Answer
$i_2 = 1.0~A$
Work Step by Step
After a long time, the inductor acts like an ordinary wire.
We can find $i_2$:
$i_2 = \frac{\Delta V}{R_2}$
$i_2 = \frac{10~V}{10~\Omega}$
$i_2 = 1.0~A$
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