I was wondering if power is the rate which energy is stored in and released by a capacitor with a sinusoidal voltage source applied? I thought this was true, but my friend said false. ):

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    \$\begingroup\$ In general, power is energy over time. But there is instantaneous power and average power \$\endgroup\$ – DKNguyen Mar 22 at 21:14
  • \$\begingroup\$ technically, for an ideal capacitor, the average power will be 0. \$\endgroup\$ – Ben Mar 22 at 21:16
  • \$\begingroup\$ @DKNguyen which is a rate, of how much energy goes in (+) or out (-) over time. Power usually mean the instantaneous one, the average power is used for estimation of consumption or other estimates, as the average might not represent that well the behavior of the system. \$\endgroup\$ – jDAQ Mar 22 at 21:20

Your friend is right, and so are you.

Power is the derivative of Energy over time. Since the field energy in your capacitor changes over time, there's obviously power needed to effect that.

However, when you look at what happens over a full period (or multiples thereof), the capacitor stores as much energy as it releases; the average (over an arbitrarily large time span) power is zero.

This is the reactive power you'll have heard about. No actual work is done with that power – it just oscillates back and forth between your voltage source and your capacitor.

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