In an ac circuit, the current is referred to as wattless current, when:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → the circuit is either purely inductive or purely capacitive
The average power in an ac circuit depends on the phase difference \( \phi \) between voltage and current through the power factor \( \cos\phi \).
\( \displaystyle P = V_{\mathrm{rms}}I_{\mathrm{rms}}\cos\phi \)
The current is called wattless when it flows but the average power is zero, which needs \( \cos\phi = 0 \), i.e. \( \phi = 90^\circ \). This happens in a purely inductive or purely capacitive circuit.
Why the other options are incorrect
Option (1) the circuit is purely resistive — Incorrect. In a purely resistive circuit \( \phi = 0 \) and \( \cos\phi = 1 \), so the power is maximum.
Option (2) the LCR circuit is at resonance — Incorrect. At resonance the circuit behaves as purely resistive, \( \phi = 0 \), and the power is again maximum.
Option (4) the phase difference between current and applied voltage is 45° — Incorrect. At \( \phi = 45^\circ \), \( \cos\phi \approx 0.71 \), so power is still consumed.
NCERT (2026-27):
Power in AC Circuit: The Power Factor – “… In a purely inductive or capacitive circuit, \( \cos\phi = 0 \) and no power is dissipated even though a current is flowing in the circuit. In such cases, current is referred to as a wattless current.”