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Prepared By :
D. R. Mehta
(B. E., M. E., GATE Qualified)
Lecturer (Electrical
Engg
. Dept.)
B. S. Patel Polytechnic,
Ganpat
Vidyanagar
,
Kherva
-
Mehsana
For Students & Staff
To get this complete presentation, send the e-mail on the
following address with your complete details;
This presentation is completely based on the FEE-text bookwritten by D. R. Mehta & T. R. Patel, published by Nirav
Prakashan.
For better understanding this presentation, you can purchasethe FEE Text Book as mention above from neareststationary shop or directly from main office of Nirav
Prakashan, at Ahmedabad.
Fundamentals
of
Electrical Engineering
1
Fundamentals of Electrical Engineering
mailto:[email protected]:[email protected]:[email protected]7/28/2019 Fee 1
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2
Fundamentals of Electrical Engineering
Chapter-1 Fundamentals of Electric and Magnetic Circuit
Chapter-2 Electromagnetic Induction
Chapter-3 A.C. Fundamentals
Chapter-8 Protection & Utilization of Electrical Power
Index
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33
Prepared By :
D. R. Mehta
(B. E., M. E., GATE Qualified)
Lecturer (Electrical
Engg
. Dept.)
B. S. Patel Polytechnic,
Ganpat
Vidyanagar
,
Kherva
-
Mehsana
Chapter 1
Fundamentals of Electric &
Magnetic Circuits
Chapter 1Fundamentals of Electric & Magnetic Circuits
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4
EMF Electromotive Force
Emf (E or V) : The electric effort required to drift free electron in one
particular direction in a conductor is known as EMF.Its full name is Electromotive Force.
V is EMF or voltage.
Its unit is volt.
Current
Current (I) : The rate of flow of charge In any electric circuit is known
as electric current.The free electrons are responsible for the flow of the current.
Its unit is Ampere or Coulombs/sec.
It is denoted by I.
Resistance
Resistance (R) : The property of the conducting material to
oppose the flow of the current flowing through it is known asresistance.
It is denoted by R. Its unit is Ohm ().
It can be written as;
where V = Voltage in volt,
I = Current in Amp.,
= Resisitivity,
l = Length of Conductor,
a = Area of Conductor in m2
.
a
lRor
I
VR
Chapter 1Fundamentals of Electric & Magnetic Circuits
V
I R
4
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5
Potential Difference
Potential Difference : The voltage difference between any two
given points in the electric circuit is known as Potential Difference(P.D.).
The potential difference between point A and B is VAB.
The potential difference between point B and C is VBC.
Its unit is volt.
It is denoted by V.
Chapter 1Fundamentals of Electric & Magnetic Circuits
V
I
R1 R2A B C
VAB VBC
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6
PowerPower (P) : The rate at which the electric work is done in any electric
circuit is known as electric power.
Its unit is Joule/sec or watt.
It can written as;
The electric power can also be expressed as;
P = VI = I2R = watt
wattVIPjoulet
WP or
EnergyEnergy : The power consumed in any electric circuit over a particular
time is known as the electric energy.
Its unit is KWh.
It can be written as;
Energy = Power Time
Energy = = P t KWhr
The power must be in KW and time must be in Hour.
It is also known as the Unit.
Chapter 1Fundamentals of Electric & Magnetic Circuits
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7
EMF & Potential DifferenceR1 & R2 = Two resistor connected
in series
S= Switch
V = Voltage or EMF
R1 R2
S
V
When the switch S is closed, the free electrons flow from the
circuit. It is nothing but the current I.
The electric effort required to flow the electric current from the
circuit is known as EMF. In the circuit, V is the EMF.
I
I
Due to this electric current I, the voltage drop occurs across the
resistance R1 (between point A & B) & resistance R2 (between point B & C.
These voltage drops are known as potential difference.
The potential difference between point A & B is known as VAB.
The potential difference between point B & C is known as VBC.
VAB VBC
A B C
Chapter 1Fundamentals of Electric & Magnetic Circuits
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8
Factors Affecting ResistanceAs we know, the resistance of any conductor can be given by;
a
lR where = Resistivity,
l = Length of Conductor,a = Area of Conductor in m2.
Factors affecting resistance
1. Length of Conductor2. Cross-sectional area of conductor3. Types of material4. Temperature : The resistance of a conductor also depends on
the temperature. As the temperature increase, the resistanceof a conducting material also increases & vice-versa.
In general, without considering the temperature effect;
alR
1. Length of Conductor
2. Cross Sectional Area of Conductor
3. Types of Material4. Temperature
Chapter 1Fundamentals of Electric & Magnetic Circuits
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This Constant is Known as Resistance.
It can be denoted by R.
