BEEE Quick Notes

GE 6252 BASIC ELECTRICAL AND ELECTRONICSENGINEERING
UNIT – I ELECTRIC CIRCUITS

Introduction
1.1 Basic Definitions
Electric current:
The continuous flow of electrons constitutes electric current. It is denoted by ‘I’ and is measured
in amperes.
‘I’ is also given by I = coulomb / sec
Electric Potential:
The electric potential at any point in an electric field is defined as the work done in brining an
unit positive charge (Q) from infinity to that point against the electric field
‘V’ is given by V =
Resistance:
It is the property of a conductor by which it opposes the flow of current. It is denoted by R and
its unit is ohms (Ω)
1.2. DC Circuits:
Prerequisites:
A DC circuit (Direct Current circuit) is an electrical circuit that consists of any
combination of constant voltage sources, constant current sources, and resistors. In this case,
the circuit voltages and currents are constant, i.e., independent of time. More technically,
a DC circuit has no memory. That is, a particular circuit voltage or current does not depend
on the past value of any circuit voltage or current. This implies that the system of equations
that represent a DC circuit do not involve integrals or derivatives.
Introduction:
In electronics, it is common to refer to a circuit that is powered by a DC voltage source such
as a battery or the output of a DC power supply as a DC circuit even though what is meant is
that the circuit is DC powered.
If a capacitor and/or inductor is added to a DC circuit, the resulting circuit is not,
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strictly speaking, a DC circuit. However, most such circuits have a DC solution. This solution
gives the circuit voltages and currents when the circuit is in DC steady state. More
technically, such a circuit is represented by a system of differential equations. The
solution to these equations usually contains a time varying or transient part as well as
constant or steady state part. It is this steady state part that is the DC solution. There are some
circuits that do not have a DC solution. Two simple examples are a constant current
source connected to a capacitor and a constant voltage source connected to an inductor.
Electro-magnetic force(E.M.F):
Electromotive Force is, the voltage produced by an electric battery or generator in
an electrical circuit or, more precisely, the energy supplied by a source of electric power
in driving a unit charge around the circuit. The unit is the volt. A difference in charge
between two points in a material can be created by an external energy source such as a
battery. This causes electrons to move so that there is an excess of electrons at one point and
a deficiency of electrons at a second point. This difference in charge is stored as electrical
potential energy known as emf. It is the emf that causes a current to flow through a circuit.
Voltage:
Voltage is electric potential energy per unit charge, measured in joules per
coulomb. It is often referred to as "electric potential", which then must be distinguished from
electric potential energy by noting that the "potential" is a "per-unit-charge" quantity. Like
mechanical potential energy, the zero of potential can be chosen at any point, so the difference
in voltage is the quantity which is physically meaningful. The difference in voltage measured
when moving from point A to point B is equal to the work which would have to be done, per
unit charge, against the electric field to move the charge from A to B.
Potential Difference:
A quantity related to the amount of energy needed to move an object from one place to
another against various types of forces. The term is most often used as an abbreviation of
"electrical potential difference", but it also occurs in many other branches of physics. Only
changes in potential or potential energy (not the absolute values) can be measured.
Electrical potential difference is the voltage between two points, or the voltage drop
transversely over an impedance (from one extremity to another). It is related to the energy
needed to move a unit of electrical charge from one point to the other against the electrostatic
field that is present. The unit of electrical potential difference is the volt (joule per coulomb).
Gravitational potential difference between two points on Earth is related to the energy needed to
move a unit mass from one point to the other against the Earth's gravitational field. The unit
of gravitational potential differences is joules per kilogram.
Ohm’s Law:
Ohm's law states that the current through a conductor between two points is directly
proportional to the potential difference or voltage across the two points, and inversely
proportional to the resistance between them. The mathematical equation that describes this
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relationship is:
where I is the current through the resistance in units of amperes,

V is the potential difference measured across the resistance in units of volts,
and R is the resistance of the conductor in units of ohms.
More specifically, Ohm's law states that the R in this relation is constant,
independent of the current.

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Kirchhoff’s law:
Kirchhoff's Current Law:
First law (Current law or Point law):
Statement:
The sum of the currents flowing towards any junction in an electric circuit equal to the sum of
currents flowing away from the junction.
Kirchhoff's Current law can be stated in words as the sum of all currents
flowing into a node is zero. Or conversely, the sum of all currents leaving a node must
be zero. As the image below demonstrates, the sum of currents Ib, Ic, and Id, must
equal the total current in Ia. Current flows through wires much like water flows
through pipes. If you have a definite amount of water entering a closed pipe system,
the amount of water that enters the system must equal the amount of water that
exists the system. The number of branching pipes does not change the net volume of
water (or current in our case) in the system.

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Kirchhoff's Voltage Law:

Second law (voltage law or Mesh law):
Statement:
In any closed circuit or mesh, the algebraic sum of all the electromotive forces and the
voltage drops is equal to zero.
Kirchhoff's voltage law can be stated in words as the sum of all voltage drops and rises in
a closed loop equals zero. As the image below demonstrates, loop 1 and loop 2 are both closed
loops within the circuit. The sum of all voltage drops and rises around loop 1 equals zero, and
the sum of all voltage drops and rises in loop 2 must also equal zero. A closed loop can be
defined as any path in which the originating point in the loop is also the ending point for the
loop. No matter how the loop is defined or drawn, the sum of the voltages in the loop must be
zero

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Steady State Solution of DC Circuits:

Resistance in series connection:
The resistors R1, R2, R3 are connected in series across the supply voltage “V”. The total current
flowing through the circuit is denoted as “I”. The voltage across the resistor R1, R2 and R3 is V1,
V2, and V3 respectively.
V1 = I*R1 (as per ohms law)
V2= I*R2
V3 = I*R3
V = V1+V2+V3
= IR1+IR2+IR3
= (R1+R2+R3) I
IR = (R1+R2+R3) I
R = R1+R2+R3
Resistance in parallel connection:
The resistors R1, R2, R3 are connected in parallel across the supply voltage “V”. The total
current flowing through the circuit is denoted as “I”. The current flowing through the resistor
R1, R2 and R3 is I1, I2, and I3 respectively.

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I = V / R (as per ohms law)

I 1 = V1 / R1
I2 = V2 / R2
I3 = V3 / R3
V1 = V2 = V3 = V
From the above diagram
I = I1+I2+I3
= V1 / R1 + V2 / R2 + V3 / R3
= V / R1+ V/R2 +V/R3
I = V (1/R1 +1/R2 +1/R3)
V / R = V (1/R1 +1/R2 +1/R3)
1/R = 1/R1 +1/R2 +1/R3
Problems based on ohm’s law

Problem 1:
A current of 0.5 A is flowing through the resistance of 10Ω.Find the potential difference
between its ends.
Given data:
Current I= 0.5A.
Resistance R=1Ω
To find
Potential difference V = ?
Formula used:
V = IR
Solution:
V = 0.5 × 10 = 5V.
Result :
The potential difference between its ends = 5 V
Problem :2
A supply voltage of 220V is applied to a 100 Ω resistor. Find the current flowing through
it.
Given data
Voltage V = 220V
Resistance R = 100Ω
To find:
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Current I = ?
Formula used:
Current I = V / R
Solution:
Current I = 220/100
= 2.2 A
Result:
The current flowing through the resistor = 2.2 A
Problem : 3
Calculate the resistance of the conductor if a current of 2A flows through it when the
potential difference across its ends is 6V.
Given data
Current I = 2A
Voltage V = 6V
To find:
Resistance R = ?
Formula used:
Resistance R = V / I
Solution:
Resistance R = 6 / 2
=3Ω
Result:
The value of resistance R = 3Ω
Problem: 4
Calculate the current and resistance of a 100 W, 200V electric bulb.
Given data:
Power P = 100W
Voltage V = 200V
To find:
Current I =?
Resistance R =?
Formula used:
Power P = V *I
Current I = P / V

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Solution:
Current I = P / V
= 100 / 200
= 0.5 A
= 200 / 0.2
= 400 Ω
Result:
The value of the current I = 0.5 A
The value of the Resistance R = 400 Ω
Problem: 5
A circuit is made of 0.4 Ω wire, a 150Ω bulb and a 120Ω rheostat connected in series. Determine
the total resistance of the circuit.
Given data:
Resistance of the wire = 0.4Ω
Resistance of bulb =150Ω
Resistance of rheostat = 120Ω
To find:
The total resistance of the circuit R T =?
Formula used:
The total resistance of the circuit R T = R1+R2+R3
Solution:
Total resistance ,R = 0.4 + 150 +120
= 270.4Ω
Result:
The total resistance of the circuit R T = 270.4 Ω
Problem 6:
Three resistances of values 2Ω, 3Ω and 5Ω are connected in series across 20 V, D.C supply
.Calculate (a) equivalent resistance of the circuit (b) the total current of the circuit (c) the voltage
drop across each resistor and (d) the power dissipated in each resistor.
Given data:
R1 = 2Ω
R2 = 3Ω
R3 = 5Ω
V = 20V

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To find:
R T =?
I T =?
V1, V2, V3 =?
P1, P2, P3 =?
Formula used:
RT = R1+R2+R3 (series connection)
IT = VT / RT
V1 = R1*I1
V2= R2*I2
V3 = R3*I3
P1=V1*I1
P2=V2*I2
P3=V3*I3
Solution:
RT = R1+R2+R3
= 2+3+5
RT = 10Ω
IT = VT / RT
= 20 / 10
IT = 2 A
In series connection I1 = I2 = I3 = IT = 2A
V1 = I1*R1
= 2*2
V1 = 4 V
V2 = I2*R2
= 2*3
V2 = 6 V
V3 = I3*R3
= 5*2
V3 = 10V
P1 = V1*I1
= 4*2
P1 = 8W
P2 = V2*I2
= 6*2
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P2 = 12W
P3 = V3*I3
= 10*2
P3 = 20W
Result:
(a). Equivalent resistance of the circuit RT = 10Ω
(b). The total current of the circuit I T = 2A
(c). Voltage drop across each resistor V1 = 4 V, V2 = 6 V, V3 = 10V
(d). The power dissipated in each resistor P1 = 8W, P2 = 12W, P3 = 20W
Star Delta transformation:

