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 sine 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 p/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
sine wave applied across a 1 Ω resistor also
produces 1 W of heat. That 1 V
rms
sine wave has a peak voltage of √2 V (≈1.414 V), and a
peak-to-peak voltage of 2√2 V (≈2.828 V).
Since finding a full derivation of the formulas for root-mean-square (V
rms
)
voltage is difficult, it is done here for you.
Form factor: Two alternating periodic waveforms of the same amplitude and frequency may
look different depending upon their wave shape/form and then their average & RMS values
will be different. In order to compare such different waveforms of the same frequency and
amplitude but of different wave shape a parameter called Form factor is defined as the ratio
of it’s RMS and Average values.
For a sinusoidal signal of peak voltage V
m
it is given by :
Form factor of a sinusoidal signal = V
rms
/V
av
= 0.707 V
m
/ 0.637 V
m
= 1.11
Peak Factor (Or Crest factor) : Is defined as the ratio of maximum value to the R.M.S value
of an alternating quantity.
Peak factor of a sinusoidal signal=V
max
/V
rms
=V
max
/(0.707 V
m
)
=1.414
