Question

Determine the current flowing $\left(\text{in A}\right)$ through an element at time $t=2\text{sec}$, if the charge flow is given by $q=(2t^2+3)\text{C}$.

• A. $8$
• B. $1$
• C. $2$
• D. $4$

Answer 1

The correct option is A $8$

We know that

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

Here, $q=2t^2+3$

$\therefore I=\frac{d}{dt}(2t^2+3)=4t$

So, at $t=2\text{s}$

$I=4t=4\times 2=8\text{A}$

Therefore, option $\left(d\right)$ is correct.

If $\Delta q$ charge flows in time interval $\Delta t$, then average current is given by $l_{av}=\frac{\Delta q}{\Delta t}$ And instantaneous current will be$$I_{ins}=\underset{\Delta t\to 0}{lim}\frac{\Delta q}{\Delta t}=\frac{dq}{dt}$$