Inductance
OBJECTIVES
After
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•
•
•
•
completing this chapter, the student should be able to:
Explain the principles of inductance.
Identify the basic units of inductance.
Identify different types of inductors.
Determine the total inductance in series and parallel circuits.
Explain L/R time constants and how they relate to inductance.
See accompanying
Chapter
CD for interactive
When a current flows through a conductor, a
magnetic field builds up around the conductor.
This field contains energy and is the foundation
for inductance.
This chapter examines inductance and its application to DC circuits. Inductance is covered in
more detail in Chapter 16.
INDUCTANCE
Inductance is the characteristic of an electrical con-
ductor that opposes a change in current flow. An
inductor is a device that stores energy in a magnetic field.
Inductance exhibits the same effect on current in an electric circuit as inertia does on velocity of a mechanical object. It takes more work to
no
presentations
and tutorials
relating to
10.
start a load moving than it does to keep it moving
because the load possesses the property of inertia.
Inertia is the characteristic of mass that opposes a
change in velocity. Once current is moving
through a conductor, inductance helps to keep it
moving. The effects of inductance are sometimes
desirable and other times undesirable.
As noted in Chapter 9, the basic principle behind inductance states, when a current flows
through a conductor, it generates a magnetic field
around the conductor As the magnetic flux lines
build up, they create an opposition to the flow of
current.
When the current changes direction or stops,
or the magnetic field changes, an electromotive
force (emf) is induced back into the conductor
through the collapsing of the magnetic field. The
opposition to the changes in current flow is iden-
CHAPTER 10 INDUCTANCE
tified as counter electromotive force (counter
emf). This effect is summarized by Lenz's law-an
induced emf in any circuit is always in a direction
to oppose the effect that produced it. The amount
of counter emf is in proportion to the rate of
change. The faster the rate of change, the greater
the counter emf.
All conductors have some inductance. The
amount of inductance depends on the conductor
and the shape of it. Straight wire has small
amounts of inductance whereas coils of wire have
much more inductance.
The unit by which inductance is measured
is the henry (H), named for Joseph Henry
(1797-1878), an American physicist. A henry is
the amount of inductance required to induce an
emf of 1 volt when the current in a conductor
changes at the rate of 1 ampere per second. The
henry is a large unit; the millihenry (mH) and microhenry (ILH) are more commonly used. The
symbol for inductance is L.
10-1
FIGURE 10-1
Schematic symbol for an inductor.
----------~~-----------FIGURE 10-2
Schematic symbol for a variable inductor.
-~FIGURE 10-3
Several types of inductors used to vary the inductance.
QUESTIONS
1. Define inductance.
2. What is the unit for measuring
FIXED INDUCTORS
inductance?
3. Define a henry.
4. What letter is used to represent inductance?
ImDINDUCTORS
Inductors are devices designed to have a specific inductance. They consist of a conductor coiled
around a core and are classifiedby the type of core
material-magnetic or nonmagnetic. Figure 10-1
shows the symbol used for inductors.
Inductors can also be fixed or variable. Figure 10-2 shows the symbol for a variable inductor. Variable inductors are created with adjustable
core material. Figure 10-3 shows several types of
VARIABLE INDUCTORS
SECTION I DC CIRCUITS
FIGURE 10-4
FIGURE 10-6
An air-core inductor.
Toroid-core inductor.
FIGURE 10-5
Schematic symbol for an iron-core inductor.
------------~~---------FIGURE 10-7
inductors used for adjusting the core material.
Maximum inductance occurs when the core material is in line with the coil of the wire.
Air-core inductors, or inductors without core
material, are used for up to 5 millihenries of inductance. They are wrapped on a ceramic or phenolic core (Figure 10-4).
Ferrite and powdered iron cores are used for
up to 200 millihenries. The symbol used for an
iron-core inductor is shown in Figure 10-5.
Toroid cores are donut-shaped and offer a
high inductance for a small size (Figure 10-6).
The magnetic field is contained within the core.
Shielded inductors have a shield made of
magnetic material to protect them from the influence of other magnetic fields (Figure 10-7).
