Owen Duffy wrote:
. . .
Thinking that through further brings a third case to the "ONLY"
conditions, and that is if the circuit is entirely resistive (eg real
power is the product of Vrms and Irms if the waveform is square and
the circuit contains only resistances).

If you look at the definition of average (as in my previous posting),
you'll see that when the load is purely resistive, average power = 1/T *
the integral over T of v^2(t) / R dt or 1/T * the integral over T of
i^2(t) * R dt, for any waveform. And using the definition of RMS(*), you
can see that this is exactly Vrms^2 / R or Irms^2 * R respectively,
again for any waveform. So Pavg = Vrms * Irms for any waveform, as long
as (and only as long as) the load is purely resistive. Again, the
average and RMS values can be calculated for any interval (as long as
they're the same), but a single cycle is adequate to determine the
long-term average and RMS values of periodic waveforms.

(*) frms = Sqrt(avg(f^2(t))) = Sqrt(1/T * integral over T of f^2(t) dt)

Roy Lewallen, W7EL