Describe the physical and electrical properties of a circuit containing a combination of resistors and a single inductor.

A resistor will dissipate energy that was stored in an inductor as the current changes.

Kirchoff’s loop rule can be applied to a series LR circuit with a battery of emf, resulting in a differential equation that describes the current in the loop. \[\mathcal{E} = IR + L \dfrac{dI}{dt}\]

The time constant is a significant feature of the behavior of an LR circuit.

The time constant of a circuit is a measure of how quickly an LR circuit will reach a steady state and is described with the equation \[\tau = \dfrac{L}{R}\]

The time constant represents the time an LR circuit would take to reach a steady state if the system continued to change at the initial rate of change.

For an inductor that has zero initial current, the time constant represents the time required for the current in the inductor to reach approximately 63 percent of its final asymptotic value.

For an inductor with an initial current, the time constant represents the time required for the current in the inductor to reach approximately 37 percent of its initial value.

The electric properties of inductors change during the time interval in which the current in the inductor changes, but will exhibit steady state behavior after a long time interval.

When a switch is initially closed or opened in a circuit containing an inductor, the induced emf will be equal in magnitude and opposite in direction to the applied potential difference across the branch containing the inductor.

The potential difference across an inductor, the current in the inductor, and the energy stored in the inductor are exponential with respect to time and have asymptotes that are determined by the initial conditions of the circuit.

After a time much greater than the time constant of the circuit, an inductor will behave as a conducting wire with zero resistance