Question

The current in a conductor varies with time $t$ as $I=2 t+3 t^{2}$, where $I$ is in ampere and $t$ in seconds. Electric charge flowing through a section of the conductor during $t=2 \sec$ to $t=3 \sec$ is

• A. 10 C
• B. 24 C
• C. 33 C
• D. 44 C

Answer 1

Answer: (B)

Given, current in a conductor, $I=2t+3t^{2}$
$\because I=\frac{dq}{dt}$
$dq=Idt$
$q=\int\limits_{2}^{3} Idt =\int\limits_{2}^{3}\left[2t+3t^{2}\right]dt $
$=2\left[\frac{t^{2}}{2}\right]_{2}^{3} +3\left[\frac{t^{3}}{3}\right]_{2}^{3}$
$=\left[t^{2}\right]_{2}^{3}+\left[t^{3}\right]_{2}^{3}$
$=\left[\left(3\right)^{2}-\left(2\right)^{2}\right]+\left[\left(3\right)^{3}-\left(2\right)^{3}\right]$
$=\left(9-4\right)+\left(27-8\right)=5+19$
$=24\,C$