# Definition of average power

I am slightly confused by the definition of average power if the power function $p(t)$ is sinusoidal. Why is it that only one period is considered?

I mean I know that it simplifies calculations but if we assume that the period of $p(t)$ is $T$ and I compute the average power over $[0,\sqrt{2}T]$, I do not get the same result had I computed the average power over $[0,T].$

Case in point: If $p(t)=\frac{1}{2}(1+\cos(2x))$ then the average power is not the same for both cases mentioned...

sophiecentaur
Gold Member
2020 Award
If you want to know the instantaneous power then you would use VI. For a mean power value, you could choose any period you liked, to integrate over, but you would need to state that period (absolute phase intervals). It seem perfectly reasonable to me to choose a single cycle (or any integral number) because it's the most likely thing that anyone else would do. Any other period would be arbitrary and could introduce a massive range of possible outcomes (as you seem to be finding).

so are you saying that this is simply a definition? I'm sorry but I still can't seem to understand it...so the average power based on this definition, then, is merely an approximation of the "real mean"?

sophiecentaur