Question

A $10\Omega$ resistance is connected across $220V-50HzAC$ supply. The time taken by the current to change from its maximum value to the rms value is:

• A. 2.5 ms
• B. 1.5 ms
• C. 3.0 ms
• D. 4.5 ms

Answer 1

Answer: (A)

$\Rightarrow i=i_0\sin \omega t$
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
$\Rightarrow \left(t_1-t_2\right)=\frac{\pi }{2\omega }-\frac{\pi }{4\omega }=\frac{\pi }{4\omega }=\frac{\pi }{4\times 2\pi f}$
$=\frac{1}{8\times 50}$
$=\frac{1}{400}\sec$
$=2.5ms$