Star to Delta transformation:

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Star Delta Transformations allow us to convert impedances connected together from one type
of connection to another. We can now solve simple series, parallel or bridge type resistive
networks using Kirchhoff´s Circuit Laws, mesh current analysis or nodal voltage analysis
techniques but in a balanced 3-phase circuit we can use different mathematical techniques to
simplify the analysis of the circuit and thereby reduce the amount of math’s involved which in
itself is a good thing.
Standard 3-phase circuits or networks take on two major forms with names that represent the
way in which the resistances are connected, a Star connected network which has the symbol of
the letter, Υ (wye) and a Delta connected network which has the symbol of a triangle, Δ (delta).
If a 3-phase, 3-wire supply or even a 3-phase load is connected in one type of configuration, it
can be easily transformed or changed it into an equivalent configuration of the other type by
using either the Star Delta Transformation or Delta Star Transformation process.
A resistive network consisting of three impedances can be connected together to form a T or

“Tee” configuration but the network can also be redrawn to form a Star or Υ type network as
shown below.
As we have already seen, we can redraw the T resistor network to produce an

equivalent Star or Υ type network. But we can also convert a Pi or π type resistor network into an
equivalent Delta or Δ type network as shown below.

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Pi-connected and Equivalent Delta Network.
Having now defined exactly what is a Star and Delta connected network it is possible to
transform the Υ into an equivalent Δ circuit and also to convert a Δ into an equivalent Υ circuit
using a the transformation process. This process allows us to produce a mathematical
relationship between the various resistors giving us a Star Delta Transformation as well as
a Delta Star Transformation.
These Circuit Transformations allow us to change the three connected resistances (or
impedances) by their equivalents measured between the terminals 1-2, 1-3 or 2-3 for either a star
or delta connected circuit. However, the resulting networks are only equivalent for voltages and
currents external to the star or delta networks, as internally the voltages and currents are different
but each network will consume the same amount of power and have the same power factor to
each other.
The value of the resistor on any one side of the delta, Δ network is the sum of all the two-product
combinations of resistors in the star network divide by the star resistor located “directly
opposite” the delta resistor being found.
For example, resistor A is given as:
A= (PQ + QR + RP) / R with respect to terminal 3
and resistor B is given as:
B = (PQ + QR + RP) / Q with respect to terminal 2 and
resistor C given as:
B = (PQ + QR + RP) / R with respect to terminal 1.
By dividing out each equation by the value of the denominator we end up with three separate
transformation formulas that can be used to convert any Delta resistive network into an
equivalent star network as given below.
Star Delta Transformation allows us to convert one type of circuit connection into another type
in order for us to easily analyze the circuit and star delta transformation techniques can be used
for either resistances or impedances.
One final point about converting a star resistive network to an equivalent delta network. If all the
resistors in the star network are all equal in value then the resultant resistors in the equivalent
delta network will be three times the value of the star resistors and equal,
giving: RDELTA = 3RSTAR

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Delta to Star Transformation
Compare the resistances between terminals 1 and 2.

P+Q= A in parallel with (B+C)
P+Q = A(B+C) / A+B+C........................ (1)
Resistance between the terminals 2 and 3.

Q+R = C in parallel with (A+B)
Q+R=C(A+B) / A+B+C ....................... (2)
Resistance between the terminals 1 and 3.

P+R = B in parallel with (A+C)
P+R = B(A+C) / A+B+C .......................(3)
This now gives us three equations and taking equation 3 from equation 2 gives:
P+R-Q-R = (B(A+C)) –( C(A+B) ) / A+B+C
P-Q =(BA + BC – CA – BC) / A+B+C
P-Q = BA – CA / (A+B+C)… ............... (4)
Then, re-writing Equation 1 will give us:

P+Q = (AB+AC) / A+B+C ................................ (5)
Equ (4) + Equ (5)

P+Q+ P-Q = (AB+AC) / A+B+C + (BA – CA) / A+B+C
2P = (AB+AC+BA-CA) / A+B+C
2P = 2AB / A+B+C
P = AB / A+B+C
Then to summarize a little about the above maths, we can now say that resistor P in a Star
network can be found as Equation 1 plus (Equation 3 minus Equation 2) or Eq1 + (Eq3 – Eq2).
Similarly, to find resistor Q in a star network, is equation 2 plus the result of equation 1 minus
equation 3 or Eq2 + (Eq1 – Eq3) and this gives us the transformation of Q as:
Q = AC / A+B+C
and again, to find resistor R in a Star network, is equation 3 plus the result of equation 2 minus
equation 1 or Eq3 + (Eq2 – Eq1) and this gives us the transformation of R as:
R = BC / A+B+C
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When converting a delta network into a star network the denominators of all of the
transformation formulas are the same: A + B + C, and which is the sum of ALL the delta
resistances. Then to convert any delta connected network to an equivalent star network
If the three resistors in the delta network are all equal in value then the resultant resistors in the
equivalent star network will be equal to one third the value of the delta resistors, giving each
branch in the star network as: RSTAR = 1/3RDELTA

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UNIT II – DC MACHINES
2.1 DC GENERATOR - INTRODUCTION
An electrical generator is a device that converts mechanical energy to electrical
energy, generally using electromagnetic induction. The source of mechanical energy may be a
reciprocating or turbine steam engine, water falling through a turbine or waterwheel, an internal
combustion engine, a wind turbine, a hand crank, or any other source of mechanical energy.
The Dynamo was the first electrical generator capable of delivering power for industry.
The dynamo uses electromagnetic principles to convert mechanical rotation into an alternating
electric current. A dynamo machine consists of a stationary structure which generates a strong
magnetic field, and a set of rotating windings which turn within that field. On small machines the
magnetic field may be provided by a permanent magnet; larger machines have the magnetic field
created by electromagnets. The energy conversion in generator is based on the principle of the
production of dynamically induced e.m.f. whenever a conductor cuts magneticic flux,
dynamically induced e.m.f is produced in it according to Faraday's Laws of Electromagnetic
induction. This e.m.f causes a current to flow if the conductor circuit is closed.
2.1.1 CONSTRUCTION OF D.C. MACHINES
A D.C. machine consists mainly of two part the stationary part called stator and the
rotating part called rotor.The stator consists of main poles used to produce magnetic flux
,commutating poles or interpoles in between the main poles to avoid sparking at the commutator
but in the case of small machines sometimes the interpoles are avoided and finally the frame or
yoke which forms the supporting structure of the machine. The rotor consist of an armature a
cylindrical metallic body or core with slots in it to place armature windings or bars,a commutator
and brush gears The magnetic flux path in a motor or generator is show below and it is called the
magnetic structure of generator or motor.
The major parts can be identified as,
1. Frame
2. Poles
3. Armature
4. Field winding
5. Commutator
6. Brush
7. Other mechanical parts
Frame
Frame is the stationary part of a machine on which the main poles and commutator poles
are bolted and it forms the supporting structure by connecting the frame to the bed plate. The
ring shaped body portion of the frame which makes the magnetic path for the magnetic fluxes
from the main poles and interpoles is called Yoke.
Why we use cast steel instead of cast iron for the construction of Yoke?

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In early days Yoke was made up of cast iron but now it is replaced by cast steel.This is
because cast iron is saturated by a flux density of 0.8 Wb/sq.m where as saturation with cast iron
steel is about 1.5 Wb/sq.m.So for the same magnetic flux density the cross section area needed
for cast steel is less than cast iron hence the weight of the machine too.If we use cast iron there
may be chances of blow holes in it while casting.so now rolled steels are developed and these
have consistent magnetic and mechanical properties.
poles:
Solid poles of fabricated steel with separate/integral pole shoes are fastened to the frame
by means of bolts. Pole shoes are generally laminated. Sometimes pole body and pole shoe are
formed from the same laminations. The pole shoes are shaped so as to have a slightly increased
air gap at the tips. Inter-poles are small additional poles located in between the main poles.
These can be solid, or laminated just as the main poles. These are also fastened to the
yoke by bolts. Sometimes the yoke may be slotted to receive these poles. The inter poles could
be of tapered section or of uniform cross section. These are also called as commutating poles or
com poles. The width of the tip of the com pole can be about a rotor slot pitch.
Armature
The armature is where the moving conductors are located. The armature is constructed by
stacking laminated sheets of silicon steel. Thickness of these lamination is kept low to reduce
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eddy current losses. As the laminations carry alternating flux the choice of suitable material,
insulation coating on the laminations, stacking it etc are to be done more carefully. The core is
divided into packets to facilitate ventilation. The winding cannot be placed on the surface of the
rotor due to the mechanical forces coming on the same. Open parallel sided equally spaced slots
are normally punched in the rotor laminations.
These slots house the armature winding. Large sized machines employ a spider on which
the laminations are stacked in segments. End plates are suitably shaped so as to serve as
’Winding supporters’. Armature construction process must ensure provision of sufficient axial
and radial ducts to facilitate easy removal of heat from the armature winding.
Field windings:
In the case of wound field machines (as against permanent magnet excited machines) the
field winding takes the form of a concentric coil wound around the main poles. These carry the
excitation current and produce the main field in the machine. Thus the poles are created
electromagnetically. Two types of windings are generally employed. In shunt winding large
number of turns of small section copper conductor is used. The resistance of such winding
would be an order of magnitude larger than the armature winding resistance. In the case of series
winding a few turns of heavy cross section conductor is used. The resistance of such windings is
low and is comparable to armature resistance. Some machines may have both the windings on
the poles. The total ampere turns required to establish the necessary flux under the poles is
calculated from the magnetic circuit calculations. The total mmf required is divided equally
between north and south poles as the poles are produced in pairs. The mmf required to be shared
between shunt and series windings are apportioned as per the design requirements. As these
work on the same magnetic system they are in the form of concentric coils. Mmf ’per pole’ is
normally used in these calculations. Armature winding As mentioned earlier, if the armature
coils are wound on the surface of the armature, such construction becomes mechanically weak.
The conductors may fly away when the armature starts rotating. Hence the armature windings
are in general pre-formed, taped and lowered into the open slots on the armature. In the case of
small machines, they can be hand wound. The coils are prevented from flying out due to the
centrifugal forces by means of bands of steel wire on the surface of the rotor in small groves cut
into it. In the case of large machines slot wedges are additionally used to restrain the coils from
flying away. The end portion of the windings are taped at the free end and bound to the winding
carrier ring of the armature at the commutator end. The armature must be dynamically balanced
to reduce the centrifugal forces at the operating speeds. Compensating winding One may find a
bar winding housed in the slots on the pole shoes. This is mostly found in d.c. machines of very
large rating. Such winding is called compensating winding. In smaller machines, they may be
absent.

