Root Mean Square

CALCULATING THE ROOT MEAN SQUARE

The rms for a collection of

N

values

\{x_1,x_2,\dots,x_N\}

is:

:

x_{\mathrm{rms}} =

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where

I_\mathrm{p}

is the peak amplitude.

It should be noted that the peak amplitude is half of the peak-to-peak amplitude.
When the peak-to-peak amplitude is known, the same formula is applied by
using half of the p-p value.

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 Voltage s for power outlets (e.g. 110 V or 240 V) are almost always quoted in RMS values, and not peak values.

From the formula given above, we can calculate also the peak-to-peak value of the mains voltage which is approx. 310 (U.S.A)and 677 (Europe) volts respectively.

In the field of audio, mean power is often (misleadingly) referred to as RMS Power . This is probably because it can be derived from the RMS voltage or RMS current. Furthermore, because RMS implies some form of averaging, expressions such as "peak RMS power", sometimes used in advertisements for audio amplifiers, are meaningless.

In Chemistry , the root mean square velocity is defined as the square root of the average velocity-squared of the molecules in a Gas . The RMS velocity of a gas is calculated using the following equation:

:

{u_\mathrm{rms}} = {\sqrt{3RT \over {M}}}

where

R

represents the Ideal Gas Constant (in this case, 8.314 J/(mol⋅K)),

T

is the temperature of the gas in Kelvin s, and

M

is the Molar Mass of the compound in kilograms per mole.

RELATIONSHIP TO THE ARITHMETIC MEAN AND THE STANDARD DEVIATION

If

\bar{x}

is the Arithmetic Mean and

\sigma_{x}

is the Standard Deviation of a population then
:

x_{\mathrm{rms}}^2 = \bar{x}^2 + \sigma_{x}^2

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	CATEGORIES ABOUT ROOT MEAN SQUARE

	statistical deviation and dispersion

	means

Information About

Root Mean Square