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# root-mean-square (RMS)

Also see peak and peak-to-peak.

In a direct current (DC) circuit, voltage or current is simple to define, but in an alternating current (AC) circuit, the definition is more complicated, and can be done in several ways. Root-mean-square (rms) refersto the most common mathematical method of defining the effective voltage or current of an AC wave.

To determine rms value, three mathematical operations are carried out onthe function representing the AC waveform:

• (1) The square of the waveform function (usually a sine wave) is determined.

• (2) The function resulting from step (1) is averaged over time.

• (3) The square root of the function resulting from step (2) is found.

In a circuit whose impedance consistsof a pure resistance, the rms value of an ACwave is often called the effective value or DC-equivalent value.For example, if an AC source of 100 volts rms is connected across a resistor, and theresulting current causes 50 watts of heat to be dissipated by the resistor, then 50 wattsof heat will also be dissipated if a 100-volt DC source is connected to the resistor.

For a sine wave, the rms value is 0.707 times the peak value, or 0.354 times thepeak-to-peak value. Household utility voltages are expressed in rms terms.? Aso-called "117-volt" AC circuit carries about 165 volts peak (pk), or 330 voltspeak-to-peak (pk-pk).

This was last updated in April 2005

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