Question

A current flowing through a wire depends on time as $I=3t^2+2t+5$. The charge flowing through the cross section of the wire in time from $t=0$ to $t=2sec$ is

• A. $22C$
• B. $20C$`
• C. $18C$
• D. $5C$

Answer 1

Answer: (A)

$\text{Step 1: Current through the wire}$

We know that,

$I=\frac{dq}{dt}$

$\Rightarrow dq=Idt$ $....\left(1\right)$

$\text{Step 2: Integrating the equation (1) with proper limits}$

Time interval: $t=0s$ to $t=2s$

$\int dq={\int }_0^{2}Idt$

$I=3t^2+2t+5$

$\Rightarrow q={\int }_0^2(3t^2+2t+5)dt=[t^3+t^2+5t{]}_0^2=(8+4+10)=22C$

Hence Option $\left(A\right)$ is correct.