# Inductors in a circuit

The problem is: There is a circuit such that a battery (source of constant emf) is connected to an inductor and a resister (in series). After an unspecified time period, a switch is thrown, effectively bypassing the battery.

I know (becuase I've seen the answer) that a) the initial current is the battery's emf divided by R and b) that once the switch has been thrown, in order to find the current, one would set the emf of the inductor equal to IR (then solved the differential equation). I just want to clarify as to why this is so.

The initial current: the inductor is acting as "back emf" so it's pushing against the current created by the battery. The battery has to do more work in order to maintain the same emf as it would were the inductor not there, however, it doesn't affect that fact that the current is (eventually) equal to the initial emf divided by the resistance. Is that right?

After the switch: the inductor is providing the only emf in the circuit, and it is effectively slowing it down. The potential difference across the resistor will then be equal to the only emf present in the circuit (ie. the inductor).