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# What is the average value of current over one cycle of an ac signal? Why, then, is a resistor heated by an ac current?

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In one cycle of an ac signal, the average current is equal to $\textbf{zero}$. This is because after one-half of a cycle, the current switches direction i.e. the values of the current past the half-cycle cancel" out the values of the current before the half-cycle. In general, any sinusoidal function (of which the ac signal is an example) has an average value of zero in an entire cycle.

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