JEE Main · 2024 · 01 Feb 2024 · Shift 1 · Current Electricity

The current in a conductor is expressed as

I = 3 t^{2} + 4 t^{3}

, where

I

is in Ampere and

t

is in second. The amount of electric charge that flows through a section of the conductor during

t = 1

s to

t = 2

s is ______ C.

Answer: 22

Solution

Charge flowing is the integral of current:

q = \int_{1}^{2} (3 t^{2} + 4 t^{3}) d t = [t^{3} + t^{4}]_{1}^{2} = (8 + 16) - (1 + 1) = 24 - 2 = 22 C

JEE Main · 2024 · 01 Feb 2024 · Shift 1 · Integer answer