Basics of Electrical SIHS'14

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MEGALEV TRAIN
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A few countries are using powerful electromagnets 
to develop high-speed trains, called maglev
trains. Maglev is short for magnetic levitation,
which means that these trains will float over a
guide way using the basic principles of magnets
to replace the old steel wheel and track
trains. MEGALEV TRAIN
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There are three main components to the meglev
system A large electrical power source Metal
coils lining a guide way or track Large guidance
magnets attached to the underside of the train
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Diamagnetic materials have a weak, negative
susceptibility to magnetic fields. Diamagnetic
materials are slightly repelled by a magnetic
field and the material does not retain the
magnetic properties when the external field is
removed. In diamagnetic materials all the
electrons are paired so there is no permanent net
magnetic moment per atom. Diamagnetic properties
arise from the re alignment of the electron paths
under the influence of an external magnetic
field. Most elements in the periodic table,
including copper, silver, and gold, are
diamagnetic.Paramagnetic materials have a small,
positive susceptibility to magnetic fields. These
materials are slightly attracted by a magnetic
field and the material does not retain the
magnetic properties when the external field is
removed. Paramagnetic properties are due to the
presence of some unpaired electrons, and from the
realignment of the electron paths caused by the
external magnetic field. Paramagnetic materials
include magnesium, molybdenum, lithium, and
tantalum.Ferromagnetic materials have a large,
positive susceptibility to an external magnetic
field. They exhibit a strong attraction to
magnetic fields and are able to retain their
magnetic properties after the external field has
been removed. Ferromagnetic materials have some
unpaired electrons so their atoms have a net
magnetic moment. They get their strong magnetic
properties due to the presence of magnetic
domains. In these domains, large numbers of
atom's moments (1012 to 1015) are aligned
parallel so that the magnetic force within the
domain is strong. When a ferromagnetic material
is in the unmagnitized state, the domains are
nearly randomly organized and the net magnetic
field for the part as a whole is zero. When a
magnetizing force is applied, the domains become
aligned to produce a strong magnetic field within
the part. Iron, nickel, and cobalt are examples
of ferromagnetic materials. Components with these
materials are commonly inspected using the
magnetic particle method.
MAGNETIC MATERIALS
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M A G N E T I S M
Electromagnetism is produced when an electrical
current flows through a simple conductor such as
a piece of wire or cable. A small magnetic field
is created around the conductor with the
direction of this magnetic field with regards to
its North and South poles being determined by
the direction of the current flowing through the
conductor. Magnetism plays an important role
in Electrical and Electronic Engineering because
without it components such as relays, solenoids,
inductors, chokes, coils, loudspeakers, motors,
generators, transformers, and electricity meters
etc, would not work if magnetism did not
exist. Then every coil of wire uses the effect of
electromagnetism when an electrical current flows
through it. But before we can look
at Magnetism and especially Electromagnetism in
more detail we need to remember back to our
physics classes of how magnets and magnetism
works.
Magnetic Molecule Alignment of a Piece of Iron
and a Magnet  
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The Nature of Magnetism Magnets can be found in a
natural state in the form of a magnetic ore, with
the two main types being Magnetite also called
iron oxide, ( FE3O4 ) and Lodestone, also
called leading stone. If these two natural
magnets are suspended from a piece of string,
they will take up a position in-line with the
Earths magnetic field always pointing north. A
good example of this effect is the needle of a
compass. For most practical applications these
natural occurring magnets can be disregarded as
their magnetism is very low and because nowadays,
man-made artificial magnets can be produced in
many different shapes, sizes and magnetic
strengths. There are basically two forms of
magnetism, Permanent Magnets and Temporary
Magnets, with the type being used dependant upon
its application. There are many different types
of materials available to make magnets such as
iron, nickel, nickel alloys, chromium and cobalt
and in their natural state some of these elements
such as nickel and cobalt show very poor magnetic
quantities on their own. However, when mixed or
alloyed together with other materials such as
iron or aluminium peroxide they become very
strong magnets producing unusual names such as
alcomax, hycomax, alni and
alnico. Magnetic material in the non-magnetic
state has its molecular structure in the form of
loose magnetic chains or individual tiny magnets
loosely arranged in a random pattern. The overall
effect of this type of arrangement results in
zero or very weak magnetism as this haphazard
arrangement of each molecular magnet tends to
neutralize its neighbor. When the material
is Magnetized this random arrangement of the
molecules changes and the tiny unaligned and
random molecular magnets become lined-up in
such a way that they produce a series magnetic
arrangement. This idea of the molecular alignment
of ferromagnetic materials is known as Webers
Theory and is illustrated above.
