Circuits that have resistors and inductors have interesting behavior. It is interesting to contrast that with the behavior exhibited by a circuit without an inductor.
Consider a circuit with a battery, a switch, and a resistor. The switch is set to either include the battery in the series circuit, or to remove the battery. In this circuit, as soon as the switch is closed, we expect the current to jump to its maximum value. As soon as the switch is opened, we expect the current to turn off immediately.
When we add an inductor in series with the resistor, the behavior is a little different. The inductor's role in the circuit is to oppose any change in magnetic flux. This means that the inductor does not allow instantaneous jumps in the current. Instead, when the switch is closed, the current increases gradually to its maximum value. When the switch is opened, removing the battery, the voltage induced in the inductor causes the current to drop gradually to zero again.
You can explore these ideas through this simulation.