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

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#### Solution

The instantaneous power supplied to the capacitor is

P = i_{m} cos(ωt)v_{m} sin(ωt)

P = i_{m}v_{m }cos(ωt)sin(ωt)

`P=(i_mv_m)/2sin(2omegat)`

Therefore, the average power is

`(:P:) = (:(i_mv_m)/2sin(2omegat):)=(i_mv_m)/2(:sin(2omegat):)`

Now, the average of sin(2ωt) over the cycle is zero.

∴ ⟨P⟩ = 0

Concept: Capacitors and Capacitance

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