Question 34 of 190

A $10\Omega$ resistance is connected across $220V-50Hz$ AC supply. The time taken by the current to change from its maximum value to the $rms$ value is:

A$2.5ms$B$1.5ms$C$3.0ms$D$4.5ms$

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Answer: (A) $2.5ms$

$\Rightarrow i={i}_{0}\sin \omega t$
When $i={i}_{0}$
${i}_{0}={i}_{0}\sin \omega {t}_{1}\Rightarrow \omega {t}_{1}=\dfrac{\pi }{2}\ldots (1)$
When $i=\dfrac{{i}_{0}}{\sqrt{2}}$
$\dfrac{{i}_{0}}{\sqrt{2}}={i}_{0}\sin \omega {t}_{2}\Rightarrow \omega {t}_{2}=\dfrac{\pi }{4}\ldots (2)$
Time taken by current from maximum value to rms value, $\Rightarrow \left({t}_{1}-{t}_{2}\right)=\dfrac{\pi }{2\omega }-\dfrac{\pi }{4\omega }=\dfrac{\pi }{4\omega }=\dfrac{\pi }{4\times 2\pi f}$
$=\dfrac{1}{8\times 50}$
$=\dfrac{1}{400}\sec$
$=2.5ms$

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