0195136047.pdf

1.2 LUMPED-CIRCUIT ELEMENTS 31

Under dc conditions, an ideal inductor acts like an ideal wire, or short circuit. Note that the
current through an inductor cannot change value instantaneously. However, there is no reason to
rule out an instantaneous change in the value of the inductor voltage. The student should justify
the statements made here by recalling Equation (1.2.27).
If the medium in the flux path has a linear magnetic characteristic (i.e., constant permeability),
then the relationship between the flux linkagesλand the currentiislinear, and the slope of the
linearλ–icharacteristic gives theself-inductance, defined as flux linkage per ampere by Equation
(1.2.26). While the inductance in general is a function of the geometry and permeability of the
material medium, in a linear system it is independent of voltage, current, and frequency. If the
inductor coil is wound around a ferrous core such as iron, theλ–irelationship will benonlinear
and even multivalued because of hysteresis. In such a case the inductance becomes a function
of the current, and the inductor is said to be nonlinear. However, we shall consider only linear
inductors here.
Series and parallel combinations of inductors are often encountered. Figure 1.2.8 illustrates
these.
By invoking the principle ofduality, it can be seen that the inductors in series combine like
resistors in series and capacitors in parallel; the inductors in parallel combine like resistors in
parallel and capacitors in series. Thus, whenL 1 andL 2 are in series,

Leq=L 1 +L 2 (1.2.34)

and whenL 1 andL 2 are in parallel,

Leq=

L 1 L 2

L 1 +L 2

or

1

Leq

=

1

L 1

+

1

L 2

(1.2.35)

A practical inductor may have considerable resistance in the wire of a coil, and sizable
capacitances may exist between various turns. A possiblemodelfor a practical inductor could
be a combination of ideal elements: a combination of resistance and inductance in series, with a
capacitance in parallel. Techniques for modeling real circuit elements will be used extensively in
later chapters.
Practical inductors range from about 0.1μH to hundreds of millihenrys. Some, meant for
special applications in power supplies, can have values as large as several henrys. In general, the
larger the inductance, the lower its frequency is in its usage. The smallest inductance values are
generally used at radio frequencies. Although inductors have many applications, the total demand
does not even remotely approach the consumption of resistors and capacitors. Inductors generally
tend to be rather bulky and expensive, especially in low-frequency applications. Industry-wide
standardization for inductors is not done to the same degree as for more frequently used devices
such as resistors and capacitors.

i

A

C

(a) (b)

B

−

L 1

L 2

A

D

B

v v

C

+

−

i

i 1 i 2

L 1 L 2

Figure 1.2.8Inductors in series and par-

allel.(a)L 1 andL 2 in series.(b)L 1 andL 2

in parallel.