Alternating Current

JEE Main level, single correct, medium

29 of 190

Question 29 of 190

A resistance of 40Ω40\Omega is connected to a source of alternating current rated 220V,50Hz220V,50Hz. Find the time taken by the current to change from its maximum value to the rms value :

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Answer: (A) 2.5ms2.5ms

The current in AC is of the form of i=i0sin⁡ωti={i}_{0}\sin \omega t. The maximum current is i0{i}_{0} and rms current is i02\dfrac{{i}_{0}}{\sqrt{2}}. The change in the phase when current change from maximum to rms value is π4rad\dfrac{\pi }{4}rad. Therefore, the time taken for the same will be,
t=∆ϕω=π4×2π×50=2.5mst=\dfrac{∆\phi }{\omega }=\dfrac{\pi }{4\times 2\pi \times 50}=2.5ms.

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