1 Plant & Electrical Distribution Systems Module ENGE 303 Module ENGE Tel No: …. Tel No: …. Room M… Room M… Week 1 Week 1

2 Recommended Text J.O Bird, Electrical Circuit Theory and Technology, Revised edition J.O Bird, Electrical Circuit Theory and Technology, Revised edition (Chapters 7, 8, 9) (Chapters 7, 8, 9) T.Floyd, Electronic Fundamentals, Circuits, Devices and Applications, 6 th Edition T.Floyd, Electronic Fundamentals, Circuits, Devices and Applications, 6 th Edition (Chapter 7) (Chapter 7)

3 Magnetism and Electromagnetism

4 The Magnetic Field A permanent magnet has a magnetic field surrounding it. A permanent magnet has a magnetic field surrounding it. Consists of lines of force that radiate from the north pole to the south pole and back to the north pole through the magnetic material. Consists of lines of force that radiate from the north pole to the south pole and back to the north pole through the magnetic material.

5 Figure 1 Magnetic lines of force around a bar magnet.

6 The Magnetic Field Consists of lines of force, (or flux lines), that radiate from the north pole (N) to the south pole (S) and back to the N. pole through the magnetic material. Consists of lines of force, (or flux lines), that radiate from the north pole (N) to the south pole (S) and back to the N. pole through the magnetic material. The many lines surround the magnet in 3 dimensions. The many lines surround the magnet in 3 dimensions. Lines shrink to the smallest possible size and blend together;- although they do not touch. Lines shrink to the smallest possible size and blend together;- although they do not touch. Forms a continuous magnetic field surrounding the magnet. Forms a continuous magnetic field surrounding the magnet.

7 Figure 2 Magnetic attraction and repulsion

8 Fig. 3 Effect of (a) nonmagnetic and (b) magnetic materials on a magnetic field.

9 Magnetic Flux, Φ The group of force lines going from the N. pole to the S. pole of a magnet is called the magnetic flux, symbolized by Φ (phi). The group of force lines going from the N. pole to the S. pole of a magnet is called the magnetic flux, symbolized by Φ (phi). No. of lines of force in a magnetic field determines the value of the flux. No. of lines of force in a magnetic field determines the value of the flux. The more lines of force, the greater the flux and the stronger the magnetic field. The more lines of force, the greater the flux and the stronger the magnetic field. Unit of magnetic flux is the weber (Wb) Unit of magnetic flux is the weber (Wb) One weber = 10 8 lines. One weber = 10 8 lines.

10 Magnetic Flux Density, (B) Is the amount of flux per unit area perpendicular to the magnetic field. Is the amount of flux per unit area perpendicular to the magnetic field. Its symbol is B, and its unit is the tesla (T). Its symbol is B, and its unit is the tesla (T). One tesla = one weber/square meter (Wb/m 2 ). One tesla = one weber/square meter (Wb/m 2 ). The following expresses the flux density: The following expresses the flux density: B = Φ A Φ is the flux, A is the c.s.a in square meters (m 2 ) of the magnetic field. Φ is the flux, A is the c.s.a in square meters (m 2 ) of the magnetic field.

11 The Gauss The tesla (T) is the SI unit for flux density, another unit called the gauss, from the CGS (centimeter-gram-second) system, is sometimes used (10 4 gauss = 1T). The tesla (T) is the SI unit for flux density, another unit called the gauss, from the CGS (centimeter-gram-second) system, is sometimes used (10 4 gauss = 1T). The instrument used to measure flux density is the gaussmeter. The instrument used to measure flux density is the gaussmeter.