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Commutator:
Commutator is the key element which made the d.c. machine of the present day possible.
It consists of copper segments tightly fastened together with mica/micanite insulating separators
on an insulated base. The whole commutator forms a rigid and solid assembly of insulated
copper strips and can rotate at high speeds. Each commutator segment is provided with a ’riser’
where the ends of the armature coils get connected. The surface of the commutator is machined
and surface is made concentric with the shaft and the current collecting brushes rest on the same.
Under-cutting the mica insulators that are between these commutator segments has to be done
periodically to avoid fouling of the surface of the commutator by mica when the commutator
gets worn out. Some details of the construction of the commutator are seen in Fig
Brush and brush holders:

Brushes rest on the surface of the commutator. Normally electro-graphite is used as brush
material. The actual composition of the brush depends on the peripheral speed of the commutator
and the working voltage. The hardness of the graphite brush is selected to be lower than that of
the commutator. When the brush wears out the graphite works as a solid lubricant reducing
frictional coefficient. More number of relatively smaller width brushes are preferred in place of
large broad brushes. The brush holders provide slots for the brushes to be placed. The connection
Brush holder with a Brush and Positioning of the brush on the commutator from the brush is
taken out by means of flexible pigtail. The brushes are kept pressed on the commutator with the
help of springs. This is to ensure proper contact between the brushes and the commutator even
under high speeds of operation. Jumping of brushes must be avoided to ensure arc free current
collection and to keep the brushcontact drop low. Other mechanical parts End covers, fan and
shaft bearings form other important mechanical parts. End covers are completely solid or have
opening for ventilation. They support the bearings which are on the shaft. Proper machining is to
be ensured for easy assembly. Fans can be external or internal. In most machines the fan is on the
non-commutator end sucking the air from the commutator end and throwing the same out.
Adequate quantity of hot air removal has to be ensured. Bearings Small machines employ ball
bearings at both ends. For larger machines roller bearings are used especially at the driving end.
The bearings are mounted press-fit on the shaft. They are housed inside the end shield in such a
manner that it is not necessary to remove the bearings from the shaft for dismantling.
End Shields or Bearings

If the armature diameter does not exceed 35 to 45 cm then in addition to poles end shields
or frame head with bearing are attached to the frame.If the armature diameter is greater than 1m
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pedestral type bearings are mounted on the machine bed plate outside the frame.These bearings
could be ball or roller type but generally plain pedestral bearings are employed.If the diameter of
the armature is large a brush holder yoke is generally fixed to the frame.
2.1.2 PRINCIPLE OF OPERATION
DC generator converts mechanical energy into electrical energy. when a conductor move
in a magnetic field in such a way conductors cuts across a magnetic flux of lines and emf
produces in a generator and it is defined by faradays law of electromagnetic induction emf
causes current to flow if the conductor circuit is closed.
The pole pieces (marked N and S) provide the magnetic field. The pole pieces are shaped
and positioned as shown to concentrate the magnetic field as close as possible to the wire loop.
The loop of wire that rotates through the field is called the ARMATURE. The ends of the
armature loop are connected to rings called SLIP RINGS. They rotate with the armature. The
brushes, usually made of carbon, with wires attached to them, ride against the rings. The
generated voltage appears across these brushes. The elementary generator produces a voltage in
the following manner (fig. 1-3). The armature loop is rotated in a clockwise direction. The initial
or starting point is shown at position A. (This will be considered the zero-degree position.) At
0º_ the armature loop is perpendicular to the magnetic field. The black and white conductors of
the loop are moving parallel to the field. The instant the conductors are moving parallel to the
magnetic field, they do not cut any lines of flux. Therefore, no emf is induced in the conductors,
and the meter at position A indicates zero. This position is called the NEUTRAL PLANE. As the
armature loop rotates from position A (0º) to position B (90º), the conductors cut through more
and more lines of flux, at a continually increasing angle. At 90º_ they are cutting through a
maximum number of lines of flux and at maximum angle. The result is that between 0º_ and
90º_, the induced emf in the conductors builds up from zero to a maximum value. Observe that
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from 0º_ to 90º_, the black conductor cuts DOWN through the field. At the same time the white
conductor cuts UP through the field.
The induced emfs in the conductors are series-adding. This means the resultant voltage across
the brushes (the terminal voltage) is the sum of the two induced voltages. The meter at position B
reads maximum value. As the armature loop continues rotating from 90º_ (position B) to 180º_
(position C), the conductors which were cutting through a maximum number of lines of flux at
position B now cut through fewer lines. They are again moving parallel to the magnetic field at
position C. They no longer cut through any lines of flux. As the armature rotates from 90º_ to
180º_, the induced voltage will decrease to zero in the same manner that it increased during the
rotation from 0º_ to 90º_. The meter again reads zero. From 0º_ to 180º_ the conductors of the
armature loop have been moving in the same direction through the magnetic field. Therefore, the
polarity of the induced voltage has remained the same. This is shown by points A through C on
the graph. As the loop rotates beyond 180º_ (position C), through 270º_ (position D), and back to
the initial or starting point (position A), the direction of the cutting action of the conductors
through the magnetic field reverses. Now the black conductor cuts UP through the field while the
white conductor cuts DOWN through the field. As a result, the polarity of the induced voltage
reverses. Following the sequence shown by graph points C, D, and back to A, the voltage will
be in the direction opposite to that shown from points A, B, and C. The terminal voltage will be
the same as it was from A to C except that the polarity is reversed (as shown by the meter
deflection at position D). The voltage output waveform for the complete revolution of the loop is
shown on the graph in figure

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2.1.3 GENERATOR E.M.F EQUATION

Let
Φ = flux/pole in weber
Z = total number of armture conductors
= No.of slots x No.of conductors/slot
P = No.of generator poles
A = No.of parallel paths in armature
N = armature rotation in revolutions per minute (r.p.m)
E = e.m.f induced in any parallel path in armature
Generated e.m.f Eg = e.m.f generated in any one of the parallel paths i.e E.
Average e.m.f geneated /conductor = dΦ/dt volt (n=1)
Now, flux cut/conductor in one revolution dΦ = ΦP Wb
No.of revolutions/second = N/60
Time for one revolution, dt = 60/N second
Hence, according to Faraday's Laws of Electroagnetic Induction,
E.M.F generated/conductor is
For a simplex wave-wound generator

No.of parallel paths = 2
No.of conductors (in series) in one path = Z/2
E.M.F. generated/path is

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For a simplex lap-wound generator

No.of parallel paths = P
No.of conductors (in series) in one path = Z/P
E.M.F.generated/path
In general generated e.m.f
where A = 2 for simplex wave-winding

A = P for simplex lap-winding
2.1.4 TYPES OF D.C. GENERATORS

The magnetic field in a d.c. generator is normally produced by electromagnets rather than
permanent magnets. Generators are generally classified according to their methods of field
excitation. On this basis, d.c. generators are divided into the following two classes:
(i) Separately excited d.c. generators
(ii) Self-excited d.c. generators
The behaviour of a d.c. generator on load depends upon the method of field excitation adopted.
(i) Separately Excited D.C. Generators

A d.c. generator whose field magnet winding is supplied from an independent external
d.c. source (e.g., a battery etc.) is called a separately excited generator. Fig shows the
connections of a separately excited generator. The voltage output depends upon the speed of
rotation of armature and the field current (Eg =PfØ ZN/60 A). The greater the speed and field
current, greater is the generated e.m.f. It may be noted that separately excited d.c. generators are
rarely used in practice. The d.c. generators are normally of self-excited type.