Its unit is ohm ().
9
Ohms LawOhms Law : The ratio of voltage applied (V) to any electric circuit
and the current flowing through the same circuit (I) is constant,
assuming temperature remains constant.
V = Applied Voltage,
I = Current
R = Resistance,
I
VR
Ohm law can be written as;
Limitations ofOhms Law :
1. This law is not applicable to non-linear devices or
semiconductor devices such as diode, zener diodes, voltage
regulators etc.2. This law does not count the effect of change in temperature.
Chapter 1Fundamentals of Electric & Magnetic Circuits
V
I R
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10
Magnetic FieldDefinition : The surrounding area of the magnet, in which the
influence of the magnet can be experienced or detected is known as the
Magnetic Field.
This magnetic field is represented by the Magnetic Lines of Force.
The direction of these lines of force is always from N-pole to S-pole,
external to the magnet.
N S
N to S
N to S
S to N
Magnetic Field of Permanent Magnet
Magnet
Chapter 1Fundamentals of Electric & Magnetic Circuits
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11
Magnetic FieldMagnetic Field of Current
Carrying Conductor
V
R
SBy applying the Right hand rule
or thumb rule, the direction of
magnetic field of current carrying
conductor can be found.
Right
Hand
Rule
The direction of magnetic field is
clockwise.
Chapter 1Fundamentals of Electric & Magnetic Circuits
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Right Hand RuleThe direction of the magnetic field produced by the current carrying
conductor can be found by Right Hand Rule.
A B
Rule : Hold the current
carrying conductor in the
right hand and place the
thumb in the direction ofthe current flowing
through the conductor
then the curled fingers
shows the direction of the
magnetic field.
1. Conductor AB of length l mt.
2. Direction of current from A to B
3. Applying right hand rule4. Direction of magnetic field is clockwise
Chapter 1Fundamentals of Electric & Magnetic Circuits
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13
Cork Screw Rule
Conductor Conductor
Rule : Ifthe direction of the advancement of the screw is the direction of
the current flowing through the conductor then the direction in which the
screw is rotated, is the direction of the magnetic field.
The direction of the magnetic field produced by the current carrying
conductor can be found by Right Hand Rule.
Chapter 1Fundamentals of Electric & Magnetic Circuits
Direction of
CurrentDirection of
Current
Direction of
Magnetic
Field
Direction of
Magnetic
Field
Direction of
Advancement
Direction of
Advancement
Direction of
Rotation
of Screw
Direction of
Rotation
of Screw
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Magnetic CircuitWhen a current is passed through a coil a magnetic field is
generated
Chapter 1Fundamentals of Electric & Magnetic Circuits
Iron Core or ring made from silicon steel material having
cross sectional area of A m2
Coil having N turns wound on
the core.
A m2
Current I flowing through circuit
I
I
Magnetic field produced in the Iron Core
Leakage Flux
Iron Core
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MMF Magneto-Motive ForceAs in the electric circuit, the emf is necessary to move the electrons
or pass the current, same way in the magnetic circuit, the mmf is
necessary to establish the magnetic flux.
It can be defined as the multiplication of the number of turns of the
coil and the current flowing through the coil.
It is denoted by Fm.
Fm (mmf) = IN
Its unit is Ampere Turns or AT.
Magnetic Field Strength or Magnetic Field IntensityDefinition : The magnetic field strength is defined as the magneto
motive force per unit length of the magnetic flux path.
It is denoted by H.
Its unit is AT/m.It can be written as;
mATH /
l
MMF
Chapter 1Fundamentals of Electric & Magnetic Circuits
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PermeabilityDefinition : The property of the magnetic material to allow for the
production of the magnetic flux in it is known as permeability.
It is denoted by .Its unit is Henry/m.
= 0r
where,
= Absolute permeability of the magnetic material
0 = Permeability of air or vacuum.= 4 10-7
r = Relative permeability of the magnetic material
w.r.t. to air or vacuum.
The relative permeability of the air or vacuum is 1.
Absolute PermeabilityDefinition : In particular medium other than vacuum or air, the ratio
of the flux density B to the magnetic field strength H required to
produce the flux density is known as absolute permeability.
It is denoted by .Its unit is Henry/m.
It can be written as;
And B = H
H
B
Permeability of Air or VacuumDefinition : If the magnetic material Is placed in the vacuum or air
then the ratio of the flux density B to the magnetic field strength H
required to produce the flux density is known as permeability of free
space or vacuum.It is denoted by 0.
Its unit is Henry/m.
It can be written as;
0= 4 10-7 H/m
mHH
B/0
Relative PermeabilityDefinition : Under the influence of the same magnetic field strength,
the ratio of the flux density produced in a medium other than the
vacuum or air to the flux density produced in the vacuum or air is
known as relative permeability.It is denoted by .
