# 8.7: Summary

The inductor is a device that stores energy in the form of a magnetic field. Inductance, L, is measured in henries, H. The idealized device consists of several loops or coils of wire. These may or may not be wrapped around a magnetic core material. Inductance is directly proportional to the permeability of the core material and the cross sectional area of the loops, and inversely proportional to the length of the coil. It is also proportional to the square of the number of loops. The most important non-ideal parameter is $$R_{coil}$$, or equivalent coil resistance. Ideally, this value is zero. Absolute accuracy, temperature stability and similar parameters round out the distinguishing features of one kind of inductor against another. When placed in series, inductors add in the same manner as resistors in series. When placed in parallel, inductors combine like resistors in parallel.

Perhaps the most important operational characteristic regarding inductors is that current through an inductor cannot change instantaneously. It will take some finite amount of time before the magnetic field reacts, leading to a predictable rise in current through it. Because of this, for DC circuits inductors initially behave like opens, but after sufficient time has passed, they behave like shorts. The amount of time required to reach steady-state is five time constants, where one time constant is defined as the inductance divided by the circuit's effective resistance. The current charge curve is of the shape $$1-\varepsilon^{−t}$$. The inductor's current starts at zero and rises to some maximum value. The corresponding voltage shape is of the form $$\varepsilon^{−t}$$. Here, the voltage starts at a maximum and eventually approaches zero as time passes.

## Review Questions

1. What are the physical characteristics of inductors and how do they affect inductance?

2. Define the voltage-current characteristic for inductors.

3. What is $$R_{coil}$$?

4. How do inductors combine when placed in series? How do they combine when placed in parallel?

5. Define the initial and steady-state behavior of inductors.

6. Define time constant for an RL circuit.

7. How do the charge and discharge characteristics of RL circuits compare to those of RC circuits?