A $10 \Omega$ resistance is connected across $220 \mathrm{~V}-50 \mathrm{~Hz}$ AC supply. The time taken by the current to change from its maximum value to the rms value is :

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Alternating Current

10Ω

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 :

Answer: (A)

The current varies as

I = I_{0} cos ω t

. When the current changes from maximum

I_{0}

to rms value

\frac{I _{0}}{2}

, we have

\frac{I _{0}}{2} = I_{0} cos ω t

, giving

cos ω t = \frac{1}{2}

. This means

ω t = \frac{π}{4}

. With

ω = 2 π f = 2 π \times 50

, we get

t = \frac{π}{4 \times 2 π \times 50} = \frac{1}{400} = 2.5

ms.

JEE Main · 2021 · 25 Jul 2021 · Shift 2 · Single correct option