Question

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

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

Answer 1

The correct option is D $2.5\times {10}^{-3}sec$

Step 1, Given data

Resistance = 20 ohm

Voltage = $V=220sin\left(100\pi t\right)$

Step 2, Finding the time

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

From the question

$V=220sin100\pi t$

So, we can write

$i=i_{0}sin100\pi t$

Now,

$\frac{1}{\sqrt{2}}\times i_0=i_{0}sin100\pi t$

Or, $sin\frac{\pi }{4}=sin100\pi t$

Or, $t=\frac{1}{400}$ sec=$2.5\times {10}^{-3}$ sec

Hence, option (C) is correct