Electrotechnics
N4
Chapter 1 – Current flow in an electrical circuit
THE ATOM AND ITS STRUCTURE
At the centre of the atom is the nucleus consisting of protons and neutrons
bound by extremely powerful nuclear forces. Rotating in orbits
around the nucleus are electrons.
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Chapter 1 – Current flow in an electrical circuit (continued)
MOVEMENT OF ELECTRONS IN A CONDUCTOR
When electrons drift in a specific direction is known as current. The electrons
flow from “negative” to “positive” and this is known as electron flow. This
electron flow is used when referring to “light current” or “electronics”.
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Chapter 1 – Current flow in an electrical circuit (continued)
ELECTROMOTIVE FORCE (EMF)
Electromotive force is that force which tends to produce an electric current in
a circuit. The unit of emf is the volt.
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Chapter 1 – Current flow in an electrical circuit (continued)
RESISTANCE
The unit of resistance is that resistance in which a current of 1 ampere
flowing for 1 second generates 1 joule of thermal energy. The unit in which it
is measured is the ohm (Ω). A resistor is said to be linear if the current
through the resistor is proportional to the pd across its terminals.
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Chapter 1 – Current flow in an electrical circuit (continued)
POWER
Power is the rate of doing work.
Power = 𝑃 = 𝑉𝐼 watts
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Chapter 1 – Current flow in an electrical circuit (continued)
RELATIONSHIP BETWEEN HEAT ENERGY AND POWER
Heat generated in a circuit is proportional to;
• The square of the current (𝐼 2 ),
• The resistance of the wire, and
• The time during which the current flows.
Heat energy generated = 𝐼 2 𝑅𝑡 joules
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Chapter 1 – Current flow in an electrical circuit (continued)
RESISTIVITY
The resistance of a material is;
• Proportional to the type of material (ρ),
• Proportional to the length of the material (ℓ), and
• Inversely proportional to its cross-sectional area (a).
𝑅 = 𝜌ℓ ohms
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Chapter 1 – Current flow in an electrical circuit (continued)
TEMPERATURE RISE IN ELECTRICAL MACHINES
The temperature of the windings of an electrical machine may be determined
by:
• Calculating the increase of resistance of the windings, and
• Thermo-couples embedded in one or more of the windings
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Chapter 1 – Current flow in an electrical circuit (continued)
TEMPERATURE COEFFICIENT OF RESISTANCE (𝜶)
The temperature coefficient of resistance of a substance is the increase in
unit resistance of a substance, per unit rise in temperature from 0°C.
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Chapter 1 – Current flow in an electrical circuit (continued)
KIRCHHOFF’S LAWS
• Kirchhoff’s Current Law states that the algebraic sum of currents entering
a point will be equal to the algebraic sum of the currents leaving that point.
• Kirchhoff’s Voltage Law states that the algebraic sum of the individual
voltage drops in a closed network is equal to the algebraic sum of the
applied voltage.
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Chapter 2 – Magnetism and electricity
MAGNETISM
Magnetism is involved in the operation of a great number of electrical
devices such as generators, motors, measuring instruments and
transformers. The magnetic field pattern can be seen:
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Chapter 2 – Magnetism and electricity (continued)
ELECTROMAGNETISM
The diagram below is able to show the manner in which the phenomenon of
electromagnetism works:
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Chapter 2 – Magnetism and electricity (continued)
THE MAGNETIC CIRCUIT
The magnetic circuit of a bar magnet consists of the path of magnetic lines
through the magnet and the surrounding space. The opposition offered to the
establishment of magnetic lines of force in a magnetic circuit is termed the
reluctance of the circuit.
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Chapter 2 – Magnetism and electricity (continued)
EDDY CURRENTS
In a conductor, circulating currents called eddy currents are undesirable as
they heat up the iron in which they circulate and result in an undesirable
waste of energy.
Solid core
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Laminated core
Chapter 2 – Magnetism and electricity (continued)
FORCE ON A CURRENT-CARRYING CONDUCTOR IN A MAGNETIC
FIELD
In general, armature windings can be divided into two groups, depending on
the manner in which the windings (coils) are connected to the commutator.
The two groups are:
• Lap windings; and
• Wave windings.
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Chapter 3 – Electromagnetism and induction
ELECTROMAGNETIC INDUCTION
An electro-magnetic field (emf) is induced when a conductor goes through a
magnetic field.
Faraday’s first law of electromagnetic induction states:
An emf is induced in an electric circuit whenever there is a change in the
magnetic flux linking with the circuit.
Faraday’s second law of electromagnetic induction:
The magnitude of the induced emf is proportional to the rate of change of flux
linking with the circuit.
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Chapter 3 – Electromagnetism and induction (continued)
SELF-INDUCED EMF (INDUCTANCE)
When a current changes in intensity, the field also changes in intensity.
When the amount of flux linking with a circuit is changed, an emf is induced
in that circuit. When the change in flux conditions is due to changing current
conditions within the conductor itself, the induced emf is called an emf of
self-induction.
