22.3 rms Values

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

or

where V_rms and I_rms are the rms values of the voltage and the current and V_o and I_max 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 .

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(c) Doug Davis, 2002; all rights reserved