Question

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

$\left(ii\right)$ Write the expression of current in terms of time.

​​​​​​​$[$1 Mark$]$

• A. $\text{i}={\text{i}}_0\frac{\text{t}}{{\text{t}}_0}$
• B. $\text{i}={\text{i}}_0(1+\frac{\text{t}}{{\text{t}}_0})$
• C. $\text{i}={\text{i}}_0(\frac{\text{t}}{{\text{t}}_0}-1)$
• D. $\text{i}={\text{i}}_0(1-\frac{\text{t}}{{\text{t}}_0})$

Answer 1

The correct option is D $\text{i}={\text{i}}_0(1-\frac{\text{t}}{{\text{t}}_0})$

The curve is a straight line having intercepts ${\text{i}}_0$ on $i-$axis and ${\text{t}}_0$ on $t-$axis.
Te equation of straight line in intercept form is
$\frac{\text{t}}{{\text{t}}_0}+\frac{\text{i}}{{\text{i}}_0}=1$
$\frac{\text{i}}{{\text{i}}_0}=1-\frac{\text{t}}{{\text{t}}_0}$
$\text{i}={\text{i}}_0(1-\frac{\text{t}}{{\text{t}}_0})$
So option $\left(d\right)$ is correct.