Laminated iron-core inductors are used for all
large inductors (Figure 10-8). These inductors
vary from 0.1 to 100 henries, the inductance depending on the amount of current flowing
through the inductor. These inductors are sometimes referred to as chokes. They are used in the filtering circuits of power supplies to remove AC
Shielded inductor.
components from the DC output. They will be discussed further later on.
Inductors typically have tolerances of ± 10%,
but tolerances of less than 1% are available. Inductors, like resistors, can be connected in series,
parallel, or series-parallel combinations. The total
inductance of several inductors connected in se-
CHAPTER
FIGURE 10-8
10 INDUCTANCE
5. What is the total inductance of a circuit
with three inductors, 10 H, 3.5 H, and 6
H, connected in parallel?
Laminated iron-core inductor.
L/R TIME CONSTANTS
A time constant is the time required for current
through a conductor to increase to 63.2 % or decrease to 36.8% of the maximum current. An RL
circuit is shown in Figure 10-9. LlR is the symbol
used for the time constant of an RL circuit. This
can be expressed as:
L
t =-
R
ries (separated to prevent their magnetic fields
from interacting) is equal to the sum of the individual inductances.
I,. = L1 + L2 + L3 ...
+ Ln
If two or more inductors are connected in
parallel (with no interaction of their magnetic
fields) the total inductance is found by using the
formula:
10-2
QUESTIONS
1. What are inductors?
2. Draw the symbols used to represent fixed
and variable inductors.
3. What is another name for a laminated
iron -core inductor?
4. What are the formulas for determining
total inductance in:
a. Series circuits?
b. Parallel circuits?
where: t = time in seconds
L = inductance in henries
R = resistance in ohms
Figure 10-10 charts the growth and decay (or
increase and decrease) of a magnetic field, in
terms of time constants. It takes five time constants to fully transfer all the energy into the magnetic field, or to build up the maximum magnetic
field. It takes five full-time constants to completely collapse the magnetic field.
FIGURE 10-9
Circuit used to determine UR time constant.
GROWTH
DECAY
114
SECTION I DC CIRCUITS
FIGURE 10-10
Time constants required to build up or collapse the magnetic field in an inductor.
I- 100
z
w
80
o
::2!
~ 60
X
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::2! 40
u...
o
‫ן‬-
mo
20
CL
0
a:
w
-------j
J
I
/
~1
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\9.3 1<
0
~
/
a:
§
---~~I
......•
I---DECAY
...•••
I----GROWTH
~
98.2%
95%
86.5%
\
\
"
63.2%
1\:%
"
i
5.0%
~
2
345
o
1
~
3
2
1.8%
4
0.7%
5
TIMECONSTANTS
10- 3
QUESTIONS
1. What is a time constant for an inductor?
2. How is a time constant determined?
3. How many time constants are required to
fully build up a magnetic field for an
inductor?
• Inductors are devices designed to have
specific inductances.
• The symbol for fixed inductance is:
----~~~-• The symbol for a variable inductor is:
4. How many time constants are required to
fully collapse a magnetic field for an
inductor?
5. How long does it take to fully build up a
magnetic field for a O.I-henry inductor in
series with a IOO,OOO-ohm
resistor?
• Types of inductors include: air core, ferrite
or powdered iron core, toroid core,
shielded, and laminated iron core.
• The total inductance for inductors connected
in series is calculated by the formula:
LT
SUMMARY
• Inductance is the ability to store energy in
a magnetic field.
• The unit for measuring inductance is the
henry (H).
• The letter L represents inductance.
= LJ + L2 + L3
...
+ Ln
• The total inductance for inductors
connected in parallel is:
1
1
III
--=--+--+4 LJ
L2
L3
... +-r.,
• A time constant is the time required for
current to increase to 63.2 % or decrease to
36.8% of the maximum current.
CHAPTER 10 INDUCTANCE
• A time constant can be determined by the
formula:
• It takes five time constants to fully build up
or collapse the magnetic field of an inductor.
L
t =-
R
.'
CHAPTER
c-.
10 SELF-TESr
\
"
.'
1. How can the magnetic field be increased for a particular inductance?
2. What is the total inductance for the circuit shown?
3. A 500-mH inductor and a 10-kilohm resistor are connected in series to a 2S-volt source. What
will be the voltage across the inductor 100 microseconds after energizing the circuit?
~=
800 /1H
L4 = 125 /1H