Principles of Electric Circuits_pp10

Principles of Electric Circuits - Floyd © Copyright 2006 Prentice-Hall

Chapter 10Chapter 10

Chapter 10



Magnetic fields are described by drawing flux lines that represent the magnetic field.

Summary

Where lines are close together, the flux density is higher.

Where lines are further apart, the flux density is lower.

Magnetic Quantities



Magnetic flux lines are invisible, but the effects can be visualized with iron filings sprinkled in a magnetic field.

SummaryMagnetic Quantities



Ferromagnetic materials such as iron, nickel and cobalt have randomly oriented magnetic domains, which become aligned when placed in a magnetic field, thus they effectively become magnets.

Magnetic Materials



The unit of flux is the weber. The unit of flux density is the weber/square meter, which defines the unit tesla, (T), which is a very large unit.

Summary

Flux density is given by the equationwhere

B = flux density (T) = flux (Wb)

A = area (m2)

B= A

F lu x l in e s (

A re a (m )2

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?

Summary

B= A

3

2-3 -34 10 Wb 50 Wb/m = 50 T

8 10 m 10 10 mB

Magnetic Quantities



• Magnetic flux lines surround a current carrying wire.

Summary

• The field lines are concentric circles as shown in Figure 10-10 of the text.

Magnetic Quantities

• 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.

Current-carrying wire

Iron filings


Chapter 10Chapter 10Summary

• Permeability () 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.

Magnetic Quantities

• Relative Permeability (r) is the ratio of the absolute permeability to the permeability of a vacuum.

• The permeability of a vacuum (0) is 4 x 10-7 weber per ampere-turn meter, which is used as a reference.

0 r



• Reluctance (R) is the opposition to the establishment of a magnetic field in a material.

R= reluctance in A-t/Wbl = length of the path = permeability (Wb/A-t m).A = area in m2

Magnetic Quantities

Al

R



Fm = NI

• Recall that magnetic flux lines surround a current-carrying wire. A coil reinforces and intensifies these flux lines.

Summary

• The cause of magnetic flux is called magnetomotive force (mmf), which is related to the current and number of turns of the coil.

Fm = magnetomotive force (A-t)N = number of turns of wire in a coil I = current (A)

Magnetic Quantities



• Ohm’s law for magnetic circuits is

Magnetic Quantities

• flux () 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 Wb

RmF



• 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.

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

Magnetic Quantities

Iron core



•A solenoid produces mechanical motion from an electrical signal.

Solenoids

One application is valves that can remotely control a fluid in a pipe, such as in sprinkler systems.

Sta tio na ry c o re Slid ing c o re(p lung e r)

Sp ring C o il



• A relay is an electrically controlled switch; a small control voltage on the coil can control a large current through the contacts.

Relays

Arm a tu reC o n ta c t p o in ts

Te rm ina lsSp ring

Ele c tro m a g ne ticc o il

Te rm ina ls

Structure Schematic symbol

C R1-1

C R1-2

N Cc o nta c ts

N Oc o nta c ts

C R1 M o va b le c o nta c t

Fixe d c o n ta c t

Fixe d c o n ta c t

Alternate schematic symbol



• Magnetic field intensity is the magnetomotive force per unit length of a magnetic path.

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)

H = F m

l H = NI

lor

• Magnetic field intensity represents the effort that a given current must put into establishing a certain flux density in a material.



• This relation between B and H is valid up to saturation, when further increase in H has no affect on B.

• 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 = H = permeability (Wb/A-t m).H= Magnetic field intensity (Wb/A-t m)

Magnetic Quantities



• As the graph shows, the flux density depends on both the material and the magnetic field intensity.

M a g n e tic F ie ld In te n s ity, , (A t/m )H

Flux

den

sity

, ,

(Wb/

/m)

B2

S a tu ra tio n b e g in sM a g n e tic m a te r ia l

N o n -m a g n e t ic m a te ria l



As H is varied, the magnetic hysteresis curve is developed.

(d )(c )

B

H

(b )

B

H

(a )

B

H

(f )

B

H

(g )

B

H

(e )

0 H sa t

Sa tura tio n

0

B sa t B R

H = 0 HH sa t

B sa tSa tura tio n B

H C

0

H0 0H = 0

B R

B

H sa t

B sa t

H C

H

B

H C



A B-H curve is referred to as a magnetization curve for the case where the material is initially unmagnetized.

Magnetization Curve

M agn etic F ield In ten sity, H , (A -t/m )200 400 600 800 1000 1200 16001400 1800 2000

0

0 .5

1 .0

1 .5

2 .0

0

Flux

Den

sity

, B, (

T)

Annealed iron



A B-H curve can be read to determine the flux density in a given core. The next slide shows how to read the graph to determine the flux density in an annealed iron core.

