An AC source rated 220V, 50Hz is connected to a resistor. The time...

AC

source rated

220V, 50Hz

is connected to a resistor. The time taken by the current to change from its maximum to the rms value is :

Options

A $2 . 5ms$
B $25ms$
C $2 . 5s$
D $0 . 25ms$

Correct answer

A. $2 . 5ms$

Step-by-step solution

$i = {i}_{0}\cos ( \omegat )$
$i = {i}_{0}$ at $t = 0$
$i = \dfrac{{i}_{0}}{\sqrt{2}}$ at $\omegat = \dfrac{\pi}{4}$
$t = \dfrac{\pi}{4\omega} = \dfrac{\pi}{4 ( 2\pif )} = \dfrac{1}{8f}$
$t = \dfrac{1}{400} = 2 . 5ms$

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