Chapter 7
Chapter 7
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Magnetic Quantities
Magnetic fields are described by drawing flux lines
that represent the magnetic field.
Where lines are close
together, the flux
density is higher.
Where lines are further
apart, the flux density
is lower.
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
The Magnetic Field
Magnetic fields are
composed of
invisible lines of
force that radiate
from the north pole
to the south pole of a
magnetic material.
Field lines can be visualized with the aid of iron filings
sprinkled in a magnetic field.
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
The Magnetic Field
The magnetic field lines surrounding a magnet actually
radiate in three dimensions. These magnetic field lines
are always associated with moving charge.
In permanent magnets, the moving
charge is due to the orbital motion
of electrons. Ferromagnetic
materials have minute magnetic
domains in their structure.
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Magnetic Materials
In ferromagnetic materials such as iron, nickel, and cobalt,
the magnetic domains are randomly oriented when
unmagnetized. When placed in a magnetic field, the
domains become aligned, thus they effectively become
magnets.
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Magnetic Quantities
The unit of flux is the weber. The unit of flux density is
the weber/square meter, which defines the unit tesla, (T),
a very large unit.
j

B=
Flux density is given by the equation
A
where
B = flux density (T)
Flux lines (j
j = flux (Wb)
A = area (m2)
2
Area (m)
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Magnetic Quantities
Example: What is the flux density in a rectangular core
that is 8 mm by 10 mm if the flux is 4 mWb?
j
B=
A
B
4  103 Wb
8 10 m10 10 m
-3
Electric Circuits Fundamentals - Floyd
-3
 50 Wb/m2 = 50 T
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Magnetic Quantities
• Magnetic flux lines surround a current carrying wire.
• The field lines are concentric circles.
• As in the case of bar magnets, the effects
of electrical current can be visualized with
iron filings around the wire – the current
must be large to see this effect.
Iron filings
Current-carrying wire
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Magnetic Quantities
• Permeability (m) defines the ease with which a
magnetic field can be established in a given material. It is
measured in units of the weber per ampere-turn meter.
• The permeability of a vacuum (m0) is 4p x 10-7 weber
per ampere-turn meter, which is used as a reference.
• Relative Permeability (mr) is the ratio of the absolute
permeability to the permeability of a vacuum.
mr 
Electric Circuits Fundamentals - Floyd
m
m0
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Magnetic Quantities
• Reluctance (R) is the opposition to the establishment
of a magnetic field in a material.
R
l
mA
R= reluctance in A-t/Wb
l = length of the path
m = permeability (Wb/A-t m).
A = area in m2
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Magnetic Quantities
• Recall that magnetic flux lines surround a current-carrying
wire. A coil reinforces and intensifies these flux lines.
• The cause of magnetic flux is called magnetomotive
force (mmf), which is related to the current and number of
turns of the coil.
Fm = NI
Fm = magnetomotive force (A-t)
N = number of turns of wire in a coil
I = current (A)
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Magnetic Quantities
• Ohm’s law for magnetic circuits is
Fm
j
R
• flux (j) is analogous to current
• magnetomotive force (Fm) is analogous to voltage
• reluctance (R) is analogous to resistance.
What flux is in a core that is wrapped with a
300 turn coil with a current of 100 mA if the
reluctance of the core is 1.5 x 107 A-t/Wb ? 2.0 mWb
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Magnetic Quantities
• The magnetomotive force (mmf) is not a true force in
the physics sense, but can be thought of as a cause of
flux in a core or other material.
Iron core
Current in the coil causes flux
in the iron core.
What is the mmf if a 250
turn coil has 3 A of current?
750 A-t
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Solenoids
•A solenoid produces mechanical motion
from an electrical signal.
Stationary core
Sliding core
(plunger)
Spring
One application is valves that can
remotely control a fluid in a pipe,
such as in sprinkler systems.
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Relays
• A relay is an electrically controlled switch; a small
control voltage on the coil can control a large current
through the contacts.
