Question

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

• A. $0.2s$
• B. $0.25s$
• C. $2.5\times {10}^{-2}s$
• D. $2.5\times {10}^{-3}s$

Answer 1

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

$I=V/R=11sin\left(100\pi t\right)$
$I_{peak}=11=11sin\left(\pi /2\right)=11sin\left(100\pi \frac{1}{200}\right)$
$I_{rms}=11/\sqrt{2}=11sin\left(3\pi /4\right)=11sin\left(100\pi \frac{3}{400}\right)$
therefore time taken by current to change from peak to rms value = $\frac{3}{400}-\frac{1}{200}=\frac{1}{400}=2.5ms$