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Magnetic Flux
All magnets, no matter what their shape, have two
regions called magnetic poles with the magnetism
both in and around a magnetic circuit producing a
definite chain of organized and balanced pattern
of invisible lines of flux around it. These lines
of flux are collectively referred to as the
magnetic field of the magnet. The shape of this
magnetic field is more intense in some parts than
others with the area of the magnet that has the
greatest magnetism being called poles. At each
end of a magnet is a pole. These lines of flux
(called a vector field) can not be seen by the
naked eye, but they can be seen visually by using
iron fillings sprinkled onto a sheet of paper or
by using a small compass to trace them out.
Magnetic poles are always present in pairs, there
is always a region of the magnet called
the North-pole and there is always an opposite
region called the South-pole. Magnetic fields are
always shown visually as lines of force that give
a definite pole at each end of the material where
the flux lines are more dense and concentrated.
The lines which go to make up a magnetic field
showing the direction and intensity are
called Lines of Force or more commonly Magnetic
Flux and are given the Greek symbol, Phi ( F )
as shown below.
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LINES OF FORCE FROM A
BAR MAGNETS MAGNETIC FIELD  
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• As shown above, the magnetic field is strongest
  near to the poles of the magnet where the lines
  of flux are more closely spaced. The general
  direction for the magnetic flux flow is from
  the North ( N ) to the South ( S ) pole. In
  addition, these magnetic lines form closed loops
  that leave at the north pole of the magnet and
  enter at the south pole. Magnetic poles are
  always in pairs.
• However, magnetic flux does not actually flow
  from the north to the south pole or flow anywhere
  for that matter as magnetic flux is a static
  region around a magnet in which the magnetic
  force exists. In other words magnetic flux does
  not flow or move it is just there and is not
  influenced by gravity. Some important facts
  emerge when plotting lines of force
• Lines of force NEVER cross.
• Lines of force are CONTINUOUS.
• Lines of force always form individual CLOSED
  LOOPS around the magnet.
• Lines of force have a definite DIRECTION from
  North to South.
• Lines of force that are close together
  indicate a STRONG magnetic field.
• Lines of force that are farther apart
  indicate a WEAK magnetic field.
• Magnetic forces attract and repel like electric
  forces and when two lines of force are brought
  close together the interaction between the two
  magnetic fields causes one of two things to
  occur
• 1.    When adjacent poles are the same,
  (north-north or south-south) they REPEL each
  other.
• 2.    When adjacent poles are not the same,
  (north-south or south-north) they ATTRACT each
  other.

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This effect is easily remembered by the famous
expression that opposites attract and this
interaction of magnetic fields can be easily
demonstrated using iron fillings to show the
lines of force around a magnet. The effect upon
the magnetic fields of the various combinations
of poles as like poles repel and unlike poles
attract can be seen below. Magnetic Field of Like
and Unlike Poles
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The Magnitude of Magnetism We now know that the
lines of force or more commonly the magnetic flux
around a magnetic material is given the Greek
symbol, Phi, ( F ) with the unit of flux being
the Weber, ( Wb ) after Wilhelm Eduard Weber. But
the number of lines of force within a given unit
area is called the Flux Density and since flux
( F ) is measured in ( Wb ) and area ( A ) in
metres squared, ( m2 ), flux density is therefore
measured in Webers/Metre2 or ( Wb/m2 ) and is
given the symbol B. However, when referring to
flux density in magnetism, flux density is given
the unit of the Tesla after Nikola Tesla so
therefore one Wb/m2 is equal to one
Tesla, 1Wb/m2  1T. Flux density is proportional
to the lines of force and inversely proportional
to area so we can define Flux Density as Magnetic
Flux Density   The symbol for magnetic flux
density is B and the unit of magnetic flux
density is the Tesla, T. It is important to
remember that all calculations for flux density
are done in the same units, e.g., flux in webers,
area in m2 and flux density in Teslas.