It is unit less.
Chapter 1Fundamentals of Electric & Magnetic Circuits
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Magnetic Flux & Flux DensityMagnetic Flux : The total number of magnetic force line exists in the
particular magnetic field is known as magnetic flux.
It is denoted by .
Its unit is Weber.
Flux Density : The flux density is defined as the flux passing per unit
cross sectional area through a plane perpendicular to the direction of
the magnetic flux.
It is denoted by B.Its unit is Wb/m2 or Tesla.
It can be written as;
It can also be written as;B = 0rH
2Wb/mArea
FluxB
A
Chapter 1Fundamentals of Electric & Magnetic Circuits
ReluctanceDefinition : The property of the magnetic material to oppose the
production of the magnetic flux in it is known as the Reluctance.
The ratio of the magneto motive force to the flux produced in the
magnetic material is known as Reluctance.It is similar to the resistance in the electric circuit.
It is denoted by S.
Its unit is AT/wb.
It can be written as;
AT/wbIN
Flux
MMFS
AT/wb
A
lS
0 r
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Leakage Flux and Leakage Factor
Useful Flux
Leakage Flux
Assume,
T = Total flux produced by the magnetic circuit
U = Useful flux
L = Leakage flux
The ratio of the totalflux to the useful flux is
known as Leakage
Factor or Hopkinsons
Leakage Co-efficient.
It is denoted by .
For the electrical
machines, the value of
is usually about 1.15
to 1.25.
u
T
FluxUseful
FluxTotal
Airgap
Chapter 1Fundamentals of Electric & Magnetic Circuits
FringingDefinition : The tendency of the useful
flux to spread outward when passing
through the air gap is known as
fringing.
Fringing
I
I
h
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Sr. No. Electric Circuit Magnetic Circuit
1 It is defined as the closed path for
electric current.
It is defined as the closed path for
magnetic flux.
2 Electromotive force (EMF).
Unit volt.
Magneto motive Force (MMF).
Unit AT.
3 Resistance Reluctance
4 Resistivity Reluctivity
5 Conductance = 1/Resistance Permeance = 1/Reluctance
6 Conductivity = 1/Resistivity Permeability = 1/Reluctivity
7 Current Flux
8 Current Density Flux Density
9 Electric Field Intensity Magnetic Field Intensity
AR
EMFI
Sr. No. Electric Circuit Magnetic Circuit
1 In the electric circuit, the current flows
actually.
In the magnetic circuit, the flux does
not flow actually.
2 The resistivity of the material is
approximately constant.
The permeability of the material varies
with magnetic field strength.
3 The continuous energy is required to
maintain the flow of current.
Once the flux is set up, the continuous
energy does not require to maintaining
it.
4 The current increases as the emf
increases.
The flux remains constant after
saturation and it does not increase withincrease in mmf.
Dissimilarities
19
Chapter 1Fundamentals of Electric & Magnetic Circuits
Similarities
a
lR AT/wb
A
lS
0 r
2/mA
A
I
2/mvolt
d
VE
WbS
MMF
2/mWb
Area
FluxB
2/mAT
l
MMFH
Comparison between Electric Circuit & Magnetic Circuit
h
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2020
Prepared By :
D. R. Mehta (B. E., M. E., GATE Qualified)
Lecturer (Electrical Engg. Dept.)
B. S. Patel Polytechnic,
Ganpat Vidyanagar,
Kherva - Mehsana
Chapter 2
Electromagnetic Induction
Chapter 2Electromagnetic Induction
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Ch 2
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2222
Chapter 2Electromagnetic Induction
Faradays Law of Electromagnetic Induction
Ch 2
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B wb/m2
A V m/s
dx
V m/s
dx
900
V m/s
dx
volt0e
01-Case
voltvBl
dt
dxBlee
902-Case
m
voltSinvBlSin
dt
dxBle
3-Case
A
A A
Definition : The emf induced in the coil due to the physical movement of the
conductor/coil is known as dynamically induced emf.
Dynamically Induced EMF
Explanation
Consider a conductor A of length l meters placed in uniform magnetic field of flux
density B wb /m2 as shown in fig.
Consider the following three cases in which the conductor cut the distance dx with
velocity v m/sec in three different directions.
Case 1
As shown in fig., the conductor cut the distance dx in the direction of magnetic field
in time dt with velocity v m/sec.
In this case, there will be no emf induced in the conductor, as there is no flux cut by
the conductor.
Case 2
As shown in fig., the conductor cut the distance dx in the direction perpendicular to the
magnetic field in time dt with velocity v m/sec. In this case, the flux cut by the
conductor is maximum i.e. B ldx and hence the maximum emf induced in theconductor.
