I can understand people assuming that RMS voltage or RMS current has to deliver RMS power, but in reality it is average power, equal to 1/2 of peak power for sinewave. It took FTC 20 years to realize that there is no such thing as RMS power or RMS watts. You can calculate RMS of any curve but for power it would not represent anything (Average power, a sum of momentary powers, represents dissipated heat).
We can obtain RMS value of sinewave current or voltage by squaring sin(x), taking mean value by calculating integral of ((sin(x))^2)/pi from 0 to pi and taking square root of it. Since mentioned integral results in 0.5 then square root of it is 0.707. Vrms=0.707Vp Irms=0.707Ip
Pavg=Vrms x Irms=0.707Vp x 0.707Ip = 0.5Pp
We can take RMS of power curve, proportional to (sin(x))^2, but taking mean value of (sin(x))^4 will result in 0.375. Square root of it is 0.612 and this value does not represent anything useful. Sometimes people assume that "RMS power" means "true" power vs "apparent" power, but it is already done by using W (watts) instead of VA (volt-amperes).
