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For a given ac i=imsinomegat, show that ...

For a given ac `i=i_msinomegat`, show that the average power dissipated in a resistor R over complete cycle is `1/2i_m^2R`.

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`i=i_msinomegat`,so`v=i_mRsinomegat`
`therefore` Power dissipated, `P=vi=i_m^2Rsin^2omegat`
The average of `sin^2omegat` over a complete cycle =`1/2`
`therefore` Average Power dissipated,
`overlineP=i_m^2R.1/2=1/2i_m^2R`
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