12 Example 1 Find the flux density in a magnetic field in which the flux in 0.1m 2 is 800μWb. Find the flux density in a magnetic field in which the flux in 0.1m 2 is 800μWb. Solution Solution B = Φ/A B = Φ/A = 800μWb/0.1m 2 = 800μWb/0.1m 2 = 8000μT = 8000μT

13 Example 2 A magnetic pole face has a rectangular section having dimensions 200 mm by 100 mm. If the total flux emerging from the pole is 150 μ Wb. Calculate the flux density. A magnetic pole face has a rectangular section having dimensions 200 mm by 100 mm. If the total flux emerging from the pole is 150 μ Wb. Calculate the flux density.Solution: Φ = 150 μ Wb = 150 x Wb Φ = 150 μ Wb = 150 x Wb c.s.a = 200 x 100 = mm 2 = x m 2 c.s.a = 200 x 100 = mm 2 = x m 2 Flux Density, B = Φ/A Flux Density, B = Φ/A = 150 x /20000 x = 150 x /20000 x = T or 7.5mT = T or 7.5mT

14 How Materials Become Magnetised Ferromagnetic materials become magnetised when placed in the magnetic field of a magnet. Ferromagnetic materials become magnetised when placed in the magnetic field of a magnet. We have all seen a permanent magnet pick up paper clips, nails, or iron filings. We have all seen a permanent magnet pick up paper clips, nails, or iron filings. Objects becomes magnetised under the influence of the permanent magnetic field and becomes attracted to the magnet. Objects becomes magnetised under the influence of the permanent magnetic field and becomes attracted to the magnet. When removed from the magnetic field, object tends to lose its magnetism. When removed from the magnetic field, object tends to lose its magnetism. Ferromagnetic materials have minute magnetic domains created within their atomic structure by the orbital motion and spin of electrons. Ferromagnetic materials have minute magnetic domains created within their atomic structure by the orbital motion and spin of electrons. These domains can be viewed as very small bar magnets with N. and S. poles. These domains can be viewed as very small bar magnets with N. and S. poles.

15 Figure 4 Magnetic domains in (a) an unmagnetized and in (b) a magnetised material.

16 Figure 5 Operation of a magnetic switch Application Example

17 Figure 6 Connection of a typical perimeter alarm system

18 Quiz 1 When the North poles of two magnets are placed close together, do they repel or attract each other? When the North poles of two magnets are placed close together, do they repel or attract each other? Ans: The North Poles repel What is magnetic flux? What is magnetic flux? Ans: Magnetic flux is the group of lines of force that make up a magnetic field. What is the flux density when Φ = 4.5μWb and A = 5 x m 2 ? What is the flux density when Φ = 4.5μWb and A = 5 x m 2 ? Ans: B = Φ/A = 900μT

19Electromagnetism Is the production of a magnetic field by current in a conductor. Is the production of a magnetic field by current in a conductor. Many types of useful devices such as tape recorders, electric motors, speakers, solenoids, and relays are based on electromagnetism. Many types of useful devices such as tape recorders, electric motors, speakers, solenoids, and relays are based on electromagnetism.

20 Fig. 7 Magnetic field around a current-carrying conductor

21 Figure 8 Visible effects of an electromagnetic field

22 Fig. 9 Magnetic lines of force around a current-carrying conductor

23 Fig. 10 Illustration of right-hand rule

24 Electromagnetic Properties Permeability (μ) Permeability (μ) The Relative Permeability (μ r ) The Relative Permeability (μ r ) Reluctance, S (R M ) Reluctance, S (R M )

25 Permeability (μ) Ease with which a magnetic field can be established in a given material is measured by the permeability of that material. Ease with which a magnetic field can be established in a given material is measured by the permeability of that material. Higher the permeability, a magnetic field can be established easier Higher the permeability, a magnetic field can be established easier Symbol μ; its value varies depending on material. Symbol μ; its value varies depending on material. μ o, permeability of a vacuum is 4π X Wb/At.m (weber/ampere-turn.meter) and is used as a reference. μ o, permeability of a vacuum is 4π X Wb/At.m (weber/ampere-turn.meter) and is used as a reference. Ferromagnetic materials typically have; Ferromagnetic materials typically have;  permeabilities hundreds of times larger than that of a vacuum  include iron, steel, and their alloys.

