### Practical Equivalent

Inductors, like capacitors, are not ideal. Associated with every inductor
are a resistance equal to the resistance of the turns and a stray capacitance due to the capacitance between the turns of the coil.

To include these effects, the equivalent circuit for the inductor is as shown in Fig. 1. However, for most applications considered in this text, the stray capacitance appearing in Fig. 1 can be ignored, resulting in the equivalent model of Fig. 2.

**Fig. 1: **Complete equivalent model for an inductor

**Fig. 2: **Practical equivalent model for an inductor

The resistance $R_l$ can play an important
role in the analysis of networks with inductive elements. For most
applications, we have been able to treat the capacitor as an ideal element and maintain a high degree of accuracy. For the inductor, however, $R_l$ must often be included in the analysis and can have a pronounced
effect on the response of a system (Chapter "Resonance"). The
level of $R_l$ can extend from a few ohms to a few hundred ohms. Keep
in mind that the longer or thinner the wire used in the construction of
the inductor, the greater will be the dc resistance as determined by $R = \rho l /A$. Our initial analysis will treat the inductor as an ideal element.
Once a general feeling for the response of the element is established,
the effects of $R_l$ will be included.

Like capacitors, commercially available inductors come in different
values and types. Typical practical inductors have inductance values
ranging from a few microhenrys ($\mu H$), as in communication systems,
to tens of henrys (H) as in power systems. Inductors may be fixed or
variable. The core may be made of iron, steel, plastic, or air. The terms
coil and choke are also used for inductors.

### Appearance

All inductors, like capacitors, can be listed under two general headings:

**fixed **and

*variable*. The fixed air-core and iron-core inductors were
described in the last section. The permeability-tuned variable coil has a
ferromagnetic shaft that can be moved within the coil to vary the flux
linkages of the coil and thereby its inductance. Several fixed and variable inductors appear in Fig. 3.