In an AC circuit:

The correct answer is Option (1) → The average value of current in one cycle is zero

An alternating current varies sinusoidally, \( i = i_m\sin\omega t \), so it is positive for one half of the cycle and negative for the other half.

    \( \displaystyle \bar{i} = \frac{1}{T}\int_{0}^{T} i_m\sin\omega t\;dt = 0 \)

Option (1) The average value of current in one cycle is zero — Correct. The positive and negative halves of the cycle are equal, so the average current over a full cycle is zero.

Option (2) The average value of the square of current is zero — Incorrect. \( i^{2} \) is never negative; its average over a cycle is \( i_m^{2}/2 \), which is why the rms current \( i_m/\sqrt{2} \) is not zero.

Option (3) The average power is zero — Incorrect. The average power is \( P = V_{\mathrm{rms}}I_{\mathrm{rms}}\cos\phi \); it is zero only in a purely inductive or purely capacitive circuit, and not zero when a resistance is present.

Option (4) The phase difference between voltage and current at resonance is \( \pi \) — Incorrect. At resonance \( X_L = X_C \), the impedance is purely resistive, and the voltage and current are in phase (phase difference zero).

NCERT (2026-27):
AC Voltage Applied to a Resistor – “… We see that, like the applied voltage, the current varies sinusoidally and has corresponding positive and negative values during each cycle. Thus, the sum of the instantaneous current values over one complete cycle is zero, and the average current is zero. The fact that the average current is zero, however, does not mean that the average power consumed is zero and that there is no dissipation of electrical energy.”