If \( I=I_0\sin\left(\omega t-\displaystyle\frac{\pi}{2}\right) \) and \( E = E_0 \sin \omega t \), then the AC power consumed is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \( P=0 \)
The average power consumed in an ac circuit is \( P = E_{\mathrm{rms}}I_{\mathrm{rms}}\cos\phi \), where \( \phi \) is the phase difference between the voltage and the current.
Comparing \( E = E_0\sin\omega t \) with \( I = I_0\sin(\omega t - \pi/2) \), the current lags the voltage by \( \phi = \pi/2 \).
\( \displaystyle P = \frac{E_0I_0}{2}\cos\frac{\pi}{2} = 0 \)
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. This current is sometimes referred to as wattless current.”