Root-Mean-Square Voltage (V
rms
)
As the name implies, V
rms
is calculated by taking the square root of the mean
average of the square of the voltage in an appropriately chosen interval. In
the case of
symmetrical waveforms like the triangle wave, a quarter cycle faithfully represents all four
quarter cycles of the waveform. Therefore, it is acceptable to choose the first quarter cycle,
which goes from 0 radians (0°) through π/2 radians (90°).
V
rms
is the value indicated by the vast majority of AC voltmeters. It is the
value that, when applied across
a resistance, produces that same amount of heat that a direct
current (DC) voltage of the same magnitude would produce. For example, 1 V applied across
a 1 Ω resistor produces 1 W of heat. A 1 V
rms
triangle wave applied across a 1 Ω
resistor also
produces 1 W of heat. That 1 V
rms
triangle wave has a peak voltage of √3 V (≈1.732 V), and a
peak-to-peak voltage of 2√3 V (≈3.464 V).
Since finding a full derivation of the formulas for root-mean-square (V
rms
)
voltage is difficult, it is done here for you.
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