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Chapter 4 – Capacitors
CAPACITANCE
Any two conductors that are separated by an insulating material, form a
simple capacitor. A capacitor comprises plates and an insulating material.
𝑄
𝐶 = 𝑓𝑎𝑟𝑎𝑑𝑠
𝑉
Whereby C = capacitance,
Q = the charge on the plate, and
V = the applied voltage.
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Chapter 4 – Capacitors (continued)
TYPES OF CAPACITORS
• Mica or air capacitors (a);
• Variable air type (b);
• Rolled type (c).
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Chapter 4 – Capacitors (continued)
CAPACITORS CONNECTED IN SERIES AND PARALLEL
Capacitors can be connected in either series or parallel:
Series connection
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Parallel connection
Chapter 5 – Construction and operation of
DC machines
CONSTRUCTION
A four-pole dc generator can be constructed as shown below:
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Chapter 5 – Construction and operation of DC machines (continued)
GENERATOR AND MOTOR PRINCIPLES
There is little difference between an electric generator and an electric motor.
In general, dc machines are capable of acting either as generators or as
motors.
Generator
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Motor
Chapter 5 – Construction and operation of DC machines (continued)
THE COMMUTATOR
A practical commutator is a cylinder at one
end of the armature formed by a large
number of copper segments. The segments
are insulated from each other and from the
shaft by thin mica or micanite sheets and
clamped together by insulated end rings.
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Chapter 5 – Construction and operation of DC machines (continued)
ARMATURE WINDINGS
Armature windings are distributed in slots over the circumference of the
armature core. In general, armature windings can be divided into two groups
depending on the manner in which the windings are connected to the
commutator. The two groups are lap windings and wave windings.
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Chapter 5 – Construction and operation of DC machines (continued)
EMF GENERATED IN AN ARMATURE WINDING
When an armature rotates through one revolution, each conductor cuts the
magnetic flux, leaving each north pole and that entering each south pole.
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Chapter 5 – Construction and operation of DC machines (continued)
FIELD COILS
• Separately-excited machines:
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• Self-excited:
Chapter 5 – Construction and operation of DC machines (continued)
ARMATURE REACTION
Armature reaction is the distortion of the main flux entering and leaving the
armature, caused by the flux set up by armature conductors when they carry
current.
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Chapter 6 – DC generators
SEPERATELY-EXCITED GENERATOR
Large dc generators are sometimes separately-excited as this allows easy
control of the field current and hence of the voltage generated. The field
excitation is supplied from an independent dc source such as a battery or
separate dc generator.
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Chapter 6 – DC generators (continued)
SELF-EXCITED GENERATORS
In the case of self-excited generators, the field windings are connected to the
armature windings in various ways.
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Chapter 6 – DC generators (continued)
SHUNT GENERATORS
As a shunt generator is brought up to speed, the armature conductors cut
through the small amount of residual flux present and a small emf will be
generated.
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Chapter 6 – DC generators (continued)
SERIES GENERATOR
A series generator is a self-excited generator with armature, field windings
and load, all connected in series; therefore:
𝐼𝑎 = 𝐼𝑠𝑒 = 𝐼𝐿
where
𝐼𝑠𝑒 = series field current
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Chapter 6 – DC generators (continued)
COMPOUND GENERATOR
Compound generators are used more extensively than other types of
generators because they may be designed to have a wide variety of
characteristics. Over-compounded generators are commonly used in
generating stations that are some distance from the loads that they supply.
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Chapter 7 – DC motors
THE DC MACHINE AS A MOTOR
There is no real difference in construction between a dc motor and a dc
generator, thus a generator can be run as a motor. The main difference is
that in a generator, the generated emf is greater than the terminal voltage,
whereas in a motor the generated emf is less than the terminal voltage.
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Chapter 7 – DC motors (continued)
STARTING OF MOTORS
As soon as the armature rotates, an emf is generated in the conductors due
to their motion through the field, but since their direction is opposite to that of
the current, it is called the back emf.
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Chapter 8 – Alternating current
FREQUENCY AND SPEED
The waveform of the emf generated in an alternator undergoes one complete
cycle of variation when the conductors move past a north and a south pole
and the shape of the wave over the negative half, is exactly the same as that
over the positive half.
𝑝𝑁
𝑓=
𝐻𝑧
60
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Chapter 8 – Alternating current (continued)
PHASOR REPRESENTATION
The current in the figure below is said to lag the voltage by an angle ϕ. The
phase difference ϕ, between the two phasors remains constant, irrespective
of their position.
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Chapter 8 – Alternating current (continued)
REVISION OF COMPLEX NUMBERS
The graphical method is time consuming and so is resolving the values into
vertical and horizontal components, especially when there are several values
to be added. A quicker way of doing this would be by making use of complex
numbers.
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Chapter 8 – Alternating current (continued)
EFFECTIVE OR RMS VALUE OF AN ALTERNATING QUANTITY
The effective value of an alternating current is that value of alternating
current, which produces the same amount of heat energy, at the same rate,
as a direct current would, if passed through an identical resistance.
