# 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 - Physics

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

#### Solution

The instantaneous power supplied to the capacitor is

P = im cos(ωt)vm sin(ωt)

P = imvcos(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
Is there an error in this question or solution?