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Armature current, Ia = IL
Terminal voltage, V = Eg - IaRa
Electric power developed = EgIa
Power delivered to load = EgIa - Ia2Ra
(ii) Self-Excited D.C. Generators

A d.c. generator whose field magnet winding is supplied current from the output of the
generator itself is called a self-excited generator. There are three types of self-excited generators
depending upon the manner in which the field winding isconnected to the armature, namely;
(a) Series generator;
(b) Shunt generator;
(c) Compound generator
(a) Series generator

In a series wound generator, the field winding is connected in series with armature
winding so that whole armature current flows through the field winding as well as the load. Fig.
shows the connections of a series wound generator. Since the field winding carries the whole of
load current, it has a few turns of thick wire having low resistance. Series generators are rarely
used except for special purposes e.g., as boosters.
Armature current, Ia = Ise = IL = I(say)

Terminal voltage, V = EG - I(Ra + Rse)
Power developed in armature = EgIa
Power delivered to load
(b) Shunt generator

In a shunt generator, the field winding is connected in parallel with the armature winding
so that terminal voltage of the generator is applied across it. The shunt field winding has many
turns of fine wire having high resistance. Therefore, only a part of armature current flows

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through shunt field winding and the rest flows through the load. Fig. shows the connections of a
shunt-wound generator.
Shunt field current, Ish = V/Rsh

Armature current, Ia = IL + Ish
Terminal voltage, V = Eg - IaRa
Power developed in armature = EgIa
Power delivered to load = VIL
(c) Compound generator

In a compound-wound generator, there are two sets of field windings on each pole—one
is in series and the other in parallel with the armature. A compound wound generator may be:
Short Shunt in which only shunt field winding is in parallel with the armature winding.Long
Shunt in which shunt field winding is in parallel with both series field and armature winding

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2.1.5 APPLICATIONS OF DC GENERATOR

DC Separately Exited Generator:
As a supply source to DC Motors, whose speed is to be controlled for certain
applications. Where a wide range of voltage is required for the testing purposes.
DC Shunt Generator
The terminal voltage of DC shunt generator is more or less constant from no load to full
load .Therefore these generators are used where constant voltage is required.
For electro plating

Battery charging
For excitation of Alternators.

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DC Series Generator
The terminal voltage of series generator increases with load current from no load to full
load .Therefore these generators are,
Used as Boosters
Used for supply to arc Lamps
DC Compound Generator:
Differential Compound generators are used to supply dc welding machines. Level compound
generators are used to supply power for offices, hostels and Lodges etc. Over compound
generators are used to compensate the voltage drop in Feeders.
2.2 DC MOTOR - INTRODUCTION
A machine that converts dc power into mechanical energy is known as dc motor. Its
operation is based on the principle that when a current carrying conductor is placed in a magnetic
field, the conductor experiences a mechanical force. The direction of the force is given by
Fleming’s left hand rule.
How DC motors work?

There are different kinds of D.C. motors, but they all work on the same principles.When
a permanent magnet is positioned around a loop of wire that is hooked up to a D.C. power
source, we have the basics of a D.C. motor. In order to make the loop of wire spin, we have to
connect a battery or DC power supply between its ends, and support it so it can spin about its
axis. To allow the rotor to turn without twisting the wires, the ends of the wire loop are
connected to a set of contacts called the commutator, which rubs against a set of conductors
called the brushes. The brushes make electrical contact with the commutator as it spins, and are
connected to the positive and negative leads of the power source, allowing electricity to flow
through the loop. The electricity flowing through the loop creates a magnetic field that interacts
with the magnetic field of the permanent magnet to make the loop spin.
2.2.1 PRINCIPLES OF OPERATION

It is based on the principle that when a current-carrying conductor is placed in a magnetic
field, it experiences a mechanical force whose direction is given by Fleming's Left-hand rule and
whose magnitude is given by
Force, F = B I l newton
Where B is the magnetic field in weber/m2.
I is the current in amperes and
l is the length of the coil in meter.
The force, current and the magnetic field are all in different directions.
If an Electric current flows through two copper wires that are between the poles of a magnet, an
upward force will move one wire up and a downward force will move the other wire down.

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2.2.2 BACK OR COUNTER EMF
When the armature of a d.c. motor rotates under the influence of the driving torque, the
armature conductors move through the magnetic field and hence an e.m.f. is induced in them.
The induced e.m.f. acts in opposite direction to the applied voltage V(Lenz’s law) and is known
as back orcounter e.m.f. Eb.

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2.2.3 SIGNIFICANCE OF BACK E.M.F

The presence of back e.m.f. makes the d.c. motor a self-regulating machine i.e., it makes
the motor to draw as much armature current as is just sufficient to develop the torque required by
the load. Back e.m.f. in a d.c. motor regulates the flow of armature current i.e., it automatically
changes the armature current to meet the load requirement.
2.2.4 CLASSIFICATION OF MOTOR

DC motors are more common than we may think. A car may have as many as 20 DC
motors to drive fans, seats, and windows. They come in three different types, classified
according to the electrical circuit used. In the shunt motor, the armature and field windings are
connected in parallel, and so the currents through each are relatively independent. The current
through the field winding can be controlled with a field rheostat (variable resistor), thus allowing
a wide variation in the motor speed over a large range of load conditions. This type of motor is
used for driving machine tools or fans, which require a wide range of speeds.
In the series motor, the field winding is connected in series with the armature winding,
resulting in a very high starting torque since both the armature current and field strength run at
their maximum. However, once the armature starts to rotate, the counter EMF reduces the
current in the circuit, thus reducing the field strength. The series motor is used where a large
starting torque is required, such as in automobile starter motors, cranes, and hoists.
The compound motor is a combination of the series and shunt motors, having parallel and series
field windings. This type of motor has a high starting torque and the ability to vary the speed and
is used in situations requiring both these properties such as punch presses, conveyors and
elevators.

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2.2.5 DC MOTOR TYPES
1. Shunt Wound
2. Series Wound
3. Compound wound
1. Shunt Motor
In shunt wound motor the field winding is connected in parallel with armature. The
current through the shunt field winding is not the same as the armature current. Shunt field
windings are designed to produce the necessary m.m.f. by means of a relatively large number of
turns of wire having high resistance. Therefore, shunt field current is relatively small compared
with the armature current
2. Series Motor
In series wound motor the field winding is connected in series with the armature.
Therefore, series field winding carries the armature current. Since the current passing through a
series field winding is the same as the armature current, series field windings must be designed
with much fewer turns than shunt field windings for the same mmf.Therefore, a series field
winding has a relatively small number of turns of thick wire and, therefore, will possess a low
resistance.
3. Compound Wound Motor

Compound wound motor has two field windings; one connected in parallel with the
armature and the other in series with it. There are two types of compound motor connections
1) Short-shunt connection
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2) Long shunt connection

When the shunt field winding is directly connected across the armature terminals it is called
short-shunt connection.
When the shunt winding is so connected that it shunts the series combination of armature and
series field it is called long-shunt connection.
2.2.6 VOLTAGE EQUATION OF MOTORS

Let in a d.c. motor
V = applied voltage
Eb = back e.m.f.
Ra = armature resistance
Ia = armature current

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Since back e.m.f. Eb acts in opposition to the applied voltage V, the net voltage across the
armature circuit is V-Eb.
The armature current Ia is given by
2.2.7 APPLICATIONS OF DC MOTORS:
1. D.C Shunt Motors:

It is a constant speed motor.Where the speed is required to remain almost constant from noload
to full load.Where the load has to be driven at a number of speeds and any one of which is nearly
constant.
Industrial use:
Lathes
Drills
Boring mills
Shapers
Spinning and Weaving machines.
2. D.CSeries motor:
It is a variable speed motor.The speed is low at high torque.At light or no load ,the motor
speed attains dangerously high speed.The motor has a high starting torque.(elevators,electric
traction)
Industrial Uses:
Electric traction
Cranes
Elevators
Air compressor
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3. D.C Compound motor:

Differential compound motors are rarely used because of its poor torque characteristics.
Industrial uses:
PressesShears
Reciprocating machine.

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UNIT 3.TRANSFORMERS – INTRODUCTION
A TRANSFORMER is a device that transfers electrical energy from one circuit to

another by electromagnetic induction (transformer action). The electrical energy is always
transferred without a change in frequency, but may involve changes in magnitudes of voltage
and current. Because a transformer works on the principle of electromagnetic induction, it must
be used with an input source voltage that varies in amplitude. There are many types of power that
fit this description; for ease of explanation and understanding, transformer action will be
explained using an ac voltage as the input source.
2.2.8 BASIC OPERATION OF A TRANSFORMER
In its most basic form a transformer consists of:

A primary coil or winding.
A secondary coil or winding.
A core that supports the coils or windings.
Refer to the transformer circuit in figure as you read the following explanation: The primary
winding is connected to a 60 hertz ac voltage source. The magnetic field (flux) builds up
(expands) and collapses (contracts) about the primary winding. The expanding and contracting
magnetic field around the primary winding cuts the secondary winding and induces an
alternating voltage into the winding. This voltage causes alternating current to flow through the
load. The voltage may be stepped up or down depending on the design of the primary and
secondary windings.

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2.2.9 AN IDEAL TRANSFORMER

An ideal transformer is shown in the adjacent figure. Current passing through the primary
coil creates a magnetic field. The primary and secondary coils are wrapped around a core of very
high magnetic permeability, such as iron, so that most of the magnetic flux passes through both
the primary and secondary coils.
2.2.10 BASIC WORKING PRINCIPLE OF TRANSFORMER

A transformer can be defined as a static device which helps in the transformation of
electric power in one circuit to electric power of the same frequency in another circuit. The
voltage can be raised or lowered in a circuit, but with a proportional increase or decrease in the
current ratings.
The main principle of operation of a transformer is mutual inductance between two
circuits which is linked by a common magnetic flux. A basic transformer consists of two coils
that are electrically separate and inductive, but are magnetically linked through a path of
reluctance. The working principle of the transformer can be understood from the figure below.
As shown above the transformer has primary and secondary windings. The core
laminations are joined in the form of strips in between the strips you can see that there are some
narrow gaps right through the cross-section of the core. These staggered joints are said to be
‘imbricated’. Both the coils have high mutual inductance. A mutual electro-motive force is
induced in the transformer from the alternating flux that is set up in the laminated core, due to
the coil that is connected to a source of alternating voltage. Most of the alternating flux
developed by this coil is linked with the other coil and thus produces the mutual induced electro-
motive force. The so produced electro-motive force can be explained with the help of Faraday’s
laws of Electromagnetic Induction as
e=M*dI/dt
If the second coil circuit is closed, a current flows in it and thus electrical energy is transferred
magnetically from the first to the second coil.

