RMS

The root mean square (RMS or rms) is defined as the square root of the mean square, i.e. the arithmetic mean of the squares of a given set of numbers.

Root-mean-square voltage, equivalent direct current (DC) voltage of an alternating current (AC) source.

Certain electric circuits include sources of alternating?electromotive forces?of the sinusoidal form?V?=?V0?cos (ωt) or?V?=?V0?sin (ωt). The sine and cosine functions have values that vary between +1 and ?1; either of the equations for the voltage represents a potential that varies with respect to time and has values from +V0?to ?V0. The voltage varies with time at a rate given by the numerical value of ω; ω, which is called the?angular frequency, is expressed in radians per second.?The figure?shows an example with?V0?= 170 volts and ω = 377 radians per second, so that?V?= 170 cos (377t). The time interval required for the pattern to be repeated is called the?period?T, given by?T?= 2π/ω. In?the figure, the pattern is repeated every 16.7 milliseconds, which is the period. The?frequency?of the voltage is symbolized by?f?and given by?f?= 1/T. In terms of ω,?f?= ω/2π, in hertz.

The?root-mean-square (rms) voltage of a sinusoidal source of electromotive force (Vrms) is used to?characterize?the source. It is the?square root?of the time average of the voltage squared. The value of?Vrms?is?V0/√2, or, equivalently, 0.707V0. Thus, the 60-hertz, 120-volt?alternating current, which is available from most electric outlets in American homes and which is illustrated in?the figure, has?V0?= 120/0.707 = 170 volts; that is, 120 volts is the rms voltage. The potential difference at the outlet varies from +170 volts to ?170 volts and back to +170 volts 60 times each second. The rms values of voltage and?current?are especially useful in calculating average power in AC circuits.