For the given circuit the current i through the battery when the key in closed and the steady state has been reached is

Step-by-step solution

In a steady state, the inductor behaves as a conducting wire. So, the equivalent circuit becomes, 1 R e q = 1 R 1 + 1 R 2 + 1 R 3 = 1 3 + 1 3 + 1 3 = 1 ⇒ R e q = 1   Ω so, the circuit becomes, ⇒ I = 30 3 = 10   A