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Magnetomotive force (MMF)

Around a magnet there is a magnetic field and
this gives a flow of magnetic energy around the
magnet. It is this flow of energy that we call
magnetic flux ( F ).Magnetic flux is given the
symbol ( F )   and is measured in Webers
(Wb).In position B there are a smaller number
of magnetic field lines passing through the loop
than in position A. We call the amount of flux
passing through a unit area at right angles to
the magnetic field lines the flux density (B) at
that point.Flux density is measured in Tesla
(T) where 1 T 1 Wbm-2Flux (F) Flux density
(B) x area through which flux passes (A) 
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MAGNETIC RELUCTANCE OR MAGNETIC RESISTANCEIt is
a concept used in the analysis of magnetic
circuits. It is analogous to resistance in an
electrical circuit, but rather than dissipating
electric energy it stores magnetic energy
In a DC field, the reluctance is the ratio of the
"magnetomotive force (MMF) in a magnetic
circuit to the magnetic flux in this circuit. In
a pulsating DC or AC field, the reluctance is the
ratio of the amplitude of the "magnetomotive
force (MMF) in a magnetic circuit to the
amplitude of the magnetic flux in this circuit.

• The definition can be expressed as follows
• where
•   ("R") is the reluctance in ampere-turns per we
  ber (a unit that is equivalent to turns
  per henry). "Turns" refers to the winding
  number of an electrical conductor comprising an
  inductor.
•  ("F") is the magnetomotive force (MMF) in
  ampere-turns
• F ("Phi") is the magnetic flux in webers.

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Magnetic flux leakage (MFL) is
a magnetic method of nondestructive testing that
is used to detect corrosion and pitting in steel
structures, most commonly pipelines and storage
tanks. The basic principle is that a
powerful magnet is used to magnetize the steel.
Magnetic lines of force that go beyond their
intended path and do not serve their intended
purpose.  But the leakage
can be applied as detection/testing of Metals
MAGNETIC FLUX LEAKAGE
FLAW DETECTION TECHNIQUES USING FLUX LEAKAGE
Magnetic flux leakage (MFL) is a magnetic method
of nondestructive testing that is used to
detect corrosion and pitting in steel structures,
most commonly pipelines and storage tanks. The
basic principle is that a powerful magnet is used
to magnetize the steel. At areas where there is
corrosion or missing metal, the magnetic
field "leaks" from the steel. In an MFL tool, a
magnetic detector is placed between the poles of
the magnet to detect the leakage field. Analysts
interpret the chart recording of the leakage
field to identify damaged areas and hopefully to
estimate the depth of metal loss. This article
currently focuses mainly on the pipeline
application of MFL, but links to tank floor
examination are provided at the end.
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FRINGING EFFECT The fringing effect results
from the presence of the air gap in the magnetic
circuit. The main consequence of the fringing
effect is to make the magnetic flux density of
the air gap different from the flux density of
the core due to the path of the flux. some
times air gaps are introduced in the magnetic
circuits to linearize the B-H curve. For a given
current, the flux density will be smaller due to
the air gap presence and saturation is not
reached.
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The Hysteresis Loop and Magnetic PropertiesB- H
Relationaship
A great deal of information can be learned about
the magnetic properties of a material by studying
its hysteresis loop. A hysteresis loop shows the
relationship between the induced magnetic flux
density (B) and the magnetizing force (H). It is
often referred to as the B-H loop. An example
hysteresis loop is shown below.
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The loop is generated by measuring the magnetic
flux of a ferromagnetic material while the
magnetizing force is changed. A ferromagnetic
material that has never been previously
magnetized or has been thoroughly demagnetized
will follow the dashed line as H is increased. As
the line demonstrates, the greater the amount of
current applied (H), the stronger the magnetic
field in the component (B). At point "a" almost
all of the magnetic domains are aligned and an
additional increase in the magnetizing force will
produce very little increase in magnetic flux.
