Physics - Alternating current PYQ series

 Q.Α10 Ω resistance is connected across 220 V - 50 Hz AC supply. The time taken by the current to change from its maximum value to the rms value is:

                                                          ( JEE mains 2021)

A. 2.5 ms

B. 4.5 ms

C. 3.3 ms

D. 7.2 msl

(a) \(I = I_0 \cos \omega t\)

Since the current is changing from its maximum value to RMS value, therefore,

\(I = I_0 / \sqrt{2}\)

\(\therefore \frac{I_0}{\sqrt{2}} = I_0 \cos \omega t\)

\(\cos \omega t = \frac{1}{\sqrt{2}}\)

\(\cos(2\pi ft) = \cos \frac{\pi}{4} \implies 2\pi \times 50t = \frac{\pi}{4}\)

\(t = 2.5 \, \text{ms}\)

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