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A resistance of 20 ohms is connected to a source of an alternating potential $V=220 \sin (100 \pi t)$. The time taken by the current to change from its peak value to r.m.s value is
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$2.5 \times 10^{-3} \mathrm{sec}$
Peak value to r.m.s value means, current becomes $\frac{1}{\sqrt{2}}$ times.
So from $i=i_0 \sin 100 \pi t \Rightarrow \frac{1}{\sqrt{2}} \times i_0=i_0 \sin 100 \pi t$
$\Rightarrow \sin \frac{\pi}{4}=\sin 100 \pi t \Rightarrow t=\frac{1}{400} \mathrm{sec}=2.5 \times 10^{-3} \mathrm{sec}$
So from $i=i_0 \sin 100 \pi t \Rightarrow \frac{1}{\sqrt{2}} \times i_0=i_0 \sin 100 \pi t$
$\Rightarrow \sin \frac{\pi}{4}=\sin 100 \pi t \Rightarrow t=\frac{1}{400} \mathrm{sec}=2.5 \times 10^{-3} \mathrm{sec}$
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