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  4. An alternating current in a circuit is given by I = 20 sin (100πt + 0.05π) A. The r.m.s. value and the frequency of current respectively are

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Q. An alternating current in a circuit is given by $I = 20$ sin $(100πt + 0.05π)$ A. The r.m.s. value and the frequency of current respectively are

WBJEEWBJEE 2013Alternating Current

Solution:

Given, $l=20 \sin (100 \,\pi t+0.05\, \pi)$
The root mean square value of alternating current
$=I_{ ms }=\frac{I_{0}}{\sqrt{2}}=\frac{20}{\sqrt{2}}=10 \sqrt{2} A$
Also, $\omega=100\, \pi$
$\Rightarrow 2 \pi f=100 \,\pi$ or $f=50 \,Hz$