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

A

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

B

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

C

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

D

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