Question

Two inductors $L_{1}$ and $L_{2}$ are connected in parallel and a time varying current flows as shown in figure. Then the ratio of currents $i_{1} / i_{2}$ at any time $t$ is

• A. $L_{1} / L_{2}$
• B. $L_{2} / L_{1}$
• C. $\frac{L_{1}^{2}}{\left(L_{1}+L_{2}\right)^{2}}$
• D. $\frac{L_{2}^{2}}{\left(L_{1}+L_{2}\right)^{2}}$

Answer 1

Answer: (B)

Two inductors are in parallel. Therefor potential difference across them is same.
Hence, $V_{1}=V_{2}$
or $ L_{1}\left(\frac{d i_{1}}{d t}\right)=L_{2}\left(\frac{d i_{2}}{d t}\right)$
or $ L_{1}\left(d i_{1}\right)=L_{2}\left(d i_{2}\right)$
Integrating, we get
$L_{1} i_{1} =L_{2} i_{2} $
$\frac{i_{1}}{i_{2}} =\frac{L_{2}}{L_{1}}$