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)

$2.5 \times 10^{- 3}$sec

Answer 2

Peak value to r.m.s. value means, current becomes $\frac{1}{\sqrt{2}}$ times.

So from $i = i_{0}\sin 100\pi t \Rightarrow \frac{1}{\sqrt{2}} \times i_{0} = i_{0}\sin 100\pi t$

$\Rightarrow \sin\frac{\pi}{4} = \sin 100\pi t \Rightarrow t = \frac{1}{400}\sec = 2.5 \times 10^{- 3}sec.$