The material has reached the point of magnetic
saturation. When H is reduced to zero, the curve
will move from point "a" to point "b." At this
point, it can be seen that some magnetic flux
remains in the material even though the
magnetizing force is zero. This is referred to as
the point of retentivity on the graph and
indicates the remanence or level of residual
magnetism in the material. (Some of the magnetic
domains remain aligned but some have lost their
alignment.) As the magnetizing force is reversed,
the curve moves to point "c", where the flux has
been reduced to zero. This is called the point of
coercivity on the curve. (The reversed
magnetizing force has flipped enough of the
domains so that the net flux within the material
is zero.) The force required to remove the
residual magnetism from the material is called
the coercive force or coercivity of the material.
As the magnetizing force is increased in the
negative direction, the material will again
become magnetically saturated but in the opposite
direction (point "d"). Reducing H to zero brings
the curve to point "e." It will have a level of
residual magnetism equal to that achieved in the
other direction. Increasing H back in the
positive direction will return B to zero. Notice
that the curve did not return to the origin of
the graph because some force is required to
remove the residual magnetism. The curve will
take a different path from point "f" back to the
saturation point where it with complete the loop.
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From the hysteresis loop, a number of primary
magnetic properties of a material can be
determined. Retentivity - A measure of the
residual flux density corresponding to the
saturation induction of a magnetic material. In
other words, it is a material's ability to retain
a certain amount of residual magnetic field when
the magnetizing force is removed after achieving
saturation. (The value of B at point b on the
hysteresis curve.) Residual Magnetism or Residual
Flux - the magnetic flux density that remains in
a material when the magnetizing force is zero.
Note that residual magnetism and retentivity are
the same when the material has been magnetized to
the saturation point. However, the level of
residual magnetism may be lower than the
retentivity value when the magnetizing force did
not reach the saturation level. Coercive Force -
The amount of reverse magnetic field which must
be applied to a magnetic material to make the
magnetic flux return to zero. (The value of H at
point c on the hysteresis curve.) Permeability, m
 - A property of a material that describes the
ease with which a magnetic flux is established in
the component. Reluctance - Is the opposition
that a ferromagnetic material shows to the
establishment of a magnetic field. Reluctance is
analogous to the resistance in an electrical
circuit.
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Permeability As previously mentioned,
permeability (m) is a material property that
describes the ease with which a magnetic flux is
established in a component. It is the ratio of
the flux density (B) created within a material to
the magnetizing field (H) and is represented by
the following equation It is clear that this
equation describes the slope of the curve at any
point on the hysteresis loop. The permeability
value given in papers and reference materials is
usually the maximum permeability or the maximum
relative permeability. The maximum permeability
is the point where the slope of the B/H curve for
the unmagnetized material is the greatest. This
point is often taken as the point where a
straight line from the origin is tangent to the
B/H curve.
m B/H
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• The shape of the hysteresis loop tells a great
  deal about the material being magnetized. The
  hysteresis curves of two different materials are
  shown in the graph.
• Relative to other materials, a material with a
  wider hysteresis loop has
• Lower Permeability
• Higher Retentivity
• Higher Coercivity
• Higher Reluctance
• Higher Residual Magnetism
• Relative to other materials, a material with the
  narrower hysteresis loop has
• Higher Permeability
• Lower Retentivity

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Video Demonstration about how Electromagnetic
induction takes place
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Electromagnetic induction is the production of
an electromotive force across a conductor when it
is exposed to a varying magnetic field. It is
described mathematically by Faraday's law of
induction, named after Michael Faraday who is
generally credited with the discovery of
induction in 1831.
Any change in the magnetic environment of a coil
of wire will cause a voltage (emf) to be
"induced" in the coil. No matter how the change
is produced, the voltage will be generated. The
change could be produced by changing the magnetic
field strength, moving a magnet toward or away
from the coil, moving the coil into or out of the
magnetic field, rotating the coil relative to the
magnet, etc.
