Q.
Two inductors $L_{1}\ and\ L_{2}$ are connected in parallel and a time varying current flows as shown in figure. The ratio of currents $i_{1}/i_{2}$ at any time t is
A) $L_{2}/L_{1}$
B) $L_{1}/L_{2}$
C) $\frac{L_{2}^{2}}{\left( L_{1} + L_{2} \right)^{2}}$
D) $\frac{L_{1}^{2}}{\left( L_{1} + L_{2} \right)^{2}}$
Explanation
(a) As the inductors are in parallel, therefore, induced emf across the two inductors is the same $ie,$
$e_{1} = e_{2}$
$L_{1}\left( \frac{di_{1}}{dt} \right)\ \ = L_{2}\left( \frac{di_{2}}{dt} \right)$
Integrating both sides w.r.t. $t,$ we get
$L_{1}i_{1} = L_{2}i_{2}$
$\therefore\ \ \ \ \frac{i_{1}}{i_{2}} = \frac{L_{2}}{L_{1}}\ $
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.