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Inductors in Circuits

Two inductors...

Question

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

A

L_{1} / L_{2}

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B

L_{2} / L_{1}

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C

\frac{L_{1}^{2}}{{(L_{1} + L_{2})}_{1}^{2}}

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D

\frac{L_{2}^{2}}{{(L_{1} + L_{2})}_{1}^{2}}

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Solution

The correct option is B $L_{2} / L_{1}$
$\begin{matrix} - L_{1} \frac{d i_{1}}{d t} = - L_{2} \frac{d i_{2}}{d t} L_{1} i_{1} = L_{2} i_{2} \frac{i_{1}}{i_{2}} = \frac{L_{2}}{L_{1}} A n s . (B) \end{matrix}$

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