Ac is a continuously varying electrical quantity. So,
naturally the question arises ,how to express the magnitude of ac voltage or ac
current ?
The best answer is to express it in terms of rms value.
RMS
Value definition
The rms value of a waveform is defined as the equivalent
direct current which produces the same amount of heat in a given resistor in
same period of time as the ac would had produced if passed through the same
resistor for same period of time under the same conditions like temperature.
Rms value is also called effective value of ac.
By using the above definition the equivalent rms value for any waveform can be found out. Lets see how to find rms value of sine wave.
RMS value for ac current and ac voltage
Let there be a resistor R which carries a dc current Irms
for time T.
The heat produced is
Just the samiliar way ac voltage rms value can be found out and it
Important points
:-
(1) Students should be
alert that rms value=0.707 times peak value is only for sinusoidal waveform and
the relationship between rms value and peak value will be different for different
waveforms as the function under intergration will be different.
(2) The above procedure
can be remembered as direct formula
i.e to find rms value of
quantity X ,square the quantity X then take mean of it and finally take root and
that is why the name Root Mean Square.
(3) Ratings of electrical equipments are provided in terms of rms values.
(4) Rms value of a dc is equal to dc itself.
(5) when a waveform X consists
of many waveforms X1 ,X2 and X3 i.e X = X1+ X2+ X3
then the rms value of X
can be found out by using formula