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The alternating current supply is given to the first coil and hence it can be called as the primary
winding. The energy is drawn out from the second coil and thus can be called as the secondary
winding.
In short, a transformer carries the operations shown below:
Transfer of electric power from one circuit to another.

Transfer of electric power without any change in frequency.
Transfer with the principle of electromagnetic induction.
The two electrical circuits are linked by mutual induction
2.2.11 TRANSFORMER CONSTRUCTION

Two coils of wire (called windings) are wound on some type of core material. In some
cases the coils of wire are wound on a cylindrical or rectangular cardboard form. In effect, the
core material is air and the transformer is called an AIR-CORE TRANSFORMER. Transformers
used at low frequencies, such as 60 hertz and 400 hertz, require a core of low-reluctance
magnetic material, usually iron. This type of transformer is called an IRON-CORE
TRANSFORMER. Most power transformers are of the iron-core type.
The principle parts of a transformer and their functions are:
• The CORE, which provides a path for the magnetic lines of flux.
• The PRIMARY WINDING, which receives energy from the ac source.
• The SECONDARY WINDING, which receives energy from the primary winding and delivers it
to the load.
• The ENCLOSURE, which protects the above components from dirt, moisture, and mechanical
damage.
(i) CORE

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There are two main shapes of cores used in laminated-steel-core transformers. One is the
HOLLOWCORE, so named because the core is shaped with a hollow square through the center.
This shape of core. Notice that the core is made up of many laminations of steel it shows how the
transformer windings are wrapped around both sides of the core.
(ii) WINDINGS
As stated above, the transformer consists of two coils called WINDINGS which are
wrapped around a core. The transformer operates when a source of ac voltage is connected to
one of the windings and a load device is connected to the other. The winding that is connected to
the source is called the PRIMARY WINDING. The winding that is connected to the load is
called the SECONDARY WINDING. The primary is wound in layers directly on a rectangular
cardboard form.
2.2.12 EMF Equation of Transformer:

Let the applied voltage V1 applied to the primary of a transformer, with secondary open-
circuited, be sinusoidal (or sine wave). Then the current I1, due to applied voltage V1, will also
be a sine wave. The mmf N1 I1 and core flux Ø will follow the variations of I1 closely. That is
the flux is in time phase with the current I1 and varies sinusoidally.
Let,
NA = Number of turns in primary
NB = Number of turns in secondary
Ømax = Maximum flux in the core in webers = Bmax X A
f = Frequency of alternating current input in hertz (HZ)
As shown in figure above, the core flux increases from its zero value to maximum value Ømax in
one quarter of the cycle , that is in ¼ frequency second.
Therefore, average rate of change of flux = Ømax/ ¼ f = 4f ØmaxWb/s
Now, rate of change of flux per turn means induced electro motive force in volts.
Therefore,
average electro-motive force induced/turn = 4f Ømaxvolt
If flux Ø varies sinusoidally, then r.m.s value of induced e.m.f is obtained by multiplying the
average value with form factor.
Form Factor = r.m.s. value/average value = 1.11
Therefore, r.m.s value of e.m.f/turn = 1.11 X 4f Ø max = 4.44f Ømax
Now, r.m.s value of induced e.m.f in the whole of primary winding
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= (induced e.m.f./turn) X Number of primary turns

Therefore,
EA = 4.44f NAØmax = 4.44fNABmA
Similarly, r.m.s value of induced e.m.f in secondary is
EB = 4.44f NB Ømax = 4.44fNBBmA
In an ideal transformer on no load, VA = EA and VB = EB , where VB is the terminal voltage
Voltage Transformation Ratio.

The ratio of secondary voltage to primary voltage is known as the voltage transformation
ratio and is designated by letter K. i.e.
Voltage transformation ratio, K = V2/V1 = E2/E1 = N2/N1
Current Ratio.
The ratio of secondary current to primary current is known as current ratio and is
reciprocal of voltage transformation ratio in an ideal transformer.
2.2.13 Transformer on No Load.

When the primary of a transformer is connected to the source of an ac supply and the
secondary is open circuited, the transformer is said to be on no load. The Transformer on No
Load alternating applied voltage will cause flow of an alternating current I0 in the primary
winding, which will create alternating flux Ø. No-load current I0, also known as excitation or
exciting current, has two components the magnetizing component Im and the energy component
Ie. Im is used to create the flux in the core and Ie is used to overcome the hysteresis and eddy
current losses occurring in the core in addition to small amount of copper losses occurring in the
primary only (no copper loss occurs in the secondary, because it carries no current, being open
circuited.)
From vector diagram shown in above it is obvious that
1. Induced emfs in primary and secondary windings, E1 and E2 lag the main flux Ø by
and are in phase with each other.
2. Applied voltage to primary V1 and leads the main flux Ø by and is in phase opposition
to E1.

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3. Secondary voltage V2 is in phase and equal to E2 since there is no voltage drop in

secondary.
4. Im is in phase with Ø and so lags V1 by
5. Ie is in phase with the applied voltage V1.
6. Input power on no load = V1Ie = V1I0 cos Ø0 where Ø0 = tan-1
2.2.14 Transformer on Load:

The transformer is said to be loaded, when its secondary circuit is completed through an
impedance or load. The magnitude and phase of secondary current (i.e. current flowing through
secondary) I2 with respect to secondary terminals depends upon the characteristic of the load i.e.
current I2 will be in phase, lag behind and lead the terminal voltage V+2+ respectively when the
load is non-inductive, inductive and capacitive. The net flux passing through the core remains
almost constant from no-load to full load irrespective of load conditions and so core losses
remain almost constant from no-load to full load. Vector diagram for an ideal transformer
supplying inductive load is shown
Resistance and Leakage Reactance In actual practice, both of the primary and secondary
windings have got some ohmic resistance causing voltage drops and copper losses in the
windings. In actual practice, the total flux created does not link both of the primary and
secondary windings but is divided into three components namely the main or mutual flux Ø
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linking both of the primary and secondary windings, primary leakage flux ØL1 linking with
primary winding only and secondary leakage flux ØL2 linking with secondary winding only. The
primary leakage flux ØL1 is produced by primary ampere-turns and is proportional to primary
current, number of primary turns being fixed. The primary leakage flux ØL1 is in phase with I1
and produces self induced emf ØL1 is in phase with I1 and produces self induced emf EL1 given
as 2f L1 I1 in the primary winding.
The self induced emf divided by the primary current gives the reactance of primary and is
denoted by X1.
i.e. X1 = EL1/I1 = 2πfL1I1/I1 = 2FL1,
Similarly leakage reactance of secondary X2 = EL2/E2 = 2fπL2I2/I2 = 2πfL2
Equivalent Resistance and Reactance. The equivalent resistances and reactance’s of transformer
windings referred to primary and secondary sides are given as below Referred to primary side
Equivalent resistance,
Equivalent resistance, = X'1 = Referred to secondary side
Equivalent resistance,
Equivalent resistance, = X2 + K2X1
Where K is the transformation ratio.
2.2.15 EQUIVALENT CIRCUIT OF TRANSFORMER
Equivalent impedance of transformer is essential to be calculated because the electrical

power transformer is an electrical power system equipment for estimating different parameters of
electrical power system which may be required to calculate total internal impedance of
an electrical power transformer, viewing from primary side or secondary side as per requirement.
This calculation requires equivalent circuit of transformer referred to primary or equivalent
circuit of transformer referred to secondary sides respectively. Percentage impedance is also
very essential parameter of transformer. Special attention is to be given to this parameter during
installing a transformer in an existing electrical power system. Percentage impedance of different
power transformers should be properly matched during parallel operation of power transformers.
The percentage impedance can be derived from equivalent impedance of transformer so, it can
be said that equivalent circuit of transformer is also required during calculation of %
impedance.
Equivalent Circuit of Transformer Referred to Primary
For drawing equivalent circuit of transformer referred to primary, first we have to

establish general equivalent circuit of transformer then, we will modify it for referring from
primary side. For doing this, first we need to recall the complete vector diagram of a transformer
which is shown in the figure below.

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Let us consider the transformation ratio be,
In the figure right, the applied voltage to the primary is V1 and voltage across the primary
winding is E1. Total current supplied to primary is I1. So the voltage V1 applied to the primary is
partly dropped by I1Z1 or I1R1 + j.I1X1 before it appears across primary winding. The
voltage appeared across winding is countered by primary induced emf E1.
The equivalent circuit for that equation can be drawn as below,
From the vector diagram above, it is found that the total primary current I1 has two components,
one is no - load component Io and the other is load component I2′. As this primary current has
two a component or branches, so there must be a parallel path with primary winding of

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transformer. This parallel path of current is known as excitation branch of equivalent circuit of
transformer. The resistive and reactive branches of the excitation circuit can be represented as
The load component I2′ flows through the primary winding of transformer and induced
voltage across the winding is E1 as shown in the figure right. This induced voltage E1transforms
to secondary and it is E2 and load component of primary current I2′ is transformed to secondary
as secondary current I2. Current of secondary is I2. So the voltageE2 across secondary winding is
partly dropped by I2Z2 or I2R2 + j.I2X2 before it appears across load. The load voltage is V2.
Again I2′.N1 = I2.N2
Therefore,

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From above equation, secondary impedance of transformer referred to primary is,
So, the complete equivalent circuit of transformer referred to primary is shown in the figure
below,
Approximate Equivalent Circuit of Transformer
Since Io is very small compared to I1, it is less than 5% of full load primary current, I ochanges
the voltage drop insignificantly. Hence, it is good approximation to ignore the excitation circuit
in approximate equivalent circuit of transformer. The winding resistanceand reactance being in
series can now be combined into equivalent resistance and reactance of transformer, referred to
any particular side. In this case it is side 1 or primary side.

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Equivalent Circuit of Transformer Referred to Secondary
In similar way, approximate equivalent circuit of transformer referred to secondary can

be drawn. Where equivalent impedance of transformer referred to secondary, can be derived as
2.2.16 VOLTAGE REGULATION
The voltage regulation is the percentage of voltage difference between no load and full
load voltages of a transformer with respect to its full load voltage.

