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  4. A resistance of 40 Ω is connected to a source of alternating current rated 220 V , 50 Hz. Find the time taken by the current to change from its maximum value to rms value :

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Q. A resistance of $40\, \Omega$ is connected to a source of alternating current rated $220\, V , 50\, Hz$. Find the time taken by the current to change from its maximum value to rms value :

JEE MainJEE Main 2022Alternating Current

Solution:

Considering sinusoidal $AC$.
Phase at maximum value $=\frac{\pi}{2}$
Phase at rms value $=\frac{3 \pi}{4}$
Thus phase change $=\frac{3 \pi}{4}-\frac{\pi}{2}=\frac{\pi}{4}$
Now $\omega=2 \pi f$
$=2 \pi \times 50 $
$=100 \pi$
time taken $t =\frac{\theta}{\omega}=\frac{\pi / 4}{100 \pi}=\frac{1}{400} s$
$t =2.5 \times 10^{-3}=2.5\, ms$