I'm having trouble with visualizing the following problem, which is asking me for the final, steady current in both inductors $L_{1}$ and $L_{2}$. I was thinking that after a long time, essentially the current will be stable and thus there will be no induced current in the inductors. However, how would the current in the circuit split in this case? (I suppose that we would have two short wires as the resistance of the inductors is 0). I know that the current through the resistor is:

$I_{R} = \displaystyle\frac{e}{R}$

However, I really can't visualize how short circuits work, and mostly in this case in which we have two paths with zero resistance. How would the currents split?

The picture of the problem is here: http://imgur.com/uW1SQ8W

I'm having trouble with visualizing the following problem, which is asking me for the final, steady current in both inductors $L_{1}$ and $L_{2}$. I was thinking that after a long time, essentially the current will be stable and thus there will be no induced current in the inductors. However, how would the current in the circuit split in this case? (I suppose that we would have two short wires as the resistance of the inductors is 0). I know that the current through the resistor is:

$I_{R} = \displaystyle\frac{e}{R}$

However, I really can't visualize how short circuits work, and mostly in this case in which we have two paths with zero resistance. How would the currents split?

Here is a picture of the problem.