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Explanation of Voltage Regulation of Transformer
Say an electrical power transformer is open circuited, means load is not connected with
secondary terminals. In this situation, the secondary terminalvoltage of the transformer will be its
secondary induced emf E2. Whenever full load is connected to the secondary terminals of the
transformer, ratedcurrent I2 flows through the secondary circuit and voltage drop comes into
picture. At this situation, primary winding will also draw equivalent full load current from
source. The voltagedrop in the secondary is I2Z2 where Z2 is the secondary impedance of
transformer. Now if at this loading condition, any one measures the voltage between secondary
terminals, he or she will getvoltage V2 across load terminals which is obviously less than no load
secondary voltage E2and this is because of I2Z2 voltage drop in the transformer.
Expression of Voltage Regulation of Transformer, represented in percentage, is

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AC ROTATING MACHINES
SINGLE PHASE INDUCTION MOTOR – INTRODUCTION
The single-phase induction machine is the most frequently used motor for refrigerators, washing
machines, clocks, drills, compressors, pumps, and so forth.
• The single-phase motor stator has a laminated iron core with two windings arranged
perpendicularly.
• One is the main and
• The other is the auxiliary winding or starting winding

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• This “single-phase” motors are truly two phase machines.

• The motor uses a squirrel cage rotor, which has a laminated iron core with slots.
• Aluminum bars are molded on the slots and short-circuited at both ends with a ring.

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The single-phase induction motor operation can be described by two methods:

• Double revolving field theory; and
• Cross-field theory.
Double revolving theory is perhaps the easier of the two explanations to understand
Double revolving field theory

• A single-phase ac current supplies the main winding that produces a pulsating magnetic
field.
• Mathematically, the pulsating field could be divided into two fields, which are rotating in
opposite directions.
• The interaction between the fields and the current induced in the rotor bars generates
opposing torque
• STARTING METHODS
The single-phase IM has no starting torque, but has resultant torque, when it
rotates at any other speed, except synchronous speed. It is also known that, in a balanced
two-phase IM having two windings, each having equal number of turns and placed at a
space angle of 900(electrical), and are fed from a balanced two-phase supply, with two
voltages equal in magnitude, at an angle of 900, the rotating magnetic fields are produced,
as in a three-phase IM. The torque-speed characteristic is same as that of a three-phase
one, having both starting and also running torque as shown earlier. So, in a single-phase
IM, if an auxiliary winding is introduced in the stator, in addition to the main winding,
but placed at a space angle of 900 (electrical), starting torque is produced. The currents in
the two (main and auxiliary) stator windings also must be at an angle of 900 , to produce
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maximum starting torque, as shown in a balanced two-phase stator. Thus, rotating

magnetic field is produced in such motor, giving rise to starting torque. The various
starting methods used in a single-phase IM are described here.
1. RESISTANCE SPLIT-PHASE MOTOR
The schematic (circuit) diagram of this motor is given in Fig. As detailed earlier,
another (auxiliary) winding with a high resistance in series is to be added along with the
main winding in the stator. This winding has higher resistance to reactance () ratio as
compared to that in the main winding, and is placed at a space angle of from the main
winding as given earlier. The phasor diagram of the currents in two windings and the
input voltage is shown in Fig.The current () in the auxiliary winding lags the voltage (V)
by an angle, aaXR/°90aIaφ, which is small, whereas the current () in the main winding
lags the voltage (V) by an angle, mImφ, which is nearly . The phase angle between the
two currents is (°90aφ−°90), which should be at least . This results in a small amount of
starting torque. The switch, S (centrifugal switch) is in series with the auxiliary winding.
It automatically cuts out the auxiliary or starting winding, when the motor attains a speed
close to full load speed. The motor has a starting torque of 100−200% of full load torque,
with the starting current as 5-7 times the full load current. The torque-speed
characteristics of the motor with/without auxiliary winding are shown in Fig.The change
over occurs, when the auxiliary winding is switched off as given earlier. The direction of
rotation is reversed by reversing the terminals of any one of two windings, but not both,
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before connecting the motor to the supply terminals. This motor is used in applications,
such as fan, saw, small lathe, centrifugal pump, blower, office equipment, washing
machine, etc.
2. CAPACITOR-START MOTOR
The schematic (circuit) diagram of this motor is given in Fig. It may be observed
that a capacitor along with a centrifugal switch is connected in series with the auxiliary
winding, which is being used here as a starting winding. The capacitor may be rated only
for intermittent duty, the cost of which decreases, as it is used only at the time of starting.
The function of the centrifugal switch has been described earlier. The phasor diagram of
two currents as described earlier, and the torque-speed characteristics of the motor
with/without auxiliary winding, are shown in Fig. This motor is used in applications, such
as compressor, conveyor, machine tool drive, refrigeration and air-conditioning
equipment, etc.

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3. Capacitor-start and Capacitor-run Motor

In this motor two capacitors − Csfor starting, and Cr for running, are used. The first
capacitor is rated for intermittent duty, as described earlier, being used only for starting. A
centrifugal switch is also needed here. The second one is to be rated for continuous duty, as it is
used for running. The phasor diagram of two currents in both cases, and the torque-speed
characteristics with two windings having different values of capacitors, are shown in
respectively. The phase difference between the two currents is (φ m+φa>900) in the first case
(starting), while it is900 for second case (running). In the second case, the motor is a balanced
two phase one, the two windings having same number of turns and other conditions as given
earlier, are also satisfied. So, only the forward rotating field is present, and the no backward
rotating field exists. The efficiency of the motor under this condition is higher. Hence, using two
capacitors, the performance of the motor improves both at the time of starting and then running.
This motor is used in applications, such as compressor, refrigerator, etc.
Beside the above two types of motors, a Permanent Capacitor Motor with the same
capacitor being utilised for both starting and running, is also used. The power factor of this
motor, when it is operating (running), is high. The operation is also quiet and smooth. This motor
is used in applications, such as ceiling fans, air circulator, blower, etc.
4. Shaded-pole Motor
A typical shaded-pole motor with a cage rotor is shown in Fig. 34.8a. This is a single-
phase induction motor, with main winding in the stator. A small portion of each pole is covered
with a short-circuited, single-turn copper coil called the shading coil. The sinusoidally varying
flux created by ac (single-phase) excitation of the main winding induces emf in the shading coil.
As a result, induced currents flow in the shading coil producing their own flux in the shaded
portion of the pole.
Let the main winding flux be φm=φmaxsinwt
The reversal of the direction of rotation, where desired, can be achieved by providing two
shading coils, one on each end of every pole, and by open-circuiting one set of shading coils and
by short-circuiting the other set.
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The fact that the shaded-pole motor is single-winding (no auxiliary winding) self-starting
one, makes it less costly and results in rugged construction. The motor has low efficiency and is
usually available in a range of 1/300 to 1/20 kW. It is used for domestic fans, record players and
tape recorders, humidifiers, slide projectors, small business machines, etc. The shaded-pole
principle is used in starting electric clocks and other single-phase synchronous timing motors.
no starting torque is produced in the single-phase induction motor with only one (main)
stator winding, as the flux produced is a pulsating one, with the winding being fed from single
phase supply. Using double revolving field theory, the torque-speed characteristics of this type of
motor are described, and it is also shown that, if the motor is initially given some torque in either
direction, the motor accelerates in that direction, and also the torque is produced in that direction.
Then, the various types of single phase induction motors, along with the starting methods used in
each one are presented. Two stator windings − main and auxiliary, are needed to produce the
starting torque. The merits and demerits of each type, along with their application area, are
presented. The process of production of starting torque in shade-pole motor is also described in
brief. In the next module consisting of seven lessons, the construction and also operation of dc
machines, both as generator and motor, will be discussed.

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UNIT4. RECTIFIERS AND LINEAR IC’S

Prerequisites
The semiconductor device i.e., solid state device is capable of amplifying the weak
signal. The devices are solid rather than hollow like the vaccum tube. These semiconductor
devices are smaller in size, more rugged and less power consumption than vaccum tubes. The
various semiconductor devices include semiconductor diode, Zener diode, transistor, JFET,
MOSFET, UJT, SCR, DIAC and TRIAC etc. The semiconductor devices have very wide range
of applications in various fields such as communication systems, medical electronics,
microprocessor based systems, instrumentation, process control, aerospace, consumer
electronics, etc.
1. INTRODUCTION
1.1 Basic Definitions

Valence electrons
The electrons present in the outer most orbit that are loosely bound to the nucleus are
called valence electrons.
Conduction electrons
When an electric field is applied, the valence electrons get detached themselves from the
nucleus, constituting the flow of current. These electrons are called conduction electrons.
Energy band
The (range of) energy possessed by the electrons in an atom is called energy band.
Conduction band
The (range of) energy possessed by the conduction electrons is called conduction band.
Valence electrons
The (range of) energy possessed by the valence electrons is called valence band.
Forbidden energy gap

The gap between the valence band and the conduction band is called forbidden energy
gap.
2. CLASSIFICATION OF MATERIALS
The materials are classified based on their conducting property. Energy band theory can
be used to explain the classification of materials.

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Materials
Conductor semiconductor insulators
2.1 Conductors
Conductor is materials that easily conducts or pass the current. There are plenty of free
electrons available for electric conduction. In terms of energy band theory, the conductors have
overlapping of valence band and conductive band.
Example: Copper, Aluminum, iron, etc
Properties: 1. It is rigid, non directional and crystalline in nature.

