Question

The current through a wire depends on time as i = $i_0+\alpha t,$ where $i_0$ = 10 A and $\alpha =4A{s}^{-1}$. Find the charge crossed through a section of the wire in 10 seconds.

Answer 1

$i=i_0+\alpha t,t=10\text{sec},$

$i_0=10A,\alpha =4\text{sec}$

$\text{So,}q={\int }_0^{t}idt={\int }_0^t(i_0+\alpha t)dt$

= ${\int }_0^t{i}_{0}dt+{\int }_0^t\alpha tdt$

= $i_{0}t+\frac{\alpha t^2}{2}$

= $10\times 10+4\times \frac{10\times 10}{2}$

=$100+200=300C$