26 The Relative Permeability (μ r ) of a material is the ratio of its absolute permeability (μ) to the permeability of a vacuum (μ o ). (μ r ) of a material is the ratio of its absolute permeability (μ) to the permeability of a vacuum (μ o ). Since μ r is a ratio, it has no units. Since μ r is a ratio, it has no units. μr = μμr = μμr = μμr = μ μ o μ o

27 Reluctance (S) Opposition to the establishment of a magnetic field in a material is called reluctance (S). Opposition to the establishment of a magnetic field in a material is called reluctance (S). Value of reluctance is directly proportional to the length ( ℒ ) of the magnetic path, and inversely proportional to the permeability (μ) and to the c.s.a. (A) of the material; Value of reluctance is directly proportional to the length ( ℒ ) of the magnetic path, and inversely proportional to the permeability (μ) and to the c.s.a. (A) of the material; S = ℒ  μA (At/Wb) S = ℒ  μA (At/Wb)

28 Example 2 What is the reluctance of a material that has a length of 0.05 m, a cross-sectional area of m 2, and a permeability of 3500 μWb/At.m? What is the reluctance of a material that has a length of 0.05 m, a cross-sectional area of m 2, and a permeability of 3500 μWb/At.m? Solution: Solution: S = ℒ / μA S = ℒ / μA = 0.05/ (3500 x Wb/At.m) (0.012m 2 ) = 0.05/ (3500 x Wb/At.m) (0.012m 2 ) = 1190 At/Wb = 1190 At/Wb

29 Magnetomotive Force (mmf) Current in a conductor produces a magnetic field. Current in a conductor produces a magnetic field. Force that produces the magnetic field is called the magnetomotive force (mmf). Force that produces the magnetic field is called the magnetomotive force (mmf). Unit of mmf, (At), is established on the basis of the current in a single loop (turn) of wire. Unit of mmf, (At), is established on the basis of the current in a single loop (turn) of wire. Formula for mmf is: Formula for mmf is: Fm = NI Fm is the magnetomotive force, N is the no. of turns of wire, I is the current in amperes. Fm is the magnetomotive force, N is the no. of turns of wire, I is the current in amperes.

30 Figure 11 A basic magnetic circuit

31 Ohm's law for magnetic circuits The amount of flux depends on the magnitude of the mmf and on the reluctance of the material, as expressed by: The amount of flux depends on the magnitude of the mmf and on the reluctance of the material, as expressed by: Φ = Fm R

32 How much flux is established in the magnetic path of Fig. 12 if the reluctance of the material is 0.28 X 10 5 At/WB? How much flux is established in the magnetic path of Fig. 12 if the reluctance of the material is 0.28 X 10 5 At/WB? Example 3 Figure 12

33 Solution to Example 3  Φ = Fm/R = NI/R = (5 t) (3 A) 0.28 X 10 5 At/Wb 0.28 X 10 5 At/Wb = 5.36 X Wb = 5.36 X Wb = 536μWb = 536μWb

34 Example 4 There are two amperes of current through a wire with 5 turns. There are two amperes of current through a wire with 5 turns. (a) What is the mmf? (a) What is the mmf? (b) What is the reluctance of the circuit if the flux is 250 μWb? (b) What is the reluctance of the circuit if the flux is 250 μWb?Solution (a) N = 5 and I = 2A Fm = NI = (5t)(2A) = 10 At Fm = NI = (5t)(2A) = 10 At (b) R = Fm/Φ = 10At/250μWb = 0.04 X 10 6 At/Wb = 0.04 X 10 6 At/Wb = 4.0 X 10 4 At/Wb = 4.0 X 10 4 At/Wb

35 The Electromagnet A basic electromagnet is simply a coil of wire wound around a core material that can be easily magnetised. A basic electromagnet is simply a coil of wire wound around a core material that can be easily magnetised. The shape of the electromagnet can be designed for various applications. The shape of the electromagnet can be designed for various applications.

