Question:
An AC source rated $220 \mathrm{~V}, 50 \mathrm{~Hz}$ is connected to a resistor. The time taken by the current to change from its maximum to the rms value is :
Correct Option: 1
Solution:
$\mathrm{i}=\mathrm{i}_{0} \cos (\omega \mathrm{t})$
$\mathrm{i}=\mathrm{i}_{0}$ at $\mathrm{8}=0$
$\mathrm{i}=\frac{\mathrm{i}_{0}}{\sqrt{2}}$ at $\omega \mathrm{t}=\frac{\pi}{4}$
$\mathrm{t}=\frac{\pi}{4 \omega}=\frac{\pi}{4(2 \pi \mathrm{f})}=\frac{1}{8 \mathrm{f}}$
$\mathrm{t}=\frac{1}{400}=2.5 \mathrm{~ms}$