question_answer

Two inductors \[{{\operatorname{L}}_{1}}\,\,and\,\,{{L}_{2}}\] 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)  \[\frac{{{L}_{1}}}{{{L}_{2}}}\]                                 

B)  \[\frac{{{L}_{2}}}{{{L}_{1}}}\]

C)  \[\frac{{{L}_{1}}{{L}_{2}}}{{{({{L}_{1}}+{{L}_{2}})}^{2}}}\]                 

D)  \[\frac{{{({{L}_{1}}{{L}_{2}})}^{2}}}{{{(L_{1}^{2}+L_{2}^{2})}^{2}}}\]

Correct Answer: B

Solution :

Clearly from above diagram \[{{i}_{1}}\times \omega {{L}_{1}}={{i}_{2}}\times \omega {{L}_{2}}\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{{{i}_{1}}}{{{i}_{2}}}=\frac{\omega {{L}_{2}}}{\omega {{L}_{1}}}=\frac{{{L}_{2}}}{{{L}_{1}}}\]