## Explain why the average power delivered to a resistor is not zero?

Question

The average current in a resistor in an ac circuit is zero. Explain why the average power delivered to a resistor is not zero.

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General Physics
3 years
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## Answer ( 1 )

Let us simplify the problem.

For half the time the current is moving to the right. Charge = 1/2 I t

For half the time the current is moving to the left. Charge = – 1/2 t

Add them together and divide by time. 0 / t = 0

So our average current becomes zero.

Now do the same for power.

Power = I^2 R -> energy = I^2 R t

so we have for the first half E = 1/2 I^2 R t

and for the second half we have E = 1/2 (-I)^2 R t = 1/2 I^2 R t

Add them together to get the total power and divide by t to get average power.

P = I^2 R

Power is a scalar. It can never be negative so energy is being emitted whichever way the current is moving.

This is similar to friction. If I push a 300 kg mass across the floor and back again the mass has not moved. It is exactly where it started from. But if you try it you will find that it takes you work and effort BOTH ways.