Question

The current in a conductor varies with time according to the equation $i =3+2 t$, 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 $t =3\, s$ to $t =6\, s$.

Answer 1

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