Contac t points
StructureAlternate
schematic symbol
Schematic
Arm ature
Term inals
Spring
symbol
Fixed
contact
NC
contacts
CR1 -1
CR1
Movable contact
NO
contacts
Elec trom agnetic
c oil
Electric Circuits Fundamentals - Floyd
CR1 -2
Fixed
Term inals
contact
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
• Magnetic field intensity is the magnetomotive force
per unit length of a magnetic path.
H=
Fm
l
or
H = NI
l
H= Magnetic field intensity (Wb/A-t m)
Fm = magnetomotive force (A-t)
l = average length of the path (m)
N = number of turns
I = current (A)
• Magnetic field intensity represents the effort that a
given current must put into establishing a certain flux
density in a material.
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Magnetic Quantities
• If a material is permeable, then a greater flux density
will occur for a given magnetic field intensity. The
relation between B (flux density) and H (the effort to
establish the field) is
B = mH
m = permeability (Wb/A-t m).
H= Magnetic field intensity (Wb/A-t m)
• This relation between B and H is valid up to saturation,
when further increase in H has no affect on B.
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
• As the graph shows, the flux density depends on both
the material and the magnetic field intensity.
Magnetic material
Flux density, B, (Wb//m2)
Saturation begins
Non-magnetic material
Magnetic Field Intensity, H, (At/m)
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
As H is varied, the magnetic hysteresis curve is developed.
B
B
B
Saturation
Bsat
H
0
BR
Hsat
0
H
Hsat
H
H= 0
0
H
Bsat
Saturation
(a)
(b)
(c )
(d)
B
B
HC
Bsat
H
H = 0
0
0
BR
H
Hsat
H
H
HC
HC
B
(e)
Electric Circuits Fundamentals - Floyd
B
B
(f )
(g)
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Magnetization Curve
A B-H curve is referred to as a magnetization curve for
the case where the material is initially unmagnetized.
The B-H curve differs for different materials; magnetic
materials have in common much larger flux density for a
given magnetic field intensity, such as the annealed iron
shown here.
Flux Density, B, (T)
2.0
1.5
Annealed iron
1.0
0.5
0
0
200
400
600
800
1000
1200
1400
1600
1800
2000
Magnetic Field Intensity, H, (A-t/m)
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Relative motion
S
When a wire is moved across a magnetic field,
there is a relative motion between the wire and
the magnetic field.
N
S
When a magnetic field is moved past a
stationary wire, there is also relative motion.
In either case, the relative motion results in
an induced voltage in the wire.
N
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Induced voltage
The induced voltage due to the relative motion
between the conductor and the magnetic field when the
motion is perpendicular to the field is dependent on
three factors:
• the relative velocity (motion is perpendicular)
• the length of the conductor in the magnetic field
• the flux density
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Faraday’s law
Faraday experimented with generating current by
relative motion between a magnet and a coil of wire.
The amount of voltage induced across a coil is
determined by two factors:
S
1. The rate of change of the
Nmagnetic flux with respect
to the coil.
-V+
Voltage is indicated only
when magnet is moving.
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Faraday’s law
Faraday also experimented generating current by
relative motion between a magnet and a coil of wire.
The amount of voltage induced across a coil is
determined by two factors:
S
1. The rate of change of the
magnetic flux with respect
N
to the coil.
2. The number of turns of
wire in the coil.
-V+
Voltage is indicated only
when magnet is moving.
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
Magnetic field around a coil
Just as a moving magnetic field induces a voltage,
current in a coil causes a magnetic field. The coil acts as
an electromagnet, with a north and south pole as in the
case of a permanent magnet.
South
Electric Circuits Fundamentals - Floyd
North
© Copyright 2007 Prentice-Hall
Chapter 7
Summary
DC Generator
A dc generator includes a rotating coil,
which is driven by an external
mechanical force (the coil is
shown as a loop in this
simplified view). As the coil
rotates in a magnetic field, a
pulsating voltage is generated.
