Question

The currect through a wire depends on time as,
$i=(10+4t)$
Here, $i$ is in ampere and $t$ in seconds. Find the charge crossed through a section in time interval between $t=0$ to $t=10\text{s}$.

• A. $300\text{C}$
• B. $400\text{C}$
• C. $500\text{C}$
• D. $600\text{C}$

Answer 1

The correct option is A $300\text{C}$

$i=10+4t\Rightarrow \frac{dq}{dt}=10+4t$
$\Rightarrow \underset{0}{\overset{q}{\int }}dq=\underset{0}{\overset{10}{\int }}(10+4t)dt$
$\Rightarrow q=[10t+2t^2{]}_0^{10}=300\text{C}$