What is the average value of alternating current over a complete cycle?
Answer
The average value of alternating current over one complete cycle is zero, because it flows equally in both directions during the cycle.
The working
Key result
Over a full cycle, the mean or average value of a symmetric alternating current is exactly zero.
Reason
During the first half cycle the current is positive and during the second half it is equally negative, so the two halves cancel out.
Why we use rms
Because the average is zero, alternating current is instead described by its root mean square value, which relates to the effective current.
Half-cycle note
The average over just a half cycle is not zero; it equals (2 ÷ π) times the peak value, about 0.637 times I₀.
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