Can anyone explain RMS vs average? (particularly the math portion, and the intuition)? Answered
My current understanding of RMS (Root Mean Square) is that it is the equivalent AC voltage/current/power necessary to drive a resistive load the same around as the DC voltage/current/power counterpart. However, I am a bit confused about the math involved that can apply to all waveform.
I know the conversation factor for sine waves is 1/ sqrt(2),
and that the conversion factor for square waves is 1:1 (no difference)
On my graphing calculator, if I take the square root of the definite integral (from 0 to pi, integrating the x ) of the sin(x)^2, then divide that by the period, pi, I get the correct answer. However, what is the purpose of the squaring, then square-rooting? is it purely to perform a absolute value mathematically? If so, then I should be able to simply integrate the absolute value of the sine, and divide the result the the period the integration was performed over. If it period it was performed over was 0-pi, then there is no need to even take the absolute value! But this method returnees 0.636619... not 0.707106...
Intuitively, it makes much more sense to me to somehow take the mean average of the continues |sin(x)| function. I know this can be done with desecrate numbers (a sequence, perhaps) and by taking the sum of them, and dividing it by the number of 'elements.' (series's, anyone?). I would expect this average is what determined the average power used by a load.
EDIT: Wikipedia states that "The true RMS value is actually proportional to the square-root of the average of the square of the curve, and not to the average of the absolute value of the curve." So it appears I have just proven this. But Why???? What is so special about the squaring and rooting???
Please don't bombard me with heavy math, as I am not familiar with calculus, and have barely passed pre-calculus (The class was supposed to touch upon series and sequences, and integrals, derivatives, limits, etc. but due to show days and delays, the class only covered trigonometry --the bare essentials--). I do not yet fully understand single-variable integrals, let alone multi-variable calculus. I really just want a better intuition of RMS. More than likely, there is probably some confusion I have about integrals in general, and how to calculate them on-paper.