Question
Two inductors $L_1$ and $L_2$ are connected in parallel and $a$ time varying current flow as shown the Ratio of currents $i_1/i_2$ at any time $t$ is
✓
Answer
since $L_{1}$ and $L_{2}$ are connected in parallel. Potential difference across $L_{1}$ is equal to
that across $L_{2}$ i.e. $\mathcal{E}_{1}=\mathcal{E}_{2}$
Or $-L_{1} \frac{d i_{1}}{d t}=-L_{2} \frac{d I_{2}}{d t}$
Or $L_{1} \int d i_{1}=L_{2} \int d i_{2}$
Or $L_{2} i_{2}=L_{1} i_{1}$
or $\frac{i_{1}}{i_{2}}=\frac{L_{2}}{L_{1}}$
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