Show that the average value if ac over a full cycle is 0
Hi Abhishek, the equation for a.c. current is i = i0 sin w t
So total of current for full cycle is ∫ i0 sin w t dT within limits 0 to T
And average of current for full cycle = ∫ i0 sin w t dT / ∫ dT
==> i0 ∫ sin w t dT / (T) = (i0 / T) * [ - cos wt / (w)] with limits 0 to T
Or (-i0 / wT) [cos 0 - cos wT] = (-i0 / wT) [cos 0 - cos 2π] = 0 {since cos 0 = cos 2π = 1}
Hence average value of ac over full cycle is ZERO (PROVED)
So total of current for full cycle is ∫ i0 sin w t dT within limits 0 to T
And average of current for full cycle = ∫ i0 sin w t dT / ∫ dT
==> i0 ∫ sin w t dT / (T) = (i0 / T) * [ - cos wt / (w)] with limits 0 to T
Or (-i0 / wT) [cos 0 - cos wT] = (-i0 / wT) [cos 0 - cos 2π] = 0 {since cos 0 = cos 2π = 1}
Hence average value of ac over full cycle is ZERO (PROVED)