With S₁ closed in figure, what is the eventual steady state value of current?

Concept:

For a Series RL circuit;

At the steady state, the inductor will behave as a short circuit which means the voltage across the inductor will be zero.

Calculation:

Given;

At steady state inductor will be replaced by a short circuit;

Then;

I_L = 25/1 KΩ = 25 mA