In the given circuit switch is closed. In steady state the current will be :
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6 A
An inductor opposes only a change of current, through the emf \( L\,dI/dt \). In the steady state the currents no longer change, so this emf is zero and an ideal inductor acts as a plain connecting wire (zero resistance).
Each of the three branches then has only a resistance \( R = 9\,\Omega \), and the three branches are in parallel across the cell.
\( \displaystyle R_{\mathrm{eq}} = \frac{R}{3} = \frac{9\,\Omega}{3} = 3\,\Omega \)
\( \displaystyle I = \frac{\varepsilon}{R_{\mathrm{eq}}} = \frac{18\,\mathrm{V}}{3\,\Omega} = 6\,\mathrm{A} \)
The value \( L = 2\,\mathrm{mH} \) decides only how quickly the current grows to this value, not the steady current itself.