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Electromagnetic Induction We have seen previously
that when a DC current pass through a long
straight conductor a magnetizing force, H and a
static magnetic field, B is developed around the
wire. If the wire is then wound into a coil, the
magnetic field is greatly intensified producing a
static magnetic field around itself forming the
shape of a bar magnet giving a distinct North and
South pole. Air-core Hollow Coil The magnetic
flux developed around the coil being proportional
to the amount of current flowing in the coils
windings as shown. If additional layers of wire
are wound upon the same coil with the same
current flowing through them, the static magnetic
field strength would be increased. Therefore,
the Magnetic Field Strength of a coil is
determined by the ampere turns of the coil. With
more turns of wire within the coil the greater
will be the strength of the static magnetic field
around it. But what if we reversed this idea by
disconnecting the electrical current from the
coil and instead of a hollow core we placed a bar
magnet inside the core of the coil of wire. By
moving this bar magnet in and out of the coil
a current would be induced into the coil by the
physical movement of the magnetic flux inside
it. Likewise, if we kept the bar magnet
stationary and moved the coil back and forth
within the magnetic field an electric current
would be induced in the coil. Then by either
moving the wire or changing the magnetic field we
can induce a voltage and current within the coil
and this process is known as Electromagnetic
Induction and is the basic principal of operation
of transformers, motors and generators.
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Flemings Left Hand Rule
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Electromagnetic Induction was first discovered
way back in the 1830s by Michael Faraday.
Faraday noticed that when he moved a permanent
magnet in and out of a coil or a single loop of
wire it induced an ElectroMotive Force or emf, in
other words a Voltage, and therefore a current
was produced.
Faradays Law of Electromagnetic Induction
When the magnet shown below is moved towards
the coil, the pointer or needle of the
Galvanometer, which is basically a very sensitive
centre zeroed moving-coil ammeter, will deflect
away from its centre position in one direction
only. When the magnet stops moving and is held
stationary with regards to the coil the needle of
the galvanometer returns back to zero as there is
no physical movement of the magnetic
field. Likewise, when the magnet is moved away
from the coil in the other direction, the needle
of the galvanometer deflects in the opposite
direction with regards to the first indicating a
change in polarity. Then by moving the magnet
back and forth towards the coil the needle of the
galvanometer will deflect left or right, positive
or negative, relative to the directional motion
of the magnet.
Faradays Law of Induction Definition From the
above description we can say that a relationship
exists between an electrical voltage and a
changing magnetic field to which Michael
Faradays famous law of electromagnetic induction
statesthat a voltage is induced in a circuit
whenever relative motion exists between a
conductor and a magnetic field and that the
magnitude of this voltage is proportional to the
rate of change of the flux.
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In other words, Electromagnetic Induction is the
process of using magnetic fields to produce
voltage, and in a closed circuit, a current.
So how much voltage (emf) can be induced into the
coil using just magnetism. this is determined by
the following 3 different factors. 1).
Increasing the number of turns of wire in the
coil.  By increasing the amount of individual
conductors cutting through the magnetic field,
the amount of induced emf produced will be the
sum of all the individual loops of the coil, so
if there are 20 turns in the coil there will be
20 times more induced emf than in one piece of
wire. 2). Increasing the speed of the relative
motion between the coil and the magnet.  If the
same coil of wire passed through the same
magnetic field but its speed or velocity is
increased, the wire will cut the lines of flux at
a faster rate so more induced emf would be
produced. 3). Increasing the strength of the
magnetic field.  If the same coil of wire is
moved at the same speed through a stronger
magnetic field, there will be more emf produced
because there are more lines of force to cut.
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Simple Generator using Magnetic Induction
If we were able to move the magnet in the diagram
above in and out of the coil at a constant speed
and distance without stopping we would generate a
continuously induced voltage that would alternate
between one positive polarity and a negative
polarity producing an alternating or AC output
voltage and this is the basic principal of how
a Generator works similar to those used in
dynamos and car alternators. In small generators
such as a bicycle dynamo, a small permanent
magnet is rotated by the action of the bicycle
wheel inside a fixed coil. Alternatively, an
electromagnet powered by a fixed DC voltage can
be made to rotate inside a fixed coil, such as in
large power generators producing in both cases an
alternating current.