2. Conductivity is good.
3. Low melting and boiling temperatures.
2.2 Semiconductors
Semiconductor is a material with partially filled conduction band and valence band. The
current in the semiconductor is due to the movement of electrons and holes. As the temperature
increases the conduction increases.
Example: Silicon, Germanium, etc.
Properties: 1. It is rigid, directional and crystalline in nature.
2. Conductivity can be increased if proper doping material is added.
3. Low melting and boiling temperatures.
2.3 Insulators
In the case of insulators, the valence electrons are very tightly bound to their parent atom.
The valence band and conduction band are separated by a large forbidden energy gap. The
insulators have full valence band and an empty conduction band.
Example: Paper, Mica. Sodium chloride, etc.
Properties: 1. It is rigid, Unidirectional and crystalline in nature.
2. Conductivity is poor in the solid form.
3. High melting and boiling temperatures.

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Energy band structure
2.4 Comparison of Conductors,Semiconductors and Insulators
S.No Conductors Semiconductors Insulators
Conducts the electric current

Easily conducts the Does not conduct any
1 less than conductor and greater
electrical current. current.
than insulator.
Has only one valence Has eight valence

Has four valence electron in its
2 electron in its outermost electron in its
outermost orbit.
orbit. outermost orbit.
Conductor formed using Semiconductors are formed Insulators are formed

3
metallic bonding. due to covalent bonding. due to ionic bonding.
Valence and
Valence and conduction bands conduction bands are
Valence and conduction
4 are separated by forbidden separated by forbidden
bands are overlapped.
energy gap of 1.1eV. energy gap of 6 to
10eV.
Resistance is very
5 Resistance is very small Resistance is high
high
It has negative
It has positive temperature It has negative temperature
6 temperature
coefficient coefficient
coefficient
7 Ex: copper,aluminium,etc Ex: silicon, germanium, etc Ex: Mica, Paper, etc

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2.5 Classification of Semiconductor
Semiconductor
Intrinsic Semiconductor Extrinsic Semiconductor
2.6 Intrinsic Semiconductor
An intrinsic semiconductor also called an undoped semiconductor or i- type

semiconductor.
It is a pure semiconductor without any significant dopant species present.
The number of charge carriers determined by the properties of the m aterial itself instead
of the amount of impurities.
In intrinsic semiconductors the number of excited electrons and the number of holes are
equal: n = p.
Conductivity of Intrinsic semiconductor
 The electrical conductivity of intrinsic semiconductors can be due to crystal defects

or to thermal excitation.
 Both electrons and holes contribute to current flow in an intrinsic
semiconductor.

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 The current which will flow in an intrinsic semiconductor consists of both electron and
hole current.
 That is, the electrons which have been freed from their lattice positions into the
conduction band can move through the material.
 In addition, other electrons can hop between lattice positions to fill the vacancies left
by the freed electrons.
 This additional mechanism is called hole conduction because it is as if the holes are
migrating across the material in the direction opposite to the free electron movement.
 The current flow in an intrinsic semiconductor is influenced by the density of energy

states which in turn influences the electron density in the conduction band.
 This current is highly temperature dependent.

Thermal excitation:
 In an intrinsic semiconductor like silicon at temperatures above absolute zero, there

will be some electrons which are excited across the band gap into the conduction
band and which can produce current.
 When the electron in pure silicon crosses the gap, it leaves behind an electron vacancy or
"hole" in the regular silicon lattice.
 Under the influence of an external voltage, both the electron and the hole can move across
the material. 
 In n-type semiconductor:
The dopant contributes extra electrons, dramatically increasing the conductivity
 In p-type semiconductor:
The dopant produces extra vacancies or holes, which likewise increase the
conductivity.
2.7 Extrinsic Semiconductor
 The electrical conductivity of a pure semiconductor is very small.

 To increase the conductivity, impurities are added.
 The impurity added semiconductor is called extrinsic semiconductor.
 The process of adding impurity is called doping.
 The added impurity is called dopant.
6
 Usually one or two atoms of impurity is added per 10 atoms of a
semiconductor.
 There are two types (i) p-type and (ii) n-type semiconductors.

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(i) n-type semiconductor:
 When an impurity, from V group elements like arsenic (As), antimony having 5
valence electrons is added to Ge (or Si), the impurity atom donates one electron to
Ge (or Si).
 The 4 electrons of the impurity atom is engaged in covalent bonding with Si atom.
 The fifth electron is free. This increases the conductivity.
 The impurities are called donors.
 The impurity added semiconductor is called n-type semiconductor, because their
increased conductivity is due to the presence of the negatively charged electrons,
which are called the majority carriers.
 The energy band of the electrons donated by the impurity atoms is just below the
conduction band.
 The electrons absorb thermal energy and occupy the conduction band.
 Due to the breaking of covalent bond, there will be a few holes in the valence band
at this temperature.
 These holes in n-type are called minority carriers.

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(ii) p-type semiconductor:
 If a III group element, like indium (In), boron (B), aluminium (AI) etc., having three
valence electrons, is added to a semiconductor say Si, the three electrons form
covalent bond.
 There is a deficiency of one electron to complete the 4th covalent bond and is called a
hole.The presence of the hole increases the conductivity because these holes move to
the nearby atom, at the same time the electrons move in the opposite direction.
 The impurities added semiconductor is called p-type semiconductor.
 The impurities are called acceptors as they accept electrons from the
semiconductor
 Holes are the majority carriers and the electrons produced by the breaking of bonds are
the minority carriers.
3. PN JUNCTION DIODE
 A p–n junction is formed by joining P-type and N-type semiconductors together in very
close contact.
 The term junction refers to the boundary interface where the two regions of the
semiconductor meet.
 Diode is a two-terminal electronic component that conducts electric current in only one
direction.
 The crystal conducts conventional current in a direction from the p-type side (called the
anode) to the n-type side (called the cathode), but not in the opposite direction.

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Symbol of PN junction diode
3.1 Biasing
“Biasing” is providing minimum external voltage and current to activate the device to
study its characteristics.
There are two operating regions and two "biasing" conditions for the standard
Junction Diode and they are:
 Zero Bias:
When a diode is Zero Biased no external energy source is applied and a natural Potential
Barrier is developed across a depletion layer.

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(i) Forward Bias:
 When the positive terminal of a battery is connected to P-type semiconductor and negative
terminal to N-type is known as forward bias of PN junction.
 The applied forward potential establishes an electric field opposite to the potential barrier.
Therefore the potential barrier is reduced at the junction. As the potential barrier is very small
(0.3V for Ge and 0.7V for Si),a small forward voltage is sufficient to completely eliminate the
barrier potential, thus the junction resistance becomes zero.
 In otherwords, the applied positive potential repels the holes in the ‘P’ region so that the holes
moves towards the junction and applied negative potential repels the electrons in the ‘N’ region
towards the junction results in depletion region starts decreasing. When the applied potential is
more than the internal barrier potential then the depletion region completely disappear, thus the
junction resistance becomes zero.
 Once the potential barrier is eliminated by a forward voltage, j unction establishes the low
resistance path for the entire circuit, thus a current flows in the circuit, it is called as forward
current.
(ii) Reverse Bias:

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 For reverse bias, the negative terminal is connected to P-type semiconductor and positive terminal
to N type semiconductor.
 When reverse bias voltage is applied to the junction, all the majority carriers of ‘P’ region are
attracted towards the negative terminal of the battery and the majority carriers of the N region
attracted towards the positive terminal of the battery, hence the depletion region increases.
 The applied reverse voltage establishes an electric field which acts in the same direction of the
potential barrier. Therefore, the resultant field at the junction is strengthened and the barrier width
is increased. This increased potential barrier prevents the flow of charge carriers across the
junction, results in a high resistance path.
 This process cannot continue indefinitely because after certain extent the junction break down
occurs. As a result a small amount of current flows through it due to minority carriers. This
current is known as “reverse saturation current”.
3.2 V-I characteristics of PN junction diode
Forward Bias:
 The application of a forward biasing voltage on the junction diode results in the
depletion layer becoming very thin and narrow which represents a low impedance
path through the junction thereby allowing high currents to flow. 
 The point at which this sudden increase in current takes place is represented on the static
I-V characteristics curve above as the "knee" point.
Reverse Bias:
 In Reverse biasing voltage a high resistance value to the PN junction and practically
zero current flows through the junction diode with an increase in bias voltage.
 However, a very small leakage current does flow through the junction which can be
measured in microamperes, (μA).
 One final point, if the reverse bias voltage Vr applied to the diode is increased to a
sufficiently high enough value, it will cause the PN junction to overheat and fail due to
the avalanche effect around the junction.
 This may cause the diode to become shorted and will result in the flow of maximum
circuit current, and this shown as a step downward slope in the reverse static
characteristics curve below.

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4. ZENER EFFECT
 In a general purpose PN diode the doping is light; as a result of this the breakdown
voltage is high. If a P and N region are heavily doped then the breakdown voltage can be
reduced.
 When the doping is heavy, even the reverse voltage is low, the electric field at barrier will
be so strong thus the electrons in the covalent bonds can break away from the bonds. This
effect is known as Zener effect.
5. ZENER DIODE
 A diode which exhibits the zener effect is called a Zener Diode. Hence it is defined as a
reverse biased heavily doped PN junction diode which operates in breakdown region. The
zener diodes have been designed to operate at voltages ranging from a few volts to
several hundred volts.
 Zener Breakdown occurs in junctions which is heavily doped and have narrow depletion
layers. The breakdown voltage sets up a very strong electric field. This field is so strong
enough to break or rupture the covalent bonds thereby generating electron hole pairs.

