We know that the voltage and current vary sinusodially with time in AC circuits.
The "equivalent" values in a DC circuit are called the "rms values" and are given by
where Vrms and Irms are the rms values of the voltage and the current and Vo and Imax are the maximum values of the voltage and the current.
Both v(t) and i(t) vary sinusodially -- as the sine function (or cosine function). That means their mean value is zero. So taking just their mean value would be meaningless. A useful alternate is to take the mean value of the square. The mean value of the square of the sine (or cosine) is one-half,
The square root of the mean of the square of a sine function is one over the square root of two,
That is why these are called rms values and that is where the constant comes from .
(c) Doug Davis, 2002; all rights reserved
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