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  4. The time required for a 50 Hz sinusoidal altemating current to change its value from zero to the r.m.s. value

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Q. The time required for a $50\, Hz$ sinusoidal altemating current to change its value from zero to the r.m.s. value

Alternating Current

Solution:

$I=I_{0} \sin \omega t$
$I_{\text {rms }}=\frac{I_{0}}{\sqrt{2}}$
So $\frac{I_{0}}{\sqrt{2}}=I_{0} \sin \omega t$
$\sin \frac{\pi}{4}=\sin (2 \pi)(50) t$
$\frac{\pi}{4}=2 \pi(50) t$
$t=\frac{1}{400} s$
$t=0.25 \times 10^{-2} $
$\Rightarrow 2.5 \times 10^{-3}\, s$