# Question #23191

Sep 23, 2016

We know
$\text{The current in AC at t th instant } I = {I}_{m} \sin \omega t \ldots . \left(1\right)$
$\text{where " I_m ="peak value of the current and "omega="frequency}$
$\text{Here " omega =50Hz=50xx2pi"rad/s"=100pi"rad/s}$
${I}_{r m s} = {I}_{m} / \sqrt{2}$

We are to find out the value of t to reach $I \to {I}_{r m s}$

Inserting values in equation (1)

${I}_{m} / \sqrt{2} = {I}_{m} \sin \left(100 \pi \times t\right)$

$\implies \sin \left(100 \pi \times t\right) = \frac{1}{\sqrt{2}} = \sin \left(\frac{\pi}{4}\right)$

$t = \frac{1}{400} s = 2.5 \times {10}^{-} 3 s = 2.5 m s$