36 Figure 13 Reversing the current in the coil causes the electromagnetic field to reverse.

37 Figure 14 Read/write function on a magnetic surface. Application Examples

38 The Magneto – Optical Disk Uses an electromagnet and laser beams to read and write (record) data on a magnetic surface. Uses an electromagnet and laser beams to read and write (record) data on a magnetic surface. Formatted in tracks and sectors similar to magnetic floppy disks and hard disks. Formatted in tracks and sectors similar to magnetic floppy disks and hard disks. Laser beam precisely directed to an extremely small spot Laser beam precisely directed to an extremely small spot Capable of storing much more data than standard magnetic hard disks. Capable of storing much more data than standard magnetic hard disks.

39 Figure 15 Basic concept of the magneto-optical disk.

40 Electromagnetic Devices Magnetic disk/tape read/write head Magnetic disk/tape read/write head Magneto-optical disk Magneto-optical disk Transformer Transformer Solenoid Solenoid Relay Relay Speaker Speaker

41 The Solenoid Is a type of electromagnetic device that has a movable iron core called a plunger. Is a type of electromagnetic device that has a movable iron core called a plunger. Movement of this iron core depends on both an electromagnetic field and a mechanical spring force. Movement of this iron core depends on both an electromagnetic field and a mechanical spring force.

42 Figure 16 Basic solenoid structure.

43 Figure 17 Basic solenoid operation

44 The Relay Differs from solenoids in that the electromagnetic action is used to open or close electrical contacts rather than to provide mechanical movement. Differs from solenoids in that the electromagnetic action is used to open or close electrical contacts rather than to provide mechanical movement.

45 Fig. 18 Basic structure of a single-pole-double-throw relay

46 Reed Relay like the armature relay, uses an electromagnetic coil. like the armature relay, uses an electromagnetic coil. Contacts are thin reeds of magnetic material and are usually located inside the coil. Contacts are thin reeds of magnetic material and are usually located inside the coil.

47 Figure 20 Basic structure of a reed relay

48 Example 5  With the aid of a sketch, explain the operation of the electromagnetic relay.  Also provide an example of an application of this type of device? Solution Reference should be made to the reed relay and /or the armature relay. Reference should be made to the reed relay and /or the armature relay. electromagnetic action is used to open or close electrical contacts electromagnetic action is used to open or close electrical contacts unenergised/energised unenergised/energised Structure Structure Symbol Symbol

49 The Speaker Permanent-magnet speakers are commonly used and their operation is based on the principle of electromagnetism. Permanent-magnet speakers are commonly used and their operation is based on the principle of electromagnetism. Constructed with a permanent magnet and an electromagnet. Constructed with a permanent magnet and an electromagnet. Cone of the speaker consists of a paper-like diaphragm to which is attached a hollow cylinder with a coil around it, forming an electromagnet. Cone of the speaker consists of a paper-like diaphragm to which is attached a hollow cylinder with a coil around it, forming an electromagnet.

50 Figure 21 Basic speaker operation

51 Fig. 22 The speaker converts audio signal voltages into sound waves.

52 Meter Movement d'Arsonval meter movement is the most common type used in analog multimeters. d'Arsonval meter movement is the most common type used in analog multimeters. In this type of meter movement, the pointer is deflected in proportion to the amount of current through a coil. In this type of meter movement, the pointer is deflected in proportion to the amount of current through a coil.

53 Figure 23 The basic d’Arsonval meter movement

54 Fig. 24 When the electromagnetic field interacts with the permanent magnetic field, forces are exerted on the rotating coil assembly, causing it to move clockwise and thus deflecting the pointer.

55 Magnetising Force (H)  Magnetizing force in a material is defined to be the magnetomotive force (Fm) per unit length ( ℒ ) of the material. magnetomotive force (Fm) per unit length ( ℒ ) of the material.  Unit of magnetizing force (H) is ampere-turns per meter (At/m). H = Fm H = Fm ℒ Where, Fm = NI. Note  Magnetising force depends on the no. of turns (N) of the coil of wire, the current (I) through the coil, and the length ( ℒ ) of the material. wire, the current (I) through the coil, and the length ( ℒ ) of the material.  It does not depend on the type of material.

