The current flowing through an ac circuit is given by $I=5 \sin (120 \pi t) A$ How long will the current take to reach the peak value starting from zero?

(D) $\frac{1}{240} \mathrm{~s}$

(A) $\frac{1}{60} \mathrm{~s}$

(C) $\frac{1}{120} \mathrm{~s}$

JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Alternating Current

The current flowing through an ac circuit is given by

I = 5 sin (120 π t) A

How long will the current take to reach the peak value starting from zero?

Answer: (D)

The current is given by

I = 5 sin (120 π t)

, where

ω = 120 π

rad/s.

The angular frequency relates to the period by:

ω = \frac{2 π}{T} ⟹ T = \frac{2 π}{ω} = \frac{2 π}{120 π} = \frac{1}{60} s

The current reaches its peak value at

t = \frac{T}{4}

(one quarter of the period):

t = \frac{1}{60 \times 4} = \frac{1}{240} s

Therefore, the answer is (D).

JEE Main · 2022 · 27 Jun 2022 · Shift 1 · Single correct option