EEE
 Even a small reverse voltage is capable of producing large number of current carrier.
When a zener diode is operated in the breakdown region care must be taken to see that
the power dissipation across the junction is within the power rating of the diode otherwise
heavy current flowing through the diode may destroy it.
5.1 V-I characteristics of Zener diode
 The illustration above shows this phenomenon in a current vs voltage graph with a
zener diode connected in the forward direction .It behaves exactly as a standard diode.
 In the reverse direction however there is a very small leakage current between 0v
and the zener voltage –i.e. just a tiny amount of current is able to flow.
 Then, when the voltage reaches the breakdown voltage (vz),suddenly current can flow
freely through it.
5.2 Application of Zener diode

a) as voltage regulator
b) as peak clippers
c) for reshaping waveforms

EEE
6. RECTIFIERS
The “rectifier” is a circuit that converts AC voltages and currents into pulsating DC
voltages and currents. It consists of DC components and the unwanted ac ripple or harmonic
components which can be removed by using filter circuit. Thus the output obtained will be
steady DC voltage and magnitude of DC voltage can be varied by varying the magnitude of AC
voltage.
Filters: A circuit that removes ripples (unwanted ac components) present in the pulsating
dc voltage.
Regulator: A circuit that maintains the terminal voltage as constant even if the input
voltage or load current varying.
6.1 Types of rectifiers:
Rectifiers are grouped into two categories depending on the period of conduction.
(a)Half wave rectifier (b) Full wave rectifier
Half wave Rectifier:
Principle
It is a circuit that converts alternating voltage or current into pulsating voltage or current
for half the period of input cycle hence it is named as “half wave rectifier”.
Construction
 It consists of step-down transformer, semiconductor diode and the load resistance.
 The step-down transformer – reduce the available ac voltage into required level of
smaller ac voltage.
 The diode can be used to convert the ac into pulsating dc.
Operation
 During the positive half cycle of input, the diode D is forward biased, it offers very small
resistance and it acts as closed switch and hence conducts the current through the load
resistor.
 During the negative half cycle of the input diode D is heavily reverse biased, it offers
very high resistance and it acts as open switch hence it does not conduct any current. The
rectified output voltage will be in phase with AC input voltage for completely resistive
load.

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Full wave Rectifier:
Principle
A circuit that converts the ac voltage or current into pulsating voltage or current during
both half cycle of input is known as “full wave rectifier”.
Operation
 During positive half cycle of ac input, diode D1 becomes forward biased, provides
very small resistance and acts as closed switch, resulting in the flow of current.
 During negative half cycle, diode D1 reverse biased, offers high resistance and it
acts as open circuit.

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Voltage Regulation:
Ratio of Difference of secondary voltage to Primary voltage to secondary

voltage.

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UNIT5 .BIPOLAR JUNCTION TRANSISTOR
 A bipolar junction transistor is a three terminal semiconductor device in which the

operation depends on the interaction of majority and minority carriers.
 Transistor refers to Transfer Resistor i.e., signals are transferred from low resistance
circuit into high resistance circuit.
 BJT consists of silicon crystal in which a layer of ‘N’ type silicon is sandwiched between
two layers of ‘P’ type silicon. The semiconductor sandwiched is extremely smaller in
size.
 In other words, it consists of two back to back PN junction joined together to form single
piece of semiconductor crystal. These two junctions gives three region called Emitter,
Base and Collector.
 There are two types of transistors such as PNP and NPN. The arrow on the emitter
specifies whether the transistor is PNP or NPN type and also determines the direction of
flow of current, when the emitter base junction is forward biased.

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Emitter: It is more heavily doped than any of the other region because its main function is to
supply majority charge carriers to the base.
Base: It forms the middle section of the transistor. It is very thin as compared to either the
emitter or collector and is very lightly doped.
Collector: Its main function is to collect the majority charge carriers coming from the emitter
and passing through the base. In most transistors, collector region is made physically larger than
the emitter because it has to dissipate much greater power.
7.1 Operation of Transistor
 The basic operation will be described using the pnp transistor. The operation of the pnp
transistor is exactly the same if the roles played by the electron and hole are interchanged.
 One p-n junction of a transistor is reverse-biased, whereas the other is forward-biased.
 Both biasing potentials have been applied to a pnp transistor and resulting majority and
minority carrier flows indicated.
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Forward biased junction of a pnp transistor
Reverse biased junction of pnp transistor

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 Majority carriers (+) will diffuse across the forward-biased p-n junction into the n-type
material.
 A very small number of carriers (+) will through n-type material to the base terminal.
Resulting IB is typically in order of microamperes.
 The large number of majority carriers will diffuse across the reverse-biased junction into
the p-type material connected to the collector terminal.
 Majority carriers can cross the reverse-biased junction because the injected majority
carriers will appear as minority carriers in the n-type material.
 Applying KCL to the transistor :
IE = IC + IB
 The comprises of two components – the majority and minority carriers
IC = ICmajority + ICOminority
 ICO – IC current with emitter terminal open and is called leakage current.

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7.2 Common Base configuration
 Common-base terminology is derived from the fact that the :
- base is common to both input and output of the configuration.

- base is usually the terminal closest to or at ground potential.
 All current directions will refer to conventional (hole) flow and the arrows in all
electronic symbols have a direction defined by this convention.
 Note that the applied biasing (voltage sources) are such as to establish current in the
direction indicated for each branch.
 To describe the behavior of common-base amplifiers requires two set of characteristics:
o Input or driving point characteristics.

o Output or collector characteristics
 The output characteristics has 3 basic regions:
o Active region –defined by the biasing arrangements
o Cutoff region – region where the collector current is 0A
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o Saturation region- region of the characteristics to the left of VCB = 0V

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 The curves (output characteristics) clearly indicate that a first approximation to the
relationship between IE and IC in the active region is given by
IC ≈IE
 Once a transistor is in the ‘on’ state, the base-emitter voltage will be assumed to be
VBE = 0.7V
 In the dc mode the level of IC and IE due to the majority carriers are related by a quantity
called alpha

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= IC / IE
IC = IE + ICBO
 It can then be summarize to IC = IE (ignore ICBO due to small value)

 For ac situations where the point of operation moves on the characteristics curve, an ac
alpha defined by
 Alpha a common base current gain factor that shows the efficiency by calculating the
current percent from current flow from emitter to collector. The value of is typical from
0.9 ~ 0.998.
7.3 Common Emitter configuration
 It is called common-emitter configuration since :
o emitter is common or reference to both input and output terminals.

o emitter is usually the terminal closest to or at ground potential.
 Almost amplifier design is using connection of CE due to the high gain for current and
voltage.
 Two set of characteristics are necessary to describe the behavior for CE; input (base
terminal) and output (collector terminal) parameters.

EEE

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Input characteristics for CE configuration
 IB in microamperes compared to milliamperes of IC.
 IB will flow when VBE > 0.7V for silicon and 0.3V for germanium
 Before this value IB is very small and no IB.
 Base-emitter junction is forward bias
 Increasing VCE will reduce IB for different values.

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Output characteristics for CE configuration
 For small VCE (VCE < VCESAT, IC increase linearly with increasing of VCE
 VCE > VCESAT IC not totally depends on VCE  constant IC
 IB(uA) is very small compare to IC (mA). Small increase in IB cause big increase in IC
 IB=0 A  ICEO occur.
 Noticing the value when IC=0A. There is still some value of current flows.

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7.4 Common Collector configuration
 Also called emitter-follower (EF).

 It is called common-emitter configuration since both the
o signal source and the load share the collector terminal as a common connection
point.
 The output voltage is obtained at emitter terminal.
 The input characteristic of common-collector configuration is similar with common-
emitter. configuration.
 Common-collector circuit configuration is provided with the load resistor connected from
emitter to ground.

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 It is used primarily for impedance-matching purpose since it has high input impedance
and low output impedance.
 For the common-collector configuration, the output characteristics are a plot of I E

vs VCE for a range of values of IB.

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Input characteristics of CC configuration

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7.5 Small Signal Amplifier
When the input signal is so weak as to produce small fluctuations in the collector current
compared to its quiescent value, the amplifier is known as Small Signal Amplifier.
In other words, as the name indicates, the input applied to the circuit is V in << Vth. It has only
one amplifying device.
= IC / IE
IC = IE + ICBO
Voltage and current equation for hybrid parameters:
V1 = h11 i1 + h12V2
I2 = h21 i1 + h22V2
The values of h-parameters:
h11 = V1/ i1
h12 = V1 / V2
h21 = i2 / i1
h22 = i2 / V2

EEE

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GE 6252 BASIC ELECTRICAL AND ELECTRONICSENGINEERING

UNIT – I ELECTRIC CIRCUITS

If a capacitor and/or inductor is added to a DC circuit, the resulting circuit is not,

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where I is the current through the resistance in units of amperes,

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Kirchhoff's Voltage Law:

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Steady State Solution of DC Circuits:

Resistance in parallel connection:

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I = V / R (as per ohms law)

Problems based on ohm’s law

The potential difference between its ends = 5 V

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Star Delta transformation:

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A resistive network consisting of three impedances can be connected together to form a T or

As we have already seen, we can redraw the T resistor network to produce an

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Pi-connected and Equivalent Delta Network.

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Delta to Star Transformation

Compare the resistances between terminals 1 and 2.

Resistance between the terminals 2 and 3.

Resistance between the terminals 1 and 3.

Then, re-writing Equation 1 will give us:

Equ (4) + Equ (5)

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2.1.1 CONSTRUCTION OF D.C. MACHINES

The major parts can be identified as,

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Brush and brush holders:

End Shields or Bearings

2.1.2 PRINCIPLE OF OPERATION

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2.1.3 GENERATOR E.M.F EQUATION

For a simplex wave-wound generator

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For a simplex lap-wound generator

In general generated e.m.f

where A = 2 for simplex wave-winding

2.1.4 TYPES OF D.C. GENERATORS

(i) Separately Excited D.C. Generators

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(ii) Self-Excited D.C. Generators

(a) Series generator

Armature current, Ia = Ise = IL = I(say)

(b) Shunt generator

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Shunt field current, Ish = V/Rsh

(c) Compound generator

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2.1.5 APPLICATIONS OF DC GENERATOR

For electro plating

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