Q.What is the average value of alternating current over a complete cycle?

Positive and negative half-cycles of a sinusoidal AC exactly cancel over one full cycle.

The mean value of $i = I_0\sin(\omega t)$ over one complete cycle $\left(\dfrac{1}{T}\int_0^T i\,dt\right)$ is zero, because the positive half-cycle's area is exactly cancelled by the equal-and-opposite negative half-cycle's area. This is precisely why the r.m.s. value (based on the mean of $i^2$, …

Over a full cycle, the positive and negative half-cycles of a sine wave cancel exactly.

For a sinusoidal AC, $i = I_0\sin\omega t$. Averaged over one complete cycle, $\langle \sin\omega t\rangle = 0$ because the positive half-cycle exactly cancels the negative half-cycle. Hence the average value of AC over a ful …