Question

The relation between current in a conductor and time is shown in the figure.

$\left(i\right)$ The total charge flowing through the conductor is

​​​​​​​$[$1 Mark$]$

• A. $\frac{{\text{i}}_0{\text{t}}_0}{2}$
• B. ${\text{i}}_0{\text{t}}_0$
• C. $\frac{{\text{i}}_0{\text{t}}_0}{4}$
• D. $2{\text{i}}_0{\text{t}}_0$

Answer 1

The correct option is A $\frac{{\text{i}}_0{\text{t}}_0}{2}$

The total charge is given by
$Q=\int \text{i}dt=\text{Area of curve on i vs t graph}$
$\text{Area of the triangle}=\frac{1}{2}\times \text{base}\times \text{height}$
$Q=\frac{1}{2}{\text{i}}_0{\text{t}}_0$
$\therefore Q=\frac{{\text{i}}_0{\text{t}}_0}{2}$
So, the correct option is $\left(a\right)$.