The current and voltage in ac circuit are given by \( I=5\sin\left(100t-\frac{\pi}{2}\right)\,\mathrm{A} \) and \( V=200\sin(100t)\,\mathrm{V} \). The power dissipated in the circuit is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 0
The average power in an ac circuit depends on the phase difference \( \phi \) between the voltage and the current:
\( \displaystyle P = V_{\mathrm{rms}}\,I_{\mathrm{rms}}\cos\phi = \frac{V_0 I_0}{2}\cos\phi \)
Comparing the two equations, the current lags the voltage by \( \pi/2 \), so \( \phi = \pi/2 \) and \( \cos\phi = 0 \).
\( \displaystyle P = \frac{200 \times 5}{2} \times \cos\frac{\pi}{2} = 500 \times 0 = 0 \)
The power factor is zero, as for a pure inductor: energy stored in one quarter-cycle is returned in the next, so no power is dissipated.
Note: This question is from NCERT (2026-27). NTA sets numerical questions from NCERT too, so do not ignore NCERT while practising numericals.
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.”