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Lenzs Law of Electromagnetic Induction Faradays
Law tells us that inducing a voltage into a
conductor can be done by either passing it
through a magnetic field, or by moving the
magnetic field past the conductor and that if
this conductor is part of a closed circuit, an
electric current will flow. This voltage is
called an induced emf as it has been induced into
the conductor by a changing magnetic field due to
electromagnetic induction with the negative sign
in Faradays law telling us the direction of the
induced current (or polarity of the induced
emf). But a changing magnetic flux produces a
varying current through the coil which itself
will produce its own magnetic field as we seen
earliar in the Electromagnets topic. This
self-induced emf opposes the change that is
causing it and the faster the rate of change of
current the greater is the opposing emf. This
self-induced emf will, by Lenzs law oppose the
change in current in the coil and because of its
direction this self-induced emf is generally
called a back-emf.
Lenzs Law states that  the direction of an
induced emf is such that it will always opposes
the change that is causing it. In other words,
an induced current will always OPPOSE the motion
or change which started the induced current in
the first place and this idea is found in the
analysis of Inductance.
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EDDY CURRENTS
Likewise, if the magnetic flux is decreased then
the induced emf will oppose this decrease by
generating and induced magnetic flux that adds to
the original flux. Lenzs law is one of the basic
laws in electromagnetic induction for determining
the direction of flow of induced currents and is
related to the law of conservation of
energy. According to the law of conservation of
energy which states that the total amount of
energy in the universe will always remain
constant as energy can not be created nor
destroyed. Lenzs law is derived from Michael
Faradays law of induction. We now know that when
a relative motion exists between a conductor and
a magnetic field, an emf is induced within the
conductor. But the conductor may not actually be
part of the coils electrical circuit, but may be
the coils iron core or some other metallic part
of the system, for example, a transformer. The
induced emf within this metallic part of the
system causes a circulating current to flow
around it and this type of core current is known
as an Eddy Current.
Eddy currents generated by electromagnetic
induction circulate around the coils core or any
connecting metallic components inside the
magnetic field because for the magnetic flux they
are acting like a single loop of wire. Eddy
currents do not contribute anything towards the
usefulness of the system but instead they oppose
the flow of the induced current by acting like a
negative force generating resistive heating and
power loss within the core. However, there are
electromagnetic induction furnace applications in
which only eddy currents are used to heat and
melt ferromagnetic metals.
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EDDY CURRENTS CIRCULATING IN A TRANSFORMER
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The changing magnetic flux in the iron core of a
transformer above will induce an emf, not only in
the primary and secondary windings, but also in
the iron core. The iron core is a good conductor,
so the currents induced in a solid iron core will
be large. Furthermore, the eddy currents flow in
a direction which, by Lenzs law, acts to weaken
the flux created by the primary coil.
Consequently, the current in the primary coil
required to produce a given B field is increased,
so the hysteresis curves are fatter along
the H axis.
Laminating the Iron Core
Eddy current and hysteresis losses can not be
eliminated completely, but they can be greatly
reduced. Instead of having a solid iron core as
the magnetic core material of the transformer or
coil, the magnetic path is laminated. These
laminations are very thin strips of insulated
(usually with varnish) metal joined together to
produce a solid core. The laminations increase
the resistance of the iron-core thereby
increasing the overall resistance to the flow of
the eddy currents, so the induced eddy current
power-loss in the core is reduced, and it is for
this reason why the magnetic iron circuit of
transformers and electrical machines are all
laminated.
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Ohms Law
Ohms law gives a relationship between the
voltage (V), current (I), and resistance (R) as
follows V I R
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• Georg Simon Ohm (1787-1854), A German physicist,
  discovered Ohms law in 1826.
• Statement of Ohm's Law
• The relationship between Voltage, Current and Resi
  stance in any DC electrical circuit was firstly
  discovered by the German physicist Georg
  Ohm. Ohm found that, at a constant temperature,
  the electrical current flowing through a fixed
  linear resistance is directly proportional to the
  voltage applied across it, and also inversely
  proportional to the resistance. This relationship
  between the Voltage, Current and Resistance forms
  the bases of Ohms Law and is shown below.

OHMS LAW RELATIONSHIP
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Ohms Law

• Georg Ohm showed that the flow of an electric
  current through a wire depended on its
  'resistance' and the potential difference between
  its ends

A graph drawn between the voltmeter readings and
ammeter readings, shows a straight line pattern.
