Q77 / 90 · JEE Main 2024 (01 Feb Shift 1) · Physics

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 ____________ $C .$

Correct answer: 22

Solution

For variable current, integrate to get the total charge flown in a given interval. $q = \int_{1}^{2} i d t = \int_{1}^{2} (3 t^{2} + 4 t^{3}) d t$

${\Rightarrow q = (t^{3} + t^{4})}_{1}^{2}$

$\Rightarrow q = 22 C$

Hence, the correct answer is 22.