The resistance in the following circuit is increased at a particular instant. At this instant the value of resistance is 10 Ω. The current in the circuit will be now

If resistance is constant ( 10 Ω) then steady current in the circuit i = 5/10 : 0.5A. But resistance is increasing it means current through the circuit start decreasing. Hence inductance comes in picture which induces a current in the circuit in the same direction of main current. So i > 0.5 A.