Case - 3
As shown in fig., the conductor cut the distance dx in time dt in the direction makes
the angle with the magnetic field axis.
In this case the flux cut by the conductor is Bldx Sin .
Chapter 2Electromagnetic Induction
Ch t 2
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Magnetic
Field
S
Direction of
Magnetic Field
ConductorMotion
Motion
24
Chapter 2Electromagnetic Induction
Flemings Left Hand Rule
Hold your left hand with first finger, middle finger and thumb at right angles.
Put the first finger in direction of magnetic field, middle finger in direction of current
flowing through conductor then the direction of thumb shows the direction of force
acting on the conductor.
Flemings Left Hand Rule
N
A
BMotion
Current
Direction
of Current
Motion
NS
Direction of
Magnetic Field
Motion
A
B
Conductor
Motion
Magnetic
Field
EMF
Flemings Right Hand Rule
Hold your right hand with first finger, middle finger and thumb at right
angles. Put the first finger in direction of magnetic field, thumb in direction of force
then the direction of middle finger shows the direction of emf induced in the
conductor.
Flemings Right Hand Rule
Direction of EMF
Ch t 2
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25
Chapter 2Electromagnetic Induction
II Es
AlternatingMagnetic Field
EM
COIL A COIL B
Statically Induced EMF
There is no physical motion of conductor but due the alternating waveform of flux,
the flux link with the coil is changed and so, emf induced in the coil.
This emf is known as statically induced emf.
There are two types of statically induced emf;
1. Self induced EMF2. Mutually induced EMF
Self Induced EMF
The emf induced in the coil due to change of its own flux linked with it is
known as self induced emf.
Mutually Induced EMF
The emf induced in one coil due to the change in flux of another coil linked
with it, is known as mutually induced emf.
Lenzs Law
The direction of the statically emf induced in the can be found by using Lenzs
Law. It states that;
The direction of the emf induced in the conductor due to the
electromagnetic induction is such that it oppose the very cause for producing it.
Ch t 2
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26
Fundamentals of Electrical EngineeringChapter 2
Electromagnetic Induction
Definition : The property of the coil to oppose the instantaneous change in the current
is known as self inductance. It is denoted by L. Its unit is Henry (H).
Self Inductance
Co-efficient of Self Inductance
The co-efficient of the self inductance can be defined in following three ways;
First Method :
The co-efficient of self inductance is defined as the ratio of the flux link with the coil to
the current flowing through the coil.
Third MethodSecond Method
HI
NL
HlANL
2
r0 voltdt
di
L-e
Factors Affecting Co-efficient of Self Inductance
The co-efficient of self inductance is given by
Hl
ANL
2
r0
1. No. of Turns (N)
2. Cross Sectional Area of Magnetic Path (A)
3. Length of Magnetic Path (l)
4. Relative Permeability or Types of Magnetic Material (r)
The factors affecting the co-efficient of self inductance can be summarized as below;Definition : The property of the coil to produce the emf in another coil placed nearer
to them when the current flowing through the first coil changes is known as the mutual
inductance. It is denoted by M. Its unit is Henry (H).
Mutual Inductance
Co-efficient of Self Inductance
The co-efficient of the self inductance can be defined in following three ways;First Method
The co-efficient of self inductance is defined as the ratio of the flux link with the coil to
the current flowing through the coil.
Third MethodSecond Method
HI
NM
1
12
Hl
NANM 21r0 volt
dtdiM-e 1M
Factors Affecting Co-efficient of Mutual Inductance
The co-efficient of mutual inductance is given by;
1. No. of Turns of Both Coil (N1
& N2
)
2. Cross Sectional Area of Magnetic Path (A)
3. Length of Magnetic Path (l)
4. Relative Permeability or Types of Magnetic Material
The factors affecting the co-efficient of mutual inductance can be summarized as
below;
Hl
NANM 21r0
Ch t 2
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Chapter 2Electromagnetic Induction
II
Alternating
Magnetic FieldCOIL A COIL B
II
Alternating
Magnetic Field
BA
Coupling Co-efficient
Consider the magnetically coupled two coils A & B. The coil A has N1 turns
and the coil B has N2 turns.
N1 N2
The coupling co-
efficient given
by;
LL
MK
21
The constant K is known as the co-efficient of coupling. It can be defined as the
ratio of the mutual inductance to the maximum possible value of the self inductance.
For the different values of the K, the couplings between coils are classified as
below;
1. K = 1 : The coils are said to be magnetically tight coupled.2. K =0 : The coils are said to be magnetically isolated from each other.
