# Derivation of mean value and average value of alternating e.m.f.

Please find below the solution to the asked query:

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

This is the mean and the average value of current of an alternating EMF

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