Average or Mean Value of Alternating Current and Voltage:
We know that the average value of a.c. over complete cycle is zero, so to impart some meaning to the average value of A.C., we find out its average over the half cycle only.
Average Value of A.C: It is defined as that value of steady current (d.c.) which sends the same amount of charge through the circuit in a time equal to that sent by a.c. in half the time period. It is denoted by
I = Im sin ωt
Assuming that this current remains constant for a small time dt, then charge dq flowing the circuit in the small time dt is given by
dq = i dt = Im sin ωt dt
If total charge q flows through the circuit in time T/2, then
Hence, the mean value or average value of a.c. over one half cycle is 0.637 times its peak value.
Similarly, it can be proved,, that average alternating emf over one half cycle is
Vav = \(\frac{2}{\pi}\) Vm = 0.637Vm
