S.T. average power over a complete cycle in a pure inductor connected to ac is zero.

Explanation

The instantaneous power supplied to an inductor
`P_(L)=iv`
`=i_(m)sin(omegat-pi//2)(v_(m)sinomegat)`
`=-i_(m)cosomegatv_(m)sinomegat`
i.e., `P_(L)=-(1)/(2)i_(m)v_(m)(sin2omegat)` where `sin2omegat=2sinomegatcosomegat`
The average power over a complete cycle is
`P_(L)=(:-(i_(m)v_(m))/(2)sin2omegat:)`
`=-(i_(m)v_(m))/(2)(:sin2omegat:)`
= 0
`therefore (:sin2omegat:)=(:cos2omegat:)=0`
Thus average power supplied to an inductor over one complete cycle is zero.