Average Voltage

I agree with KISS. If you want to measure actual power in a circuit with reactance then you need to multiply the instantaneous current by the instantaneous voltage, either with an A/D converter and a micro, or with an analog multiplier. The average value of that multiplication is the real power. You can't do any voltage or current averaging before you do the multiplication if you want an accurate power measurement.

Here is a better explanation: https://edn.com/design/test-and-measurement/4417651/Product-How-To--Calculate-power-with-a-scope--

The problem is, it does require and implicit knowledge of Calculus to understand it. The two critical numbers are real and apparent power and these can't be calculated without the instantaneous product of V(t) and I(t).

Then a problem results when you have to determine a period.

There really needs to be a better explanation on the web.

P=V*I*cos(theta) is a special case: Sine wave voltage and sine wave current.