Both alternating current and direct current are measured in ampere. But how is ampere defined for alternating current? It cannot be defined from two mutual attraction of two parallel wires carrying ac current, as dc current is defined. My guess is that since an ac current changes direction with the source frequency and attractive force would average to zero, the ac current should be defined of some property that is independent of direction of current. Also, there is one ampere of RMS value of alternating current in a circuit if the current produces same average heating effect as one ampere of dc current would produce under same condition.
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1$\begingroup$ You could ask the same about velocity of a box on a spring. An instantaneous velocity is fine. You can talk about an RMS velocity which is literally the square root of the average of the squared of the velocity (RootMeanSquare=RMS) but I bet engineers have a standard like make hey pretend a charge per second is different than an Ampere or that it is different than a Volt per Ohm. So your question might be field specific. So please state your field. $\endgroup$– TimaeusCommented Aug 29, 2015 at 16:39
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$\begingroup$ en.wikipedia.org/wiki/Root_mean_square $\endgroup$– Solomon SlowCommented Aug 29, 2015 at 21:25
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I think you are correct. Joule's heating effect is such a property which is used to define 1Amp for AC source as it does not depend on the direction of current. Over a full cycle the average current supplied by an AC source is zero.