When an ac source is connected to an ideal capacitor, show that the average power supplied by the source over a complete cycle is zero.

Explanation

The instantneous power supplied to the capacitor,
`P=I_0cos(omegat)V_0sin(omegat)`
`P=I_0V_0cos(omegat)sin(omegat)`
`P=(I_0V_0)/2sin(2omegat)`
Therefore, the average power,
`overlineP=(I_0V_0)/2sin(2omegat)=(I_0V_0)/2sin(2omegat)`
Now, the average of `sin(2omegat)` over the cycle is zero.
`overlineP=0`