Q. The current flowing through a wire depends on time as $I = 3t^{2} + 2t + 5.$ The charge flowing through the cross-section of the wire in time from $t = 0$ to $t = 2\ \sec$. is
A) 22 C
B) 20 C
C) 18 C
D) 5 C
Explanation
(a) $I = \frac{dq}{dt} = 3t^{2} + 2t + 5$
$\therefore dq = (3t^{2} + 2t + 5)dt$
$\therefore q = \int_{t = 0}^{t = 2}{(3t^{2} + 2t + 5)dt}$
$= \frac{3t^{3}}{3} + \frac{2t^{2}}{2} + 5t\left| \begin{matrix}
2 \\
0
\end{matrix} = t^{3} + t^{2} + 5t \right|\begin{matrix}
2 \\
0
\end{matrix} = 22\ C$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.