Plant

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Plant Electrical Distribution Systems

• Module ENGE 303
• H.Gallagher_at_gcal.ac.uk
• hugo_at_logis-tech.co.uk
• Tel No 0141 331 .
• Room M
• Week 1

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Recommended Text

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

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Magnetismand Electromagnetism
4
The Magnetic Field

• 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.

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Figure 1 Magnetic lines of force around a bar
magnet.
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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.
• The many lines surround the magnet in 3
  dimensions.
• Lines shrink to the smallest possible size and
  blend together- although they do not touch.
• Forms a continuous magnetic field surrounding the
  magnet.

7
Figure 2 Magnetic attraction and repulsion
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Fig. 3 Effect of (a) nonmagnetic and (b)
magnetic materials on a magnetic field.
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Magnetic Flux, F

• The group of force lines going from the N. pole
  to the S. pole of a magnet is called the magnetic
  flux, symbolized by F (phi).
• 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.
• Unit of magnetic flux is the weber (Wb)
• One weber 108 lines.

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Magnetic Flux Density, (B)

• Is the amount of flux per unit area perpendicular
  to the magnetic field.
• Its symbol is B, and its unit is the tesla (T).
• One tesla one weber/square meter (Wb/m2).
• The following expresses the flux density
• B F
• A
• F is the flux, A is the c.s.a in square meters
  (m2) of the magnetic field.

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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 (104 gauss 1T).
• The instrument used to measure flux density is
  the gaussmeter.

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Example 1

• Find the flux density in a magnetic field in
  which the flux in 0.1m2 is 800µWb.
• Solution
• B F/A
• 800µWb/0.1m2
• 8000µT

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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.
• Solution
• F 150 µ Wb 150 x 10-6 Wb
• c.s.a 200 x 100 20000 mm2 20000 x 10-6 m2
• Flux Density, B F/A
• 150 x 10-6/20000
  x 10-6
• 0.0075 T or 7.5mT

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How Materials Become Magnetised

• 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.
• 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.
• 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.

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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
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Quiz 1

• 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?
• Ans Magnetic flux is the group of lines of force
  that make up a magnetic field.
• What is the flux density when F 4.5µWb and A
  5 x 10-3 m2?
• Ans B F/A 900µT

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Electromagnetism

• 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.

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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)
• The Relative Permeability (µr)
• Reluctance, S (RM)

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Permeability (µ)

• 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
• Symbol µ its value varies depending on material.
  
• µo, permeability of a vacuum is 4p X 10-7 Wb/At.m
  (weber/ampere-turn.meter) and is used as a
  reference.
• Ferromagnetic materials typically have
• permeabilities hundreds of times larger than that
  of a vacuum
• include iron, steel, and their alloys.

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The Relative Permeability

• (µr) of a material is the ratio of its absolute
  permeability (µ) to the permeability of a vacuum
  (µo).
• Since µr is a ratio, it has no units.
• µr µ
• µo

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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
• S L/µA (At/Wb)

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Example 2

• What is the reluctance of a material that has a
  length of 0.05 m, a cross-sectional area of 0.012
  m2, and a permeability of 3500 µWb/At.m?
• Solution
• S L/ µA
• 0.05/ (3500 x 10-6 Wb/At.m) (0.012m2)
• 1190 At/Wb

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Magnetomotive Force (mmf)

• Current in a conductor produces a magnetic field.
  
• 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.
• 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.

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Figure 11 A basic magnetic circuit
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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
• F Fm
• R

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Example 3

• How much flux is established in the magnetic path
  of Fig. 12 if the reluctance of the material is
  0.28 X 105 At/WB?

Figure 12
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Solution to Example 3

• F Fm/R NI/R (5 t) (3 A)
• 0.28 X 105 At/Wb
  
• 5.36 X 10-4 Wb
• 536µWb

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Example 4

• There are two amperes of current through a wire
  with 5 turns.
• (a) What is the mmf?
• (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
• (b) R Fm/F 10At/250µWb
• 0.04 X 106 At/Wb
• 4.0 X 104 At/Wb

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The Electromagnet

• 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.

