JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Alternating Current

An AC source rated

220 V, 50 Hz

is connected to a resistor. The time taken by the current to change from its maximum to the rms value is :

Answer: (B)

Solution

With time measured from the instant the current is at its peak,

i = i_{0} cos ω t

. The current equals its rms value when

cos ω t = \frac{1}{2} \Rightarrow ω t = \frac{π}{4}

For

f = 50

Hz,

ω = 2 π f = 100 π

rad/s, so

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

The current takes

2.5

ms to fall from its maximum to its rms value.

JEE Main · 2021 · 18 Mar 2021 · Shift 1 · Single correct option