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RMS: Voltage & Average Power

In mathematics, the root mean square (abbreviated RMS or rms), also known as the quadratic mean, is a statistical measure of the magnitude of a varying quantity. It is especially useful when variates are positive and negative, e.g., sinusoids. It can be calculated for a series of discrete values or for a continuously varying function. The name comes from the fact that it is the square root of the mean of the squares of the values. - Wikipedia

General Equation for RMS Voltage:

RMS (effective) value of any periodic function with period T.

Average of Instantaneous Power:

RMS Equation for a Sine Wave:

,  ...for positive or negative half-cycle