Page 283 - Basic Electrical Engineering

effective or RMS value let us find out the value of dc current, I which gives
the same amount of heating as that of ac when it flows through a resistance of
value, say, R. The alternating quantity is represented as, say, i = I Sin ωt.
m
The power dissipated in R by the dc current,

2
P = I R watts (i)
av

The instantaneous value of power dissipated in R by the ac current,

The average value of the second term is zero as it is a cosine function

varying with time.
The average value of power, P for the ac current,

Equating the power dissipated due to dc current, I and the ac. current, i we

can get the effective value as

or,

The effective or RMS value of an alternating quantity is either for one-half

of a cycle or for a full cycle as