An AC source rated 220V, 50 Hz is connected to a resistor.
Question:

An $\mathrm{AC}$ 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:

1. (1) $2.5 \mathrm{~ms}$

2. (2) $25 \mathrm{~ms}$

3. (3) $2.5 \mathrm{~s}$

4. (4) $0.25 \mathrm{~ms}$

Correct Option: 1

Solution:

(1)

$\mathrm{i}=\mathrm{i}_{0} \cos (\omega t)$

$\mathrm{i}=\mathrm{i}_{0}$ at $\mathrm{t}=0$

$\mathrm{i}=\frac{\mathrm{i}_{0}}{\sqrt{2}}$ at $\omega \mathrm{t}=\frac{\pi}{4}$

$\mathrm{t}=\frac{\pi}{4 \omega}=\frac{\pi}{4(2 \pi \mathrm{f})}=\frac{1}{8 \mathrm{f}}$

$\mathrm{t}=\frac{1}{400}=2.5 \mathrm{~ms}$