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. $\frac{ L_1^2 }{ (L_1 + L_2)^2 }$
• D. $\frac{ L_2^2 }{ (L_1 + L_2)^2 }$

Answer 1

Answer: (B)

$L_2/ L_1$

Answer 2

Since $L _{1}$ and $L _{2}$ are connected in parallel. Potential difference across $L _{1}$ is equal to that across $L _{2}$ i.e. $E _{1}= E _{2}$ Or $- L _{1} \frac{ di _{1}}{ dt }=- L _{2} \frac{ dI _{2}}{ dt }$ Or $L _{1} \int di _{1}= L _{2} \int di _{2}$ Or $L _{2} i _{2}= L _{1} i _{1}$ Or $\frac{ i _{1}}{ i _{2}}=\frac{ L _{2}}{ L _{1}}$