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 $L_1\left(\frac{d{i}_1}{dt}\right)=L_2\left(\frac{d{i}_2}{dt}\right)$
or $L_1\left(d{i}_1\right)=L_2\left(d{i}_2\right)$
Integrating, we get
$L_1{i}_1=L_2{i}_2$
$\frac{i_1}{i_2}=\frac{L_2}{L_1}$