The straight line indicates a relationship and is
named as ohm's law. Expressed mathematically,
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To find the Voltage, ( V )  V  I x R       V 
(volts)  I (amps) x R (O) To find the Current,
( I )  I  V  R       I (amps)  V (volts)  R
 (O) To find the Resistance, ( R )  R  V  I 
      R (O)  V (volts)  I (amps)
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OHMS LAW TRIANGLE  
and transposing the above Ohms Law equation gives
us the following combinations of the same
equation
40
Then by using Ohms Law we can see that a voltage
of 1V applied to a resistor of 1O will cause a
current of 1A to flow and the greater the
resistance, the less current will flow for any
applied voltage. Any Electrical device or
component that obeys Ohms Law that is, the
current flowing through it is proportional to the
voltage across it ( I a V ), such as resistors or
cables, are said to be Ohmic in nature, and
devices that do not, such as transistors or
diodes, are said to be Non-ohmic devices
Electrical Power in Circuits Electrical Power,
( P ) in a circuit is the amount of energy that
is absorbed or produced within the circuit. A
source of energy such as a voltage will produce
or deliver power while the connected load absorbs
it. Light bulbs and heaters for example, absorb
power and convert it into heat or light and the
higher their value or rating in watts the more
power they will consume. The quantity symbol for
power is P and is the product of voltage
multiplied by the current with the unit of
measurement being the Watt ( W ) with prefixes
used to denote milli watts (mW 10-3W) or
kilowatts (kW 103W).
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Then by using Ohms law and substituting
for V, I andR the formula for electrical power
can be found as To find the Power (P)
P  V x I       P (watts)  V (volts) x I (amps)
Also, P  V2  R       P (watts)  V2 (volts) 
 R (O) Also, P  I2 x R       P (watts)  I2 (a
mps) x R (O) Again, the three quantities have
been superimposed into a triangle this time
called the Power Triangle with power at the top
and current and voltage at the bottom. Again,
this arrangement represents the actual position
of each quantity in the Ohms law power formulas.
The Power Triangle
  and again, transposing the basic Ohms Law
equation above for power gives us the following
combinations of the same equation to find the
various individual quantities
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So we can see that there are three possible
formulas for calculating electrical power in a
circuit. If the calculated power is positive,
(P) in value for any formula the component
absorbs the power, that is it is consuming or
using power. But if the calculated power is
negative, (-P) in value the component produces or
generates power, in other words it is a source of
electrical power such as batteries and generators.
Power Rating Electrical components are given a
power rating in watts that indicates the
maximum rate at which the component converts the
electrical power into other forms of energy such
as heat, light or motion. For example, a 1/4W
resistor, a 100W light bulb etc. Electrical
devices convert one form of power into another so
for example, an electrical motor will covert
electrical energy into a mechanical force, while
an electrical generator converts mechanical force
into electrical energy and a light bulb converts
electrical energy into both light and heat. Also,
we now know that the unit of power is the WATT,
but some electrical devices such as electric
motors have a power rating in the old measurement
of Horsepower or hp. The relationship between
horsepower and watts is given as 1hp 746W. So
for example, a two-horsepower motor has a rating
of 1492W, (2 x 746) or 1.5kW.
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Ohms Law Example No1 For the circuit shown above
find the Voltage (V), the Current (I), the
Resistance (R) and the Power (P).
  Voltage    V  I x R   2 x 12O  24V Current
    I  V  R   24  12O  2A Resistance    R 
 V  I   24  2  12 O Power    P  V x I   
24 x 2  48W
As electrical power is the product of V x I, the
power dissipated in a circuit is the same whether
the circuit contains high voltage and low current
or low voltage and high current flow. Generally,
power is dissipated in the form
of Heat (heaters), Mechanical Work such as
motors, etc Energy in the form of radiated
(Lamps) or as stored energy (Batteries).
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Electrical Energy in Circuits Electrical
Energy is the capacity to do work, and the unit
of work or energy is the joule ( J ). Electrical
energy is the product of power multiplied by the
length of time it was consumed. So if we know how
much power, in Watts is being consumed and the
time, in Seconds for which it is used, we can
find the total energy used in watt-seconds. In
other words, Energy  power x time and
Power  voltage x current. Therefore electrical
power is related to energy and the unit given for
electrical energy is the watt-seconds or joules.
