21.1.3—The fact that the mean power in a resistive load is half the maximum power

With i=I₀sinωt and fixed resistance R, instantaneous power i²R varies from zero to I₀²R; its cycle average is ½I₀²R.

Use average over a complete cycle and distinguish peak power from mean heating power.

If peak current doubles, mean resistive power quadruples because it depends on I₀².

A zero mean current does not imply zero mean power, since power depends on current squared.