Question

Two inductors of inductance $2\text{mH}$ and $5\text{mH}$ are connected in parallel and a time varying current $i$ flows as shown in the figure. The ratio of currents $i_1$ and $i_2$ at any time $t$ is-

• A. $2:5$
• B. $5:2$
• C. $2:7$
• D. $4:9$

Answer 1

The correct option is B $5:2$


Potential difference across an inductor is,

$\left|\begin{array}{c}E\end{array}\right|=L\left(\frac{di}{dt}\right)$

Since, inductors are connected in parallel, hence potential difference across them will be the same.

$\left|\begin{array}{c}{E}_1\end{array}\right|=\left|\begin{array}{c}{E}_2\end{array}\right|$

$2\frac{d{i}_1}{dt}=5\frac{d{i}_2}{dt}$

$\Rightarrow 2d{i}_1=5d{i}_2$

Integrating both sides with proper limits we get,

${\int }_0^{i_1}2d{i}_1={\int }_0^{i_2}5d{i}_2$

$\Rightarrow 2i_1=5i_2$

$\therefore i_1:i_2=5:2$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.