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

JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Alternating Current

A resistance of

40Ω

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 :

Answer: (A)

For sinusoidal AC, the current is

I = I_{0} sin (ω t)

.

Maximum occurs at phase

\frac{π}{2}

, rms value (

I_{0} / 2

) occurs at phase

\frac{3 π}{4}

.

Phase change:

Δ θ = \frac{3 π}{4} - \frac{π}{2} = \frac{π}{4}

Angular frequency:

ω = 2 π f = 2 π \times 50 = 100 π rad/s

Time:

t = \frac{Δ θ}{ω} = \frac{π /4}{100 π} = \frac{1}{400} s = 2.5 ms

JEE Main · 2022 · 24 Jun 2022 · Shift 1 · Single correct option