The average value of a.c. over a full cycle in an ac circuit is: (Given \( I_0 \) = Peak current)
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → zero
An alternating current \( I = I_0\sin\omega t \) is positive for one half of the cycle and negative for the other half, and the two halves are exactly equal, so the average over a full cycle is zero.
\( \displaystyle \langle I\rangle = \frac{1}{T}\int_0^T I_0\sin\omega t\,dt = \frac{I_0}{\omega T}\Big[-\cos\omega t\Big]_0^T = \frac{I_0}{2\pi}\left(-\cos2\pi+\cos0\right) = 0 \)
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.”