# Show that the average value if ac over a full cycle is 0

_{0}sin w t

So total of current for full cycle is ∫ i

_{0}sin w t dT within limits 0 to T

And average of current for full cycle = ∫ i

_{0}sin w t dT / ∫ dT

==> i

_{0}∫ sin w t dT / (T) = (i

_{0}/ T) * [ - cos wt / (w)] with limits 0 to T

Or (-i

_{0}/ wT) [cos 0 - cos wT] = (-i

_{0}/ wT) [cos 0 - cos 2π] = 0 {since cos 0 = cos 2π = 1}

Hence average value of ac over full cycle is ZERO (PROVED)

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