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Q.
A $10\, \Omega$ resistance is connected across $220\, V -50\, Hz AC$ supply. The time taken by the current to change from its maximum value to the rms value is:
$\Rightarrow i=i_{0} \sin \omega t$
When $i=i_{0}$
$i_{0}=i_{0} \sin \omega t_{1}$
$\Rightarrow \omega t_{1}=\frac{\pi}{2}$ ... (i)
When $i=\frac{i_{0}}{\sqrt{2}}$
$\frac{i_{0}}{\sqrt{2}}=i_{0} \sin \omega t_{2}$
$\Rightarrow \omega t_{2}=\frac{\pi}{4}$ ...(ii)
Time taken by current from maximum value to $rms$ value
$\Rightarrow\left(t_{1}-t_{2}\right)=\frac{\pi}{2 \omega}-\frac{\pi}{4 \omega}=\frac{\pi}{4 \omega}=\frac{\pi}{4 \times 2 \pi f}$
$=\frac{1}{8 \times 50}$
$=\frac{1}{400} \sec$
$=2.5\, ms$
