Two inductors L _ 1 and L _ 2 are connected in parallel and a time...

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

${e}_{1} = {e}_{2}$

${L}_{1} \left(\dfrac{d{i}_{1}}{dt}\right) = {L}_{2}\left(\dfrac{d{i}_{2}}{dt}\right)</p><p>On integrating both sides, we get<br />${L}_{1} ∫ $\dfrac{d{i}_{1}}{dt} = {L}_{2}$∫ $\dfrac{d{i}_{2}}{dt}</p><p>${L}_{1}{i}_{1} = {L}_{2}{i}_{2}$</p><p>$⇒ $\dfrac{i1}{i2} = \dfrac{L2}{L1}$