3. 0 < K < 1 : The coils are said to be magnetically loose coupled.
Ch t 2
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Chapter 2Electromagnetic Induction
I I
COIL A COIL B
I I
BA
e1S
e1M
e2S
e2M
Inductors in Series
There are two ways to connect the inductors in series;
1. Series Addition : In this type of connection, the two coils are connected in
such a way that the magnetic flux produced by them are in additive.
2. Series Opposition : In this type of connection, the two coils are connected
in such a way that the magnetic flux produced by them are in subtractive.
Series Addition
2MLLLwhere,
voltdt
di
L-e
volt2M)L(Ldt
di-e
21
21
Chapter 2
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Chapter 2Electromagnetic Induction
I I
COIL A COIL B
II
B
A
e1S
e1M
e2S
e2M
Series Subtraction
Inductors in Series
2MLLLwhere,
voltdt
diL-e
volt2M)L(Ldt
di-e
21
21
Chapter 2
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Fundamentals of Electrical EngineeringChapter 2
Electromagnetic Induction
Hysteresis Loop
Definition : The relationship between the magnetic field strength (H) and the flux
density (B) for the particular magnetic material drawn on the graph for the complete
one cycle is known as Hysteresis Loop or hysteresis Curve.
O
D
E
F
G
I
J
FLUX DENSITY B
FLUX DENSITY B
MAGNETIC FIELD
STRENGTH H
MAGNETIC FIELD
STRENGTH H
CORCIVE
FORCE
RESIDUAL
FLUX
II
AC
R
Current
O
D
E
F
G
I
D
J
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Prepared By :
D. R. Mehta (B. E., M. E., GATE Qualified)
Lecturer (Electrical Engg. Dept.)
B. S. Patel Polytechnic,
Ganpat Vidyanagar,
Kherva - Mehsana
3131
Chapter 3
A.C. FUNDAMENTALS
Chapter 3 A. C. Fundamentals
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33
Advantages of AC System
1. Step up/ Step-down possible using transformer.
2. High voltage transmission possible.
3. Very simple & robust construction of ac motor.
4. Using rectifier, dc can be obtainable very easily.
5. Possible to build up high voltage, low cost generator.
Chapter 3 A. C. Fundamentals
Generation of Alternating EMF
The ac emf can be given by ;
SinV=or vSin wtV=v
SinE=eorSin wtE=e
mm
mm
Term Related to Alternating Waveform
AC Waveform
Time
Voltage
Magnitude & Direction
Changes with Time
1. Cycle : One complete set of positive and
negative values of an alternating quantity is
known as Cycle.
2. Instantaneous Value : The value of the
alternating quantity at any time is known as
instantaneous value. This value can be found by
using following equation;
Sin wtV=v m
3. Maximum Value or Amplitude : The maximum
value of an alternating quantity, positive or
negative, is known as Amplitude or Maximum
Value. It occurs twice in the one complete cycle.
Once in positive half cycle and second in negativehalf cycle.
4. Frequency (f) : The number of cycles / sec. is
called the frequency of an alternating quantity. It
is denoted by f. Its unit is Hz. In India, 50 Hz
frequency is used.
5. Angular Frequency (w) : It is the frequency
expressed in radians per second. It is denoted by
w. It is given by w = 2f.
6. Time Period (T) : The time taken by the
alternating quantity to complete the one
complete cycle is known as the Time Period. It
is also defined as the reciprocal of the
frequency. It is denoted by T. Its unit is sec.
7. RMS Value or Effective Value : Its full name is
Root Mean Square Value. It is equal to the DC
value which when flowing through the given
circuit for given time produces the same heat
which produce by the alternating current when
flowing through the same circuit for the same
time. It can be given by; secf
1=T
8. Average Value or Mean Value : The average
value of the alternating quantity is expressed by
that DC current which transfers across the any
circuit the same charges as it transferred by that
alternating current during the same time.
2
I=I mRMS
9. Form Factor : The ratio of the rms value to the
average value is known as the Form Factor. It is
very useful in voltage generation and instrument
correction factors.
mavg I
2I
10. Peak Factor or Amplitude Factor or Crest
Factor : The ratio of the maximum value to the
rms value is known as the Peak Factor or
Amplitude Factor.
11.1ValueAverage
ValueRMSFactorForm 1.41
ValueRMS
ValueMaximumFactorPeak
11. Phase : The phase of the alternating quantity
may be defined as its position with respect to the
reference axis or reference wave.
12. Phase Difference or Phase Angle : The phase
difference or phase angle of the alternating
quantity may be defined as the angle of the lag
or lead with respect to the reference axis or
reference wave. A A
B
B
B wb/m2
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34
Chapter 3 A. C. Fundamentals
Vector Representation of an Alternating Quantity
Importance of Vector Representation
It is very difficult to represent the alternating quantity in terms of their waveforms
and mathematical equations.
The addition, subtractions of the two alternating quantity is tedious and also time
consuming in terms of their mathematical equations.
Hence, the method which representing the alternating quantity in easier way is
called a Vector Representation of an alternating quantity.
Limitations of Vector Representation
1. As we know, generally the alternating quantity is represented by rms value.
Hence, the projection Y-axis does not give the instantaneous value but it must be
multiplied by to get the instantaneous value.
2. The vector is assumed to be rotated in anti-clockwise direction at constant speed.3. Two alternating quantities of having different frequencies cannot be represented
on the same diagram.
Phase Difference
1st Definition : The phase difference or phase angle of the alternating quantity may be
defined as the angle of the lead or lag with respect to the reference axis or with
respect to the another wave.
2nd Definition : The phase difference may be defined as the difference between the
phases of the two alternating quantities or the angle difference between the two
vector representing the two alternating quantities.Zero Phase DifferenceLagging Phase Difference
Phase
Voltage
E1E2
Phase
Voltage
E1
E2
= 0
Current
AA B
B
C
C
D
D
EE
F
F
G
G
H
H
A
Anti-Clockwise
Direction
O
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35
Chapter 3 A. C. Fundamentals
Addition and Subtraction of Two Alternating Quantities
It is necessary in ac analysis to add or subtract the two or more alternating quantities
with the same frequency but different amplitudes and phases.
The additions o subtraction using waveforms is much tedious and time consuming.
So, it is preferable to add or subtract these quantities by using vectors. This is calledthe Vector Addition or Subtraction of the alternating quantity.
There are two vector methods namely;
1. Graphical Method and
2. Analytical Method
Graphical Methods
In this method, the vector diagram is required to be plotted to the scale.
IR
Im1
Im2
Im3
r 1
2
Step by step procedure to add two or more alternating quantities by using graphical
method of vector addition;
Step 5 The angle made by the resultant vector with respect to the reference is the
phase of the resultant quantity.
Step 1 Choose one of the suitable vector as a reference vector and draw it on the X
axis. Now, all other vectors to be added having their own phases.Step 2 Draw the remaining vectors one after another, considering their individual
phases.Step 3 Join the last point with the origin to complete the vector polygon.Step 4 The length of this vector from origin to last point represents maximum value
of the resultant quantity
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Step by step procedure to add two or more alternating quantities by using analytical
method of vector addition.
Chapter 3 A. C. Fundamentals
Analytical Methods
36
1. Express all the vectors in rectangular form.2. Find X component (real component) and Y component (imaginary component)
of all the quantities.
3. Add all X components and Y components algebraically to obtain the resultant X
component and Y component.4. The magnitude of the resultant vector can be obtained using;5. The phase of the resultant vector can be obtained by;
22 YXResultant XYtan 1
Mathematical Representation of an Alternating Quantity or Vector
Let, the current vector,
Now, this vector can be represented mathematically by four ways;
1. Rectangular Co-ordinate system
2. Polar Co-ordinate System
3. Trigonometric Co-ordinate System
4. Exponential Co-ordinate System
)Sin(wtIi m
1. In Rectangular Co-ordinate system ;= X + j Y
Where X = ImCos and
Y = ImSin
2. In Polar Co-ordinate System ;3. In Trigonometric Co-ordinate System ;i = ImCos + j Im Sin
4. In Exponential Co-ordinate System ;
Ii m jm eIi
Chapter 8
Chapter 8
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Prepared By :
D. R. Mehta (B. E., M. E., GATE Qualified)
Lecturer (Electrical Engg. Dept.)
B. S. Patel Polytechnic,
Ganpat Vidyanagar,
Kherva - Mehsana
37
Chapter 8Protection and Utilization of Electrical Power
37
Chapter 8Protection and Utilization of Electrical Power
Chapter 8
PROTECTION AND UTILIZATION
OF
ELECTRICAL POWER
Chapter 8
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38
Chapter 8Protection and Utilization of Electrical Power
Domestic wiring1. One lamp control from one place
There are three types of domestic wiring generally used in domestic application.
2. One lamp control from two places (Staircase wiring)
3. Fluorescent Tube
Sr. No.Position of
Switch
Condition of
Lamp
1 1 ON
2 2 OFF
Switch
Lamp
2
1
AC
One Lamp Control From One Place
I
I
38
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39
Chapter 8Protection and Utilization of Electrical Power
Switch A
Lamp
2
1
AC
One Lamp Control From Two Place1
2
Switch BPosition of
Switch A
Position of
Switch B
Condition of
Lamp
1 2 OFF
2 2 ON
2 1 OFF1 1 ON
Chapter 8
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Disadvantages of HRC Fuse :
1. After each operation, it must be replaced.
2. It cannot be interlocked with other devices.
3. Its contacts can be affected by heat produced during the operation of fuse.
STARTER1. There are also known as High Rupturing Capacity (HRC) fuse.
2. These types of fuses are used for industrial as well as distribution purpose.
3. The HRC type fuses are designed to protect the equipments against very high
current and4. In this type of fuse, the arc produced during the operation of the fuse element is
extinguished by quartz sand powder.
Advantages of HRC Fuse
1. It can interrupt very high current.
2. Its operation is very fast.
3. Inverse time current characteristics.
4. Low cost compared to other protective device.5. Required no maintainace.
6. Their operating characteristics are accurately known.
Advantages :
1. Simplest form of protective device.
2. Automatic operation
3. Very low cost.
4. Required no maintainace.5. Minimum value of current can be interrupted by fuse.
6. Inverse time current characteristics.
Disadvantages :
1. After fuse operation, fuse or fuse element required to be replaced.
2. Replacement process is time consuming.
3. Required characteristics cannot be obtainable.
The current capacity of the fuse wire should not exceed 5 A when used for lighting
load and not exceed 10 A when used for power load.
All the power devices should have different circuit.Total load in the circuit should not exceed 1000 watt and the number of points in
each circuit should not exceeds 10.
The general rules for any domestic wiring are described below;
1. Fuse
2. Miniature Circuit Breaker (MCB)
3. Earth Leakage Circuit Breaker (ELCB)
The three phase system should be indicated by Red (R phase), Yellow (Y phase), Blue
(B phase) and Black (neutral). th
Main Function : Their main function of the protective devices is to detect the faulty
condition and disconnect the faulty parts or circuit from the system.
Construction of FuseGenerally, the three protective devices are used in the household applications as
listed below;1. Fuse Element
Main Function : Function : When current flowing through the fuse element exceeds
its predetermined value then the fuse wire melts down and it interrupts the current
flowing through the circuit. Hence, it protects the circuit from the excessive current.
Capacitor
2. Fuse Body
Types of Fuse
The different types of fuses are given below;
1. Open type fuse
2. Rewirable type or semi-enclosed types fuse
3. Cartridge type fuse4. HRC fuse
Bi-Metallic
Strip
40
Fluorescent Lamp or Tube
Fluorescent Lamp
Construction
4. It consist two electrodes P and Q, made in spiral
form, each made from tungsten material.
3. The small amount of mercury and argon gas is filled
in the tube.
1. It is a one type of glass tube.2. This tube is coated by fluorescent powder
(phosphor) internally.
5. These electrodes are coated by electron emitting
material.
Chock
1. The chock is connected in series with the tube light.2. Its main function is to induce the high voltage to
produce the flow of electrons in the tube and to startthe tube light.
3. It also works as ballast.
Starter1. The starter is connected with the tube light.
2. It consist a bimetallic switch which is normally open
and capacitor C.
3. The bi-metallic switch is made from two different
materials having different temperature co-efficient.
4. Its main function is to start the tube light.
5. The capacitor is used to suppress the radio
interference produced due to arc.
General Rules for Wiring
All the switches should be connected on the live wires.Three pin plugs should be used in residential application.All the neutral wires should be linked.All the switch boards should be fixed at height of 1.5 meter from ground level.All the fans should be fixed at height of 2.5 meter from ground level.
Protective Devices
Fuse
3. End Caps
5. Arc Quenching Medium
HRC Fuse
Chapter 8Protection and Utilization of Electrical Power
AC
CHOCK
FLOURECENT
LAMPP Q
Fuse Body
End CapEnd Cap
Terminals TerminalsFuse
Element
Vacuum orQuartz Sand
powder
4. Terminals
Chapter 8
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Sr. No. MCB ELCB
1Full Name : Miniature Circuit
Breaker.
Full Name : Earth Leakage Circuit
Breaker.
2For overload and short circuit
protection.For earth leakage protection.
3
It operates when the current
flowing through it exceeds itsrated value.
It operates when the current
flowing through the phase toearth.
4 Rating: Ampere. Rating : mA.
The strip is mounted nearer to
heating resistance which
produce the heat when the
current passing from the
resistance.
41
Miniature Circuit Breaker (MCB)
Function : When current flowing through the MCB exceeds its rated value then the
bimetallic strip will be bend which disconnect the faulty parts and it interrupts the
current flowing through the circuit. Hence, it protects the circuit from the excessive
current.
Chapter 8Protection and Utilization of Electrical Power
Construction of MCB
1. The MCB consist a bi-metallic strip. The bi-metallic strip is made from two
different materials having different temperature co-efficient.
The spring is used in between
the contacts and the bi-
metallic strip.
Earth Leakage Circuit Breaker (ELCB)
The ELCB is a protective device. It protects the circuit when the leakage current
flowing through the earth. It is always connected in series with earth wire. (In
between outer frame of electrical machine and earth).
In other words, it gives the protection against electric shock. The ELCB is widely usedin the household applications to protect against earth leakage.
Function : When the leakage current flowing through the ELCB, it will operates and its
contacts placed in the main line circuit will be open. Hence, it protects against the
earth leakage.
Difference between MCB and ELCB
Electrical Earthing
Function : The different function of the earthing is describe below;
1. To maintain proper function of the electrical system.
2. To provides the protection to the person against electric shock.
3. To protect the large building against lightning.
4. To maintain constant line voltage.
Necessity of Electrical Earthing
Machine is Not Earthed Machine is Earthed
AC
P
N
Electrical
Machine
Person
Earth
I
I
IbIb
Ib
AC
P
N
Electrical
Machine
Person
Earth
I
I
IeIeIe
I
I
Heating
Resistance
Bi-metallic
Strip
To Load
Spring
Chapter 8
Chapter 8
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42
Types ofEarthing
Chapter 8Protection and Utilization of Electrical Power
The earthing can be done by connecting the outer frame of all electrical
appliances/machines to the earth through the low resistance conductor.
There are main two methods for earthing;
1. Pipe Earthing
2. Plate Earthing
42
Chapter 8Protection and Utilization of Electrical Power
Chapter 8
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Ground
2 mt
2 mt
Coal
Salt
Coal
Salt
Salt
Coal
Salt
Coal
12 mm Diameter
38 mm G.I. Pipe
15 cm 15 cm
19 mm G.I. Pipe12.7 mm
G.I. Pipe
60 cm
Cement
Concrete
Cast Iron CoverGround
Chapter 8Protection and Utilization of Electrical Power
Pipe Earthing
Chapter 8
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G.I. Plate
60 cm * 60 cm * 6.3mm
Ground
3 mt
15 cm
90 cm
Plate Earthing
12.7 mm GI. Pipe 19 mm G. I. Pipe
Tunnel
30 cm * 30 cm
60 cm
Alternative
Layer of
Coke & Salt
Chapter 8Protection and Utilization of Electrical Power
Cast Iron Cover
Ground
Chapter 8
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45
What is Electric Shock ?
Chapter 8Protection and Utilization of Electrical Power
Definition : The nervousness of the human body due to sudden passage of electric
current through the body is known as electric shock.
The electric shock depends on the following factors;
1. Magnitude of current flowing through the body.
2. Time for which the current flowing through the body.
3. Frequency of the current flowing through the body.
4. Physical condition of body of the person.
There are three main types of electrical injuries;
1. Electrocution (death due to electrical shock)
2. Electrical shock
3. Burns
Power Factor
1st Definition : The cosine of the phase angle between the supply voltage applied to
the circuit and the current flowing through the circuit is known as the power factor. It
is denoted by Cos .
2nd Definition : It is also defined as the ratio of resistance to the impedance.
Z
RCos
3rd Definition : It is also defined as the ratio of active power to the apparent power.
CosVI
CosVI
PowerApperant
PowerActiveFactorPower
Disadvantages of Low Power Factor
1. Large Cross Sectional Area of Conductor
2. Higher I2R Losses
3. Lower Efficiency
4. Less Voltage at Terminal
5. Poor Voltage Regulation6. Reduction in KW Capacity
Causes for Low Power Factor
1. Induction Motor
2. Agricultural Pump Set
3. Arc Furnace and Induction Furnace
4. Arc Lamps and Electric Discharge Lamps
5. Arc Welding6. Over Rating of Equipments
7. Increase in System Voltage
Advantages of the Power FactorImprovement
1. Small Cross Section Area of Conductor
2. Increased KW Capacity
3. Reduction in I2R Losses
4. Higher Efficiency
5. Better Voltage Regulation
6. Low Running Cost
Methods to Improve Power Factor
1. Using high power factor motors
2. Using phase advancer with induction motor
3. Using capacitor booster
4. Using static capacitor
5. Using Synchronous condenser 45
Chapter 8
Chapter 8
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Chapter 8Protection and Utilization of Electrical Power
Chapter 8Protection and Utilization of Electrical Power
Prepared By :
B.N.ASODARIYA (B.E.ELECTRICAL)
Lecturer (Electrical Engg. Dept.)
R.K DIPLOMA COLLAGE,
RAJKOT,TRAMBA,