What will be r.m.s. value of given A.C. over one cycle. - Vidyadip

MCQ

What will be $r.m.s.$ value of given $A.C.$ over one cycle.

A
${V_0}$
B
$\frac{{{V_0}}}{{\sqrt 2 }}$
✓
$\frac{{{V_0}}}{2}$
D
$\frac{{{V_0}}}{4}$

✓

Answer

Correct option: C.

$\frac{{{V_0}}}{2}$

c
$(\mathrm{RMS})^{2}=\frac{\int_{0}^{\mathrm{T} / 2} \mathrm{V}_{0}^{2} \sin ^{2} \mathrm{td} \mathrm{t}}{\mathrm{T}}=\frac{\mathrm{V}_{0}^{2}}{4}$

So $\mathrm{RMS}=\mathrm{V}_{0} / 2$

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