The electric current through a wire varies with time as $\mathrm{I}=\mathrm{I}_{0}+\beta \mathrm{t}$, where $\mathrm{I}_{0}=20 \mathrm{~A}$ and $\beta=3 \mathrm{~A} / \mathrm{s}$. The amount of electric charge crossed through a section of the wire in 20 s is:

JEE Main · 2024 · 29 Jan 2024 · Shift 1 · Current Electricity

The electric current through a wire varies with time as

I = I_{0} + β t

, where

I_{0} = 20 A

and

β = 3 A / s

. The amount of electric charge crossed through a section of the wire in 20 s is:

Answer: (B)

The current is

I = I_{0} + β t

with

I_{0} = 20 A

and

β = 3 A/s

.

Charge crossed in

20 s

q = \int_{0}^{20} I d t = \int_{0}^{20} (20 + 3 t) d t = [20 t + \frac{3 t ^{2}}{2}]_{0}^{20} = 400 + 600 = 1000 C

Key confirmed: B (1000 C).

JEE Main · 2024 · 29 Jan 2024 · Shift 1 · Single correct option