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Figure 13 Reversing the current in the coil
causes the electromagnetic field to reverse.
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Figure 14 Read/write function on a magnetic
surface.
Application Examples
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The Magneto Optical Disk

• 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.
• Laser beam precisely directed to an extremely
  small spot
• Capable of storing much more data than standard
  magnetic hard disks.

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Figure 15 Basic concept of the magneto-optical
disk.
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Electromagnetic Devices

• Magnetic disk/tape read/write head
• Magneto-optical disk
• Transformer
• Solenoid
• Relay
• Speaker

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The Solenoid

• 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.

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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.

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Fig. 18 Basic structure of a single-pole-double-th
row relay
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Reed Relay

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

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Figure 20 Basic structure of a reed relay
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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.
• electromagnetic action is used to open or close
  electrical contacts
• unenergised/energised
• Structure
• Symbol

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The Speaker

• Permanent-magnet speakers are commonly used and
  their operation is based on the principle of
  electromagnetism.
• 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.

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Figure 21 Basic speaker operation
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Fig. 22 The speaker converts audio signal
voltages into sound waves.
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Meter Movement

• 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.

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Figure 23 The basic dArsonval meter movement
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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.
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Magnetising Force (H)

• Magnetizing force in a material is defined to be
  the
• magnetomotive force (Fm) per unit length (L)
  of the material.
• Unit of magnetizing force (H) is ampere-turns per
  meter (At/m).
• 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.
• It does not depend on the type of material.

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Magnetising Force (H)

• Since F Fm/R, as Fm increases, the flux
  increases.
• Also, magnetising force (H) increases.
• Recall that flux density (B) is the flux per
  unit c.s.a. (B F/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).

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

• 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).

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Fig 26 Development of a magnetic hysteresis curve
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Fig 26(g) Complete B-H Curve The Hysteresis
Curve
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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.
• Calculate the magnetomotive force to
• produce a flux of 0.48 mWb.
• (Use B-H curve on page 78)

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Solution to Example 6

• Two parts to the circuit - mild steel and the
  air-gap
• For the mild steel
• B F/A
• 0.48 x 10-3 /4 x 10-4 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
• Hl (1800)(300 x 10-3) 540 A

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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
• For air, B µ0H from which,
• H B/µ0
• 1.2T/4p x 10-7
• 954930 A/m
• Hence the m.m.f. for the air-gap Hl
• 
  (954930)(3 ? 10-3)
• 
  2865 A
• Total m.m.f. to produce a flux of 0.48 mWb
• 540
  2865 3405 A

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Materials with a low Retentivity

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

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Electromagnetic Induction

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

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Relative Motion

• 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.
• In either case, this relative motion results in
  an induced voltage (vind) .

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Fig. 27 Relative motion between a wire and a
magnetic field
68
Fig. 28 Polarity of induced voltage depends on
direction of motion.
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Fig. 29 Induced current (iind) in a load as the
wire moves through the magnetic field.
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Fig. 30 Forces on a current-carrying conductor in
a magnetic field (motor action).
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Faradays Law

• Michael Faraday discovered the principle of
  electromagnetic induction in 1831.
• 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.

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Fig. 31 A demonstration of Faradays first
observation The amount of induced voltage is
directly proportional to the rate of change of
the magnetic field w.r.t. the coil.
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Fig. 32 A demonstration of Faradays second
observation The amount of induced voltage is
directly proportional to the no. of turns in the
coil
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Faradays 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.

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Lenzs Law

• 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.

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Applications of Electromagnetic Induction

• an automotive crankshaft position sensor
• dc generator.

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Automotive Crankshaft Position Sensor

• 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
• to set ignition timing
• adjust the fuel control system.

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Fig. 33 A crankshaft position sensor that
produces a voltage when a tab passes through the
air gap of the magnet.
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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.
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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
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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.
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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.
• Solution
• L 0.3 m, I 15 A and F 3.6 N
• F B I L gt B F / I L 3.6 / 15 x 0.3
• 0.80
  T

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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.
• Solution
• ?? 30 x 10-3 Wb
• ?t 40 x 10-3 s

Induced emf, E