Q86 / 125 · BITSAT 2018 · Physics

Two inductors $L_{1}$ and $L_{2}$ are connected in parallel and a time varying current flows as shown in figure. The ratio ot current $\frac{i_{1}}{i_{2}}$ at any ime $t$ Is

Solution

As the inductors are in parallel, induced emf across the two inductors is the same, i.e.

$e_{1} = e_{2}$

$L_{1} (\frac{d i_{1}}{d t}) = L_{2} (\frac{d i_{2}}{d t})$

On integrating both sides, we get
$L_{1} \int \frac{d i_{1}}{d t} = L_{2} \int \frac{d i_{2}}{d t}$

$L_{1} i_{1} = L_{2} i_{2}$

$\Rightarrow \frac{i_{1}}{i_{2}} = \frac{L_{2}}{L_{1}}$

Hence, the correct answer is option: 'A'.