The rms for a collection of N values {x_{1}, x_{2}, ... , x_{N}} is:
and the corresponding formula for a continuous function f(t) defined over the interval T_{1} ≤ t ≤ T_{2} is:
But what if the current is a varying function I(t)? This is where the rms value comes in. It may be shown that the rms value of I(t) can be substituted for the constant current I in the above equation to give the mean power dissipation, thus:
In the common case when I(t) is a sinusoidal current, as is approximately true for mains power, the rms value is easy to calculate from equation (2) above. The result is:
where I_{p} is the amplitude.
The rms value can be calculated using equation (2) for any waveform, for example an audio or radio signal. This allows us to calculate the mean power delivered into a specified load.
It is important to note that rms is a mean value and not an instantaneous measurement. Therefore expressions such as "peak rms power", sometimes used in advertisements for audio amplifiers, are misleading. See also PMPO.
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