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 2​π = 1}
Hence average value of ac over full cycle is ZERO (PROVED)

 

  • 11
What are you looking for?