boylistad

476 ⏐⏐⏐ INDUCTORS
Resistance of the
turns of wire
L
R l
C
Inductance of
coil
Stray capacitance
FIG. 12.7
Complete equivalent model for an inductor.
FIG. 12.8
Practical equivalent model for an inductor.
L
R l
L
tance 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.
12.7. However, for most applications considered in this text, the stray
capacitance appearing in Fig. 12.7 can be ignored, resulting in the
equivalent model of Fig. 12.8. 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 (see Chapter 20, “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 �
rl / 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.
Symbols
The primary function of the inductor, however, is to introduce inductance—not
resistance or capacitance—into the network. For this reason,
the symbols employed for inductance are as shown in Fig. 12.9.
Appearance
Air-core Iron-core Variable
(permeability-tuned)
FIG. 12.9
Inductor symbols.
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. 12.10.
Testing
The primary reasons for inductor failure are shorts that develop
between the windings and open circuits in the windings due to factors
such as excessive currents, overheating, and age. The open-circuit condition
can be checked easily with an ohmmeter (∞ ohms indication), but
the short-circuit condition is harder to check because the resistance of
many good inductors is relatively small and the shorting of a few windings
will not adversely affect the total resistance. Of course, if one is
aware of the typical resistance of the coil, it can be compared to the