Mechanical drive
turns the shaft
Brushes
Commutator
To external circuit
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Magnetic units
It is useful to review the key magnetic units from this
chapter:
Quantity
SI Unit
Magnetic flux density
Flux
Permeability
Reluctance
Magnetomotive force
Magnetizing force
Tesla
Weber
Weber/ampere-turn-meter
Ampere-turn/Weber
Ampere-turn
Ampere-turn/meter
Electric Circuits Fundamentals - Floyd
Symbol
B
f
m
R
Fm
H
© Copyright 2007 Prentice-Hall
Chapter 7
Selected Key Terms
Magnetic field A force field radiating from the north pole to
the south pole of a magnet.
Magnetic flux The lines of force between the north pole and
south pole of a permanent magnet or an
electromagnet.
Weber (Wb) The SI unit of magnetic flux, which represents
108 lines.
Permeability The measure of ease with which a magnetic
field can be established in a material.
Reluctance The opposition to the establishment of a
magnetic field in a material.
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Selected Key Terms
Magnetomotive The cause of a magnetic field, measured in
force (mmf) ampere-turns.
Solenoid An electromagnetically controlled device in
which the mechanical movement of a shaft or
plunger is activated by a magnetizing current.
Hysteresis A characteristic of a magnetic material
whereby a change in magnetism lags the
application of the magnetic field intensity.
Retentivity The ability of a material, once magnetized, to
maintain a magnetized state without the
presence of a magnetizing current.
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Selected Key Terms
Induced voltage Voltage produced as a result of a changing
(vind) magnetic field.
Faraday’s law A law stating that the voltage induced across a
coil of wire equals the number of turns in the
coil times the rate of change of the magnetic
flux.
Lenz’s law A law stating that when the current through a
coil changes, the polarity of the induced
voltage created by the changing magnetic
field is such that it always opposes the change
in the current that caused it. The current
cannot change instantaneously.
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Quiz
1. A unit of flux density that is the same as a Wb/m2 is the
a. ampere-turn
b. ampere-turn/weber
c. ampere-turn/meter
d. tesla
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Quiz
2. If one magnetic circuit has a larger flux than a second
magnetic circuit, then the first circuit has
a. a higher flux density
b. the same flux density
c. a lower flux density
d. answer depends on the particular circuit.
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Quiz
3. The cause of magnetic flux is
a. magnetomotive force
b. induced voltage
c. induced current
d. hysteresis
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Quiz
4. The measurement unit for permeability is
a. weber/ampere-turn
b. ampere-turn/weber
c. weber/ampere-turn-meter
d. dimensionless
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Quiz
5. The measurement unit for relative permeability is
a. weber/ampere-turn
b. ampere-turn/weber
c. weber/ampere-turn meter
d. dimensionless
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Quiz
6. The property of a magnetic material to behave as if it
had a memory is called
a. remembrance
b. hysteresis
c. reluctance
d. permittivity
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Quiz
7. Ohm’s law for a magnetic circuit is
a. Fm = NI
b. B = mH
Fm
c. j 
R
d. R 
l
mA
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Quiz
8. The control voltage for a relay is applied to the
a. normally-open contacts
b. normally-closed contacts
c. coil
d. armature
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Quiz
9. A partial hysteresis curve is shown. At the point
indicated, magnetic flux
B
a. is zero
b. exists with no magnetizing force
c. is maximum
BR
H
d. is proportional to the current
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Quiz
10. When the current through a coil changes, the induced
voltage across the coil will
a. oppose the change in the current that caused it
b. add to the change in the current that caused it
c. be zero
d. be equal to the source voltage
Electric Circuits Fundamentals - Floyd
© Copyright 2007 Prentice-Hall
Chapter 7
Quiz
Answers:
Electric Circuits Fundamentals - Floyd
1. d
6. b
2. d
7. c
3. a
8. c
4. c
9. b
5. d
10. a
© Copyright 2007 Prentice-Hall