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A resistance of $40 Ω$ is connected to a source of alternating current rated $220 V, 50 Hz$ . Find the time taken by the current to change from its maximum value to rms value :

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2.5 ms

2.5 s

0.25 s

1.25 ms

answer is A.

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Detailed Solution

Considering sinusoidal AC.

$Phase at maximum value = \frac{π}{2}$

$Thus phase change = \frac{3 π}{4} - \frac{π}{2} = \frac{π}{4}$

$Now , ω = 2 πf = 100 π$

$time taken t = \frac{θ}{ω} = \frac{π / 4}{100 π} = \frac{1}{400} s$

$t = 2 .5 \times 10^{- 3} = 2 .5 ms$

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