56 Magnetising Force (H) Since Φ = Fm/R, as Fm increases, the flux increases. Since Φ = Fm/R, as Fm increases, the flux increases. Also, magnetising force (H) increases. Also, magnetising force (H) increases. Recall that; flux density (B) is the flux per unit c.s.a. (B = Φ/A), so B is also proportional to H. Recall that; flux density (B) is the flux per unit c.s.a. (B = Φ/A), so B is also proportional to H. Curve showing how these two quantities (B & H) are related is called the B-H curve (hysteresis curve). Curve showing how these two quantities (B & H) are related is called the B-H curve (hysteresis curve).

57 Fig. 25 Parameters that determine the magnetising force (H) and the flux density (B).

58 The Hysteresis Curve Hysteresis is a characteristic of a magnetic material whereby a change in magnetisation lags the application of a magnetising force. Hysteresis is a characteristic of a magnetic material whereby a change in magnetisation lags the application of a magnetising force. Magnetising force (H) can be increased or decreased by varying the current through the coil of wire (reversed by reversing the voltage polarity across the coil). Magnetising force (H) can be increased or decreased by varying the current through the coil of wire (reversed by reversing the voltage polarity across the coil).

59 Fig 26 Development of a magnetic hysteresis curve

60 Fig: 26(g) Complete B-H Curve ~ The Hysteresis Curve

61 Example 6 A mild steel ring of c.s.a. 4 cm has a radial air-gap of 3 mm cut into it. If the mean length of the mild steel path is 300 mm. A mild steel ring of c.s.a. 4 cm has a radial air-gap of 3 mm cut into it. If the mean length of the mild steel path is 300 mm. Calculate the magnetomotive force to produce a flux of 0.48 mWb. (Use B-H curve on page 78)

62 Solution to Example 6 Two parts to the circuit - mild steel and the air- gap Two parts to the circuit - mild steel and the air- gap For the mild steel: For the mild steel: B = Φ/A B = Φ/A =0.48 x /4 x = 1.2 T =0.48 x /4 x = 1.2 T (From B-H curve for mild steel on p78) when B = 1.2 T, H = 1800 A/m (or close) Hence, m.m.f. for the mild steel Hence, m.m.f. for the mild steel Hl = (1800)(300 x ) = 540 A Hl = (1800)(300 x ) = 540 A

63 Solution to Example 6 (cont.d) For the air-gap: The flux density will be the same in the air-gap as in the mild steel, i.e. 1.2 T The flux density will be the same in the air-gap as in the mild steel, i.e. 1.2 T For air, B = µ 0 H from which, For air, B = µ 0 H from which, H = B/µ 0 H = B/µ 0 = 1.2T/4π x = 1.2T/4π x = A/m = A/m Hence the m.m.f. for the air-gap = Hl = (954930)(3  ) = (954930)(3  ) = 2865 A = 2865 A Total m.m.f. to produce a flux of 0.48 mWb = = 3405 A = = 3405 A

64 Materials with a low Retentivity Do not retain a magnetic field very well while those with high retentivities exhibit values of B R very close to the saturation value of B. Do not retain a magnetic field very well while those with high retentivities exhibit values of B R very close to the saturation value of B. Retentivity in a magnetic material can be an advantage or a disadvantage. Retentivity in a magnetic material can be an advantage or a disadvantage. In permanent magnets and memory cores ~ high retentivity is required. In permanent magnets and memory cores ~ high retentivity is required. In ac motors ~ retentivity is undesirable In ac motors ~ retentivity is undesirable

65 Electromagnetic Induction Relative motion between a conductor and a magnetic field, a voltage is produced across the conductor. Relative motion between a conductor and a magnetic field, a voltage is produced across the conductor. Resulting voltage is an induced voltage. Resulting voltage is an induced voltage. Transformers, electrical generators, electrical motors, and many other devices possible. Transformers, electrical generators, electrical motors, and many other devices possible.

