You will rarely find a circuit that is actually made up of a 
resistor and inductor connected in series with a DC source. However, such circuits exist in abundance and  in various disguises such as DC motors,  relays, and electromagnets--any circuit that has a DC current passing through a coil of wire. 

Where is the resistor in these examples? There may or may not be an actual resistor connected in series with the coil of 

Series RL circuits are most often equivalent circuits, or circuits that present a simplified and more manageable view of an actual circuit. 

Looking at such circuits as a simple series RL circuit can help you understand how such circuits operate and how best to go about designing, analyzing, and troubleshooting them.

The amount of energy stored in the magnetic field of an inductor is given by:  

where:  

E = the amount of stored energy in joules  
L = inductance in henries  
I = current in amperes  
 

The amount of current flowing through the inductor in a series RL circuit is determined by the values of the voltage source (V_S) and the resistor (R): 

I = V_S/R

The amount of energy stored in the magnetic field surrounding an inductor is: 

When DC power is first applied to a series RL circuit, the self-inductance effect opposes the build-up of current flow.  Current gradually increases, however, and eventually reaches a point where there is no longer any change in the current level and, therefore, no further self-inductance effect. 
 

Energy is stored in the magnetic field as long as current continues to flow through the inductor.

P
R
E
V
I
E
W

When DC power is removed from a series RL circuit, the magnetic field that had been built up around the inductor begins to collapse. There is no longer a source of energy to sustain it. 

As the field collapses, its lines of force induce a current that tends to keep current flowing through the circuit. Energy that had been stored in the magnetic field is converted to electrical energy. 

There is a limited amount of energy stored in the magnetic field, so the induced current gradually decreases to zero. 

Energy that had been stored in the magnetic field when DC power was applied to the circuit is transformed into electrical energy when the DC power source is removed.