  Electrical power can also be defined as the
rate of by which energy is transferred. If one
joule of work is either absorbed or delivered at
a constant rate of one second, then the
corresponding power will be equivalent to one
watt so power can be defined as 1Joule/sec
1Watt. Then we can say that one watt is equal to
one joule per second and electrical power can be
defined as the rate of doing work or the
transferring of energy.
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KIRCHHOFFS LAW IN MAGNETIC CIRCUITS
Kirchhoffs two Laws defined as follows
1. Kirchhoffs Flux Law 2. Kirchhoffs MMF
Law

• KFL (KCL) state that the total magnetic flux
  arriving at any junction in a magnetic circuit is
  equal to the total magnetic flux leaving that
  junction. Hence at a junction the sum of fluxes
  is zero.
• Therefore, S ( F) 0 (At a Junction)

Which states that the algebraic sum of all the
magnetic fluxes flowing out of a junction in
a magnetic circuit is zero
ANALOGY BETWEEN 'MAGNETIC CIRCUITS' AND
ELECTRICAL CIRCUITS
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KIRCHHOFFS LAW IN MAGNETIC CIRCUITS
2. Kirchhoffs MMF Law (KVL) This is similar to
in electrical circuits. It states that the
resultant m.m.f. around any closed loop of a
magnetic circuit is equal to The algebric sum of
the products of the flux and the reluctance of
each part of the magnetic circuit Hence for a
closed loop. (F) . S (reluctance)
S m.m.f. This is because mmf
reluctance x flux .
S
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KIRCHHOFFS LAW
Kirchhoff's circuit law are two equalities that
deal with the current and potential
difference (known as voltage) in
the  of electrical circuits.
KCL
(Kirchhoffs Current Law)
The law is in two modes
(Kirchhoffs Voltage Law)
KVL
This law is also called Kirchhoff's first
law, Kirchhoff's point rule, or Kirchhoff's
junction rule (or nodal rule). The principle of
conservation of electric charge implies that At
any node (junction) in an electrical circuit, the
sum of currents flowing into that node is equal
to the sum of currents flowing out of that node,
or The algebraic sum of currents in a network of
conductors meeting at a point is zero. Recalling
that current is a signed (positive or negative)
quantity reflecting direction towards or away
from a node, this principle can be stated as
n is the total number of branches with currents
flowing towards or away from the node. This
formula is valid for complex currents
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The current entering any junction is equal to the
current leaving that junction. i2  i3  i1  i4
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This law is also called Kirchhoff's second
law, Kirchhoff's loop (or mesh) rule,
and Kirchhoff's second rule. The principle of
conservation of energy implies that The directed
sum of the electrical potential
differences (voltage) around any closed network
is zero, or More simply, the sum of the emfs in
any closed loop is equivalent to the sum of the
potential drops in that loop, or The algebraic
sum of the products of the resistances of the
conductors and the currents in them in a closed
loop is equal to the total emf available in that
loop. Similarly to KCL, it can be stated as
Here, n is the total number of voltages
measured. The voltages may also be complex
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The sum of all the voltages around the loop is
equal to zero. v1 v2  v3 - v4  0
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Ohms Law problems for Series Circuits
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where A  ampere,C  coulomb,F  farad,J
 joule,kg  kilogram,m  meter,s  second,
Wb  weber,T  tesla,V  volt,O  ohm.
Watch Video on Series Parallel Circuits
Henry, unit of either self-inductance or mutual
inductance, abbreviated h (or hy), and named for
the American physicist Joseph Henry. One henry is
the value of self-inductance in a closed circuit
or coil in which one volt is produced by a
variation of the inducing current of
one ampere per second. One henry is also the
value of the mutual inductance of two coils
arranged such that an electromotive force of one
volt is induced in one if the current in the
other is changing at a rate of one ampere per
second.
Definition of Henry If the rate of change
of current in a circuit is one ampere per second a
nd the resulting electromotive force is one volt,
then the inductance of the circuit is one henry.