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=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 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
total charge carried by ac in half cycle is obtained by integrating equation ii from t = 0 to t = T/2
If Im be the average ac then charge carried by it in half cycle is
Now from equation iii and iv we get
Similarly the average value of ac over negative half cycle (t = T/2 to t = T) is
Therefore the average ac over a complete cycle is zero.
Similarly the average value of alternating emf over a half cycle is