Question

A resistance of $20\, ohms$ is connected to a source of an alternating potential $V=220\, \sin (100 \pi t)$. The time taken by the current to change from its peak value to r.m.s. value is

• A. $0.2 \,sec$
• B. $0.25\, sec$
• C. $25 \times 10^{-3} sec$
• D. $2.5 \times 10^{-3} sec$

Answer 1

Answer: (D)

Peak value to r.m.s. value means current becomes $\frac{1}{\sqrt{2}}$ times.
So from $i=i_{0} \sin 100 \pi t$
$ \Rightarrow \frac{1}{\sqrt{2}} \times i_{0}=i_{0} \sin 100 \pi t$
$\Rightarrow \sin \frac{\pi}{4}=\sin 100 \pi t $
$\Rightarrow t=\frac{1}{400} sec =2.5 \times 10^{-3} sec$