Well, don't need all that calculus. And no, it is not RMS power. You still don't get it.
No need to invoke 3 phase or anything else.
All you have to do is do a simple, basic calculation that I have posted.
Here, let me help you:
10 V rms and 10 A rms will equal 100 watts. Now the question is what to call that.
Firstly, that 10 turns out to be 14.14 peak V and A. Better be.
Therefore peak power is 200 watts.
.707 of 200 watts is 141.4 watts. So, that 100 watt is not RMS, cannot be, period.
Here are two grabs from Hyper physics under RMS. No mention of RMS power but exactly what the above calculations proved, AVERAGE power.
RMS has only one meaning and it doesn't mean average.
View attachment 28745View attachment 28746
P avg= V rms X I rms; average power, not RMS!
Yet, another. Since RMS is .707, guess what happens when you multiply .707 and .707 =.5 (average)