Question

The peak value of e.m.f. in a.c. is E0. Write its (i) rms (ii) average value over a complete cycle.

Answer 1

Given that peak value of AC is Eo

now the AC voltage is given by

$V = E_o sin\omega t$

Average value is calculated by

$E_{avg} =\frac{1}{T} \int E_osin\omega t dt$

so for one complete cycle value of above integral must be zero

So average of AC EMF must be ZERO

Again for RMS value

$E_{rms}= \sqrt{\frac{1}{T}\int E_o^2 sin^2\omega t dt}$

by solving above integral we can see

$E_{rms} = \frac{E_o}{\sqrt2}$

so above is the RMS value of AC