What is the average power consumed/cycle in ideal capacitor.

The average power consumed/cycle in an ideal capacitor is 0.

The average power consumed in an ideal capacitor is given as based on the instantaneous power which is supplied to the capacitor:

pc = iv= (im cos ωt)(vm sin ωt)
pc = imvm (cos ωt sin ωt)

[latex]p_{c}=\frac{i_{m}v_{m}}{2}sin\;2\omega t[/latex]

We know that sin ωt = 0

Therefore, average power = 0

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