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Chapter 8 – Alternating current (continued)
MEAN OR AVERAGE VALUE OF AN ALTERNATING QUANTITY
1
The value of the mean height = × 2 × 𝐼𝑚
𝜋
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Chapter 9 – Resistance, capacitance and
inductance in ac circuits
RESISTANCE IN AC CIRCUITS
An alternating current flowing through a purely resistive circuit is governed by
Ohm’s Law for every instant of time (such as: 𝑖 = 𝑒/𝑅) for every point on the
waveform cycle. This means that the current waveform for a purely resistive
circuit is exactly the same shape as the waveform of the applied pd and is in
phase with it.
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Chapter 9 – Resistance, capacitance and inductance in ac circuits
(continued)
INDUCTANCE IN AC CIRCUITS
A self-induced emf is produced in an inductance whenever the current
through, it changes. When an alternating current flows through a pure
inductor, the value of the current is constantly changing and so produces a
self-induced emf at every instant.
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Chapter 9 – Resistance, capacitance and inductance in ac circuits
(continued)
CAPACITANCE IN AC CIRCUITS
A capacitor is a device for storing electric charge (Q), the amount of charge
stored for a given pd between the plates is given by;
𝑄 = 𝑉𝐶
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Chapter 9 – Resistance, capacitance and inductance in ac circuits
(continued)
SERIES CIRCUITS INVOLVING R, L AND C
The phasor of the potential difference 𝑉𝑅
across the resistor is shown relative to 𝐼
below the resistor 𝑅. Likewise, the phasors
for the potential differences 𝑉𝐿 and 𝑉𝐶 relative
to 𝐼, are shown below the inductor 𝐿 and
capacitor 𝐶 respectively.
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Chapter 9 – Resistance, capacitance and inductance in ac circuits
(continued)
POWER IN A SINGLE-PHASE AC CIRCUIT
When there is a phase displacement between the pd and current, the actual
power in watts is less than the product of the pd and the current (VI), which is
expressed in volt amperes (VA).
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Chapter 10 – Transformers
CONSTRUCTION
The principal elements of a transformer are;
• The magnetic circuit,
• The windings,
• The cooling system and in larger transformers,
• The oil tanks, and
• Protection devices.
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Chapter 10 – Transformers (continued)
PRINCIPLE OF OPERATION OF A TRANSFORMER
Essentially a transformer is made up of a primary and secondary winding,
electrically separate from each other, but magnetically coupled by means of
an iron core.
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Chapter 11 – AC machines
INDUCTION MOTORS
In an induction motor there is no electrical connection between the stator and
the rotor. The energy is transferred entirely magnetically by means of the emf
induced in the rotor conductors by the rotating field, which is set up by the
stator windings.
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Chapter 11 – AC machines (continued)
CONSTRUCTION
An induction motor consists essentially of three main parts namely;
• A stator,
• A rotor, and
• End plates.
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Chapter 11 – AC machines (continued)
THREE-PHASE INDUCTION MOTORS
In the wound rotor, the rotor is wound with insulated windings similar to the
stator windings. The rotor phase windings are star-connected with the open
ends of each phase brought out to slip-rings mounted on the rotor shaft.
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Chapter 11 – AC machines (continued)
ROTATING MAGNETIC FIELD
A simplified stator winding layout of a two-pole, star-connected motor (seen
below) is connected to a three-phase supply. A pulsating magnetic field is set
up by each of the windings. The resultant field “rotates” around the inner
surface of the stator and is referred to as a rotating magnetic field.
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Chapter 11 – AC machines (continued)
PRINCIPLE OF OPERATION
As the field sweeps across the rotor conductors, an emf is induced in the
rotor conductors. Since the rotor circuit is completed through either end-rings
or an external resistance, the emf induced causes a current to flow through
the rotor conductors.
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Chapter 11 – AC machines (continued)
SINGLE-PHASE, SPLIT-PHASE, INDUCTION MOTORS
In a single-phase induction motors, the field is produced by the stator current
is fixed in space with its magnitude changing sinusoidally. Such a field is
equivalent to two fields of equal magnitude rotating in opposite directions at
equal speeds, each being half the maximum value of the alternating field.
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Chapter 12 – Transmission and supply of ac
power
SUPPLY
Supply often comes from power stations which are built far from consumers,
because it is relatively cheap and easy to transport the final product, in this
case, electrical power and because pollution is then kept away from densely
populated areas.
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Chapter 13 – Measuring instruments
RANGE EXTENSION
Measuring instruments are mostly required to be connected to measure
currents or voltages of values higher than their construction is able to allow
them. In ac circuits, instrument transformers may be used:
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Chapter 13 – Measuring instruments (continued)
WATTMETER
In order to connect a wattmeter in a circuit by means of a shunt resistor and
multiplier, the current coil is connected across a shunt resistor and the
voltage coil in series with a multiplier.
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Chapter 13 – Measuring instruments (continued)
MEASUREMENT OF RESISTANCE
There are several methods which can be used to measure resistance, such
as:
• Voltmeter-ammeter method –
• Long shunt method; and
• Short stunt method.
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