Chapter 7. Chapter 7. Electric Circuits Fundamentals - Floyd. Copyright 2007 Prentice-Hall

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1 Chapter 7

2 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.

3 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.

4 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.

5 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.

6 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. Flux density is given by the equation where B = flux density (T) j = flux (Wb) A = area (m 2 ) B= j A Flux lines (j Area (m) 2

7 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? B= j A B Wb m m 50 Wb/m = 50 T 2

8 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

9 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 (m 0 ) is 4p x 10-7 weber per ampere-turn meter, which is used as a reference. Relative Permeability (m r ) is the ratio of the absolute permeability to the permeability of a vacuum. m r m m 0

10 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 m 2

11 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. F m = NI F m = magnetomotive force (A-t) N = number of turns of wire in a coil I = current (A)

12 Magnetic Quantities Ohm s law for magnetic circuits is j F m R flux (j) is analogous to current magnetomotive force (F m ) 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 10 7 A-t/Wb? 2.0 mwb

13 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

14 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.

15 Relays A relay is an electrically controlled switch; a small control voltage on the coil can control a large current through the contacts. Elec trom agnetic coil Contac t points StructureAlternate Arm ature schematic symbol Schematic Spring Term inals symbol CR1 NC contacts NO contacts CR1-1 CR1-2 Term inals Fixed contact Movable contact Fixed contact

16 Magnetic field intensity is the magnetomotive force per unit length of a magnetic path. H = F m l or H = NI l H= Magnetic field intensity (Wb/A-t m) F m = 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.

17 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.

18 2 Flux density, B, (Wb//m ) Chapter 7 As the graph shows, the flux density depends on both the material and the magnetic field intensity. Saturation begins Magnetic material Magnetic Field Intensity, H, (At/m) Non-magnetic material

19 As H is varied, the magnetic hysteresis curve is developed. B B B Saturation B sat B R H 0 0 H sat H H = 0 H H H sat 0 B sat (a) (b) (c) Saturation (d) B B B B sat H C H H = H sat H H H B R H C H C (e) B (f ) (g) B

20 Flux Density, B, (T) Chapter 7 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 Annealed iron Magnetic Field Intensity, H, (A-t/m)

21 N S Chapter 7 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. In either case, the relative motion results in an induced voltage in the wire. S N

22 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

23 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 N 1. The rate of change of the magnetic flux with respect to the coil. V - + Voltage is indicated only when magnet is moving.

24 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 N V The rate of change of the magnetic flux with respect to the coil. Voltage is indicated only when magnet is moving. 2. The number of turns of wire in the coil.

25 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 North

26 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

27 Magnetic units It is useful to review the key magnetic units from this chapter: Quantity SI Unit Symbol Magnetic flux density Flux Permeability Reluctance Magnetomotive force Magnetizing force Tesla Weber Weber/ampere-turn-meter Ampere-turn/Weber Ampere-turn Ampere-turn/meter B f m R F m H

28 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 10 8 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.

29 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.

30 Selected Key Terms Induced voltage Voltage produced as a result of a changing (v ind ) 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.

31 Quiz 1. A unit of flux density that is the same as a Wb/m 2 is the a. ampere-turn b. ampere-turn/weber c. ampere-turn/meter d. tesla

32 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.

33 Quiz 3. The cause of magnetic flux is a. magnetomotive force b. induced voltage c. induced current d. hysteresis

34 Quiz 4. The measurement unit for permeability is a. weber/ampere-turn b. ampere-turn/weber c. weber/ampere-turn-meter d. dimensionless

35 Quiz 5. The measurement unit for relative permeability is a. weber/ampere-turn b. ampere-turn/weber c. weber/ampere-turn meter d. dimensionless

36 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

37 Quiz 7. Ohm s law for a magnetic circuit is a. F m = NI b. B = mh c. d. F j m R l R ma

38 Quiz 8. The control voltage for a relay is applied to the a. normally-open contacts b. normally-closed contacts c. coil d. armature

39 Quiz 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 R B H

40 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

41 Quiz Answers: 1. d 6. b 2. d 7. c 3. a 8. c 4. c 9. b 5. d 10. a

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