Root mean square Guide, Meaning , Facts, Information and Description
In mathematics, the root mean square or rms is a statistical measure of the magnitude of a varying quantity. 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.The rms for a collection of N values {x1, x2, ... , xN} is:
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The RMS value of a function is often used in physics. For example, we may wish to calculate the power P dissipated by an electrical conductor of resistance R. It is easy to do the calculation when a constant current I flows through the conductor. It is simply,
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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 of alternating current, 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:
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. For this reason, listed voltages for power outlets (eg. 110V or 240V) are almost always quoted in RMS values, and not peak-to-peak values.
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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