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A source of constant voltage V is connected to a resistance R and two ideal inductors $L_{1}$ and $L_{2}$ through a switch S as shown. There is no mutual inductance between the two inductors. The switch . S is initially open. At $t = 0,$ the switch is closed and current begins to flow. Which of the following options is/are correct?

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After a long time, the current through $L_{1}$ will be $\frac{V}{R} \frac{L_{2}}{L_{1} {+L}_{2}}$

The ratio of the currents through $L_{1}$ and $L_{2}$ is fixed at all times $(t > 0)$

After a long time , the current through $L_{2}$ will be $\frac{V}{R} \frac{L_{1}}{L_{1} {+L}_{2}}$

$At t = 0,$ the current through the resistance R is $\frac{V}{R}$

answer is A, B, C.

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Detailed Solution

After a long time the current through the resister is constant I will divide into two parts $L_{1} {and L}_{2}$ which are in parallel $∴ I_{1} L_{1} {= I}_{2} L_{2}$

Further $I_{1} = \frac{V}{R} [\frac{L_{2}}{L_{1} + L}]$

And $I_{2} = \frac{V}{R} [\frac{L_{1}}{L_{1} + L_{2}}]$

Also the ratio of currents through $L_{1} {and L}_{2}$ is fixed at all times $A t = 0, I \approx 0.$

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