Question

The current in a conductor varies with time $t$ as $I=2t+3t^2$, 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, $I=2t+3t^2$
$\because I=\frac{dq}{dt}$
$dq=Idt$
$q=\underset{2}{\overset{3}{\int }}Idt=\underset{2}{\overset{3}{\int }}\left[2t+3t^2\right]dt$
$=2{\left[\frac{t^2}{2}\right]}_2^3+3{\left[\frac{t^3}{3}\right]}_2^3$
$={\left[t^2\right]}_2^3+{\left[t^3\right]}_2^3$
$=\left[{\left(3\right)}^2-{\left(2\right)}^2\right]+\left[{\left(3\right)}^3-{\left(2\right)}^3\right]$
$=\left(9-4\right)+\left(27-8\right)=5+19$
$=24C$