The accompanying diagram represents an electrical circuit whose total resistance is a constant R ohms and whose self-inductance, shown as a coil, is L henries, also a constant. There is a switch whose terminals at a and b can be closed to connect a constant electrical source of V volts. we have

where i is the current in amperes and t is the time in seconds.

Use a phase line analysis to sketch the solution curve assuming that the switch in the RL circuit is closed at time t = 0. What happens to the current as t→∞? This value is called the steadystate solution.

di L + Ri= V, dt