66 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 wire is moved across a magnetic field, there is a relative motion between the wire and the magnetic field. Likewise, when a magnetic field is moved past a stationary wire, there is also relative motion. Likewise, when a magnetic field is moved past a stationary wire, there is also relative motion. In either case, this relative motion results in an induced voltage (v ind ). In either case, this relative motion results in an induced voltage (v ind ).

67 Fig. 27 Relative motion between a wire and a magnetic field

68 Fig. 28 Polarity of induced voltage depends on direction of motion.

69 Fig. 29 Induced current (i ind ) in a load as the wire moves through the magnetic field.

70 Fig. 30 Forces on a current-carrying conductor in a magnetic field (motor action).

71 Faraday’s Law Michael Faraday discovered the principle of electromagnetic induction in Michael Faraday discovered the principle of electromagnetic induction in Faraday's two observations: Faraday's two observations: (1) The amount of voltage induced in a coil is directly proportional to the rate of change of the magnetic field w.r.t. the coil. (2) The amount of voltage induced in a coil is directly proportional to the no. of turns of wire in the coil.

72 Fig. 31 A demonstration of Faraday’s first observation: The amount of induced voltage is directly proportional to the rate of change of the magnetic field w.r.t. the coil.

73 Fig. 32 A demonstration of Faraday’s second observation: The amount of induced voltage is directly proportional to the no. of turns in the coil

74 Faraday’s Law 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. 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.

75 Lenz’s Law Defines the polarity or direction of the induced voltage. Defines the polarity or direction of the induced voltage. 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 current that caused it. 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 current that caused it.

76 Applications of Electromagnetic Induction an automotive crankshaft position sensor an automotive crankshaft position sensor dc generator. dc generator.

77 Automotive Crankshaft Position Sensor An interesting automotive application is a type of engine sensor that detects the crankshaft position directly using electromagnetic induction. An interesting automotive application is a type of engine sensor that detects the crankshaft position directly using electromagnetic induction. The electronic engine controller in many automobiles uses the position of the crankshaft The electronic engine controller in many automobiles uses the position of the crankshaft to set ignition timing to set ignition timing adjust the fuel control system. adjust the fuel control system.

78 Fig. 33 A crankshaft position sensor that produces a voltage when a tab passes through the air gap of the magnet.

79 Fig. 34 As the tab passes through the air gap of the magnet, the coil senses a change in the magnetic field, and a voltage is induced.

80 Fig. 35 A simplified dc generator

81 Fig. 36 End view of wire loop cutting through the magnetic field

82 Fig. 37 Operation of a basic dc generator

83 Fig. 38 Induced voltage over three rotations of the wire loop in the dc generator.

84 Fig. 39 The induced voltage for a two-loop generator. There is much less variation in the induced voltage.

85 Example 7 A conductor 30 cm long is situated at right-angles to a magnetic field. Calculate the strength of the magnetic field if a current of 15 A in the conductor produces a force on it of 3.6 N. A conductor 30 cm long is situated at right-angles to a magnetic field. Calculate the strength of the magnetic field if a current of 15 A in the conductor produces a force on it of 3.6 N. Solution Solution ℒ = 0.3 m, I = 15 A and F = 3.6 N ℒ = 0.3 m, I = 15 A and F = 3.6 N F = B I ℒ => B = F / I ℒ = 3.6 / 15 x 0.3 F = B I ℒ => B = F / I ℒ = 3.6 / 15 x 0.3 = 0.80 T = 0.80 T

86 Example 8 Find the emf in a coil of 200 turns when there is a change of flux of 30 mWb linking it in 40 ms. Find the emf in a coil of 200 turns when there is a change of flux of 30 mWb linking it in 40 ms. Solution Solution Δϕ = 30 x Wb Δϕ = 30 x Wb Δt = 40 x s Δt = 40 x s Induced emf, E