1 READING MATERIAL FOR B.E STUDENTS OF RGPV AFFILIATED ENGINEERING COLLEGES SUBJECT BASIC ELECTRICAL AND ELECTRONICS Professor MD Dutt Addl General Manager (Retd) BHARAT HEAVY ELECTRICALS LIMITED Professor(Ex) of EX Department Bansal Institute of Science and Technology KOKTA ANANAD NAGAR BHOPAL Presently Head of The Department ( EX) Shri Ram College Of Technology Thuakheda BHOPAL Sub Code BE 104 Subject Basic Electrical & Electronics UNIT I Electrical Circuit Analysis
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READING MATERIAL FOR B.E STUDENTS
OF RGPV AFFILIATED ENGINEERING COLLEGES
SUBJECT BASIC ELECTRICAL AND ELECTRONICS
Professor MD Dutt
Addl General Manager (Retd)
BHARAT HEAVY ELECTRICALS LIMITED
Professor(Ex) of EX Department
Bansal Institute of Science and Technology
KOKTA ANANAD NAGAR BHOPAL
Presently Head of The Department ( EX)
Shri Ram College Of Technology
Thuakheda BHOPAL
Sub Code BE 104 Subject Basic Electrical & Electronics
UNIT I Electrical Circuit Analysis
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RGPV Syllabus
BE 104 BASIC ELECTRICAL & ELECTRONICS ENGINEERING
UNIT I
ELECTRICAL CIRCUIT ANALYSIS
Voltage and current source, Dependent and independent sources, source conversion,
DC circuit analysis using mesh and nodal method. Thevenin,s and superposition
theorem, Star delta transformation.
1 – Phase AC circuits under sinusoidal steady state , active reactive and apparent
power . Physical meaning of reactive power . Power Factor, 3 Phase balance and
unbalance supply. Star and Delta connections.
INDEX
S No Topic Page
1 Voltage and current source, Dependent and independent
sources, source conversion
3,4,5
2 DC circuit analysis using mesh and nodal method 6,7,8
3 Thevenin,s theorem, 9,10
4 Superposition theorem 11,12
5 Star delta transformation 13,14,15
6 1 – Phase AC circuits under sinusoidal steady state 15
7 Active reactive and apparent power . Physical meaning of
reactive power
16,17
8 Power Factor, 3 Phase balance and unbalance supply 17,18
9 Star and Delta connections 18,19,20
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VOLTAGE The rate at which energy is drawn from a source that produces a flow of
electricity in a circuit; expressed in volts.
Electric Current Flow of electrons from one place to another. Electric current means a
flow of charge in the same way that water current flows . A flow of electricity through a
conductor; measured in amperes
RESISTANCE A material’s opposition to the flow of electric current; measured in ohm.
VOLTAGE AND CURRENT SOURCE
Voltage source :- Most of the sources used in day to day life are constant voltage source,
such as batteries, dynamos and alternators.
Current Source :- Specifically the collector circuits of transistors, metadyne generators, are
considered as current sources.
VOLTAGE SOURCE CURRENT SOURCE
Independent Source:- A source may be said independent when it does not depend on any
other quantity of circuit. Figure below shows Independent DC source and Independent AC
Source varying with time.
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IDEAL CURRENT SOURCE:- In the figure below independent DC Current source and
independent time varying source.
DEPENDENT SOURCES:-
I) Voltage dependent voltage source
II) Current dependent voltage source
III) Voltage dependent current source
IV) Current dependent current source.
IDEAL VOLTAGE SOURCE:- A constant voltage source is an ideal source, almost
capable of supplying any current at a given voltage, considering internal resistance equal to
zero. The terminal voltage across the terminal remains constant. The ideal voltage can
never be short circuited. Practically an Ideal voltage source is not possible.
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IDEAL CURRENT SOURCE:- A source that supplies constant current to a load even its
impedance varies. The Ideal current source can never be open circuited.
SOURCE EQUIVALNCE OR TRANSFORMATION:- Consider a voltage source of Vs
and internal resistance Rin for conversion into an equivalent current