Magnetization Curve

M agn etic F ield In tensity, H , (A -t/m )200 40 0 60 0 800 100 0 12 00 16001400 1800 2000

0

0.5

1 .0

1 .5

2 .0

0

Flux

Den

sity

, B, (

T)

Annealed iron



What is B for the core?

Magnetization Curve

NIHl

M a g n etic F ie ld In te ns ity, H , (A -t/m )200 400 600 800 1000 1200 16001400 1800 2000

0

0 .5

1 .0

1 .5

2 .0

0

Flux

Den

sity

, B, (

T)

Annealed iron

380 t 0.9 A1487 A-t/m

0.23 m

Reading the graph,B = 1.63 T

I = 0 .9 A

A nn ea led iron co re

38 0 tu rns



Relative motion

When a wire is moved across a magnetic field, there is a relative motion between the wire and the magnetic field.

When a magnetic field is moved past a stationary wire, there is also relative motion.

NS

NS

In either case, the relative motion results in an induced voltage in the wire.



The induced voltage due to the relative motion between the conductor and the magnetic field when the motion is perpendicular to the field is given by

SummaryInduced voltage

B = flux density in T

l = length of the conductor in the magnetic field in m

v = relative velocity in m/s (motion is perpendicular)

vind = Blv



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:

SummaryFaraday’s law

1. The rate of change of the magnetic flux with respect to the coil.

NS

V- +Voltage is indicated only when magnet is moving.



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:

Summary

1. The rate of change of the magnetic flux with respect to the coil.

2. The number of turns of wire in the coil.

NS

V- +

Faraday’s law

Voltage is indicated only when magnet is moving.



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.

SummaryMagnetic field around a coil

No rthSo uth



A dc motor includes a rotating coil, which receives current through a split ring, called the commutator. The commutator is connected to fixed brushes, which are connected to an external circuit. The magnetic core is not shown for simplicity.

DC Motor

N S

c o m m uta to r

a rm a tureb rushe s

Small motors may use a fixed magnet, as shown.



Magnetic field

Magnetic flux

Weber (Wb)

Permeability

Reluctance

The lines of force between the north pole and south pole of a permanent magnet or an electromagnet.The SI unit of magnetic flux, which represents 108 lines.

A force field radiating from the north pole to the south pole of a magnet.

Selected Key Terms

The measure of ease with which a magnetic field can be established in a material.

The opposition to the establishment of a magnetic field in a material.



Magnetic flux densityFlux

Magnetizing forceMagnetomotive force

Permeability

TeslaWeberWeber/ampere-turn-meter Ampere-turn/WeberAmpere-turnAmpere-turn/meter

BRFm

H

Reluctance

It is useful to review the key magnetic units from this chapter:

Quantity SI Unit Symbol

Magnetic units



Magnetomotive force (mmf)

Solenoid

Hysteresis

Retentivity

An electromagnetically controlled device in which the mechanical movement of a shaft or plunger is activated by a magnetizing current.A characteristic of a magnetic material whereby a change in magnetism lags the application of the magnetic field intensity.

The cause of a magnetic field, measured in ampere-turns.

Selected Key Terms

The ability of a material, once magnetized, to maintain a magnetized state without the presence of a magnetizing current.



Induced voltage (vind)

Faraday’s law

Lenz’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.

Voltage produced as a result of a changing magnetic field.

Selected Key Terms

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.


Chapter 10Chapter 10Quiz

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



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.



3. The cause of magnetic flux is

a. magnetomotive force

b. induced voltage

c. induced current

d. hysteresis



4. The measurement unit for permeability is

a. weber/ampere-turn


c. weber/ampere-turn-meter

d. dimensionless



5. The measurement unit for relative permeability is

a. weber/ampere-turn


c. weber/ampere-turn meter

d. dimensionless



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



7. Ohm’s law for a magnetic circuit is

a.

b.

c.

d.

Fm = NI

B = H

Al

R

RmF



8. The control voltage for a relay is applied to the

a. normally-open contacts

b. normally-closed contacts

c. coil

d. armature



9. A partial hysteresis curve is shown. At the point indicated, magnetic flux

a. is zero

b. exists with no magnetizing force

c. is maximum

d. is proportional to the current

B

H

BR



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



Answers:

1. d

2. d

3. a

4. c

5. d

6. b

7. c

8. c

9. b

10. a

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Principles of Electric Circuits_pp10