Question

What is meant by mean value of A.C? Derive an expansion for mean value of alternating current and EMF.

Answer 1

The mean value or average value of AC over a complete cycle is zero. So we do not consider the average value of AC over one cycle. We, therefore, take the average value of AC over a half cycle only I.e. from $t=0$ to $t=\frac{T}{2}$

The average value of AC over a half cycle is that value of steady current that would send same amount of charge in same interval of time that would be sent by the DC in the same time.

To calculate the mean value of ac, Let us consider an Ac given by

The small amount of charge sent by an ac in small time $dt$ is

The total charge carried by ac in half cycle is obtained by integrating equation ii from $t=0tot=\frac{T}{2}$

If $Im$ be the average ac then charge carried by it in half cycle is

Now, we get

Similarly, the average value of ac over the negative half cycle $(t=\frac{T}{2}tot=T)$ is

Therefore the average ac over a complete cycle is zero.