Question

The current in a conductor varies with time according to the equation $i=3+2t$, where $i$ is in ampere and $t$ is in second. Find the total charge (in coulomb) that passes through the area of cross-section of the wire during the time $t=3s$ to $t=6s$.

Answer 1

Answer: 36

$dq=i\cdot dt$
$\therefore dq=(3+2t)dt$
Integrating both sides,
$\int dq=\underset{3}{\overset{6}{\int }}(3+2t)dt$
$q={\left[3t+\frac{2t^2}{2}\right]}_3^6$
$={\left[3t+t^2\right]}_3^6$
$=[18+36]-[9+9]$
$=54-18$
$\therefore q=36C$