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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;

    [email protected]

    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]
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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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    12

    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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    14

    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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    15

    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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    16

    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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    17

    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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    18

    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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    23

    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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    27

    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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    28

    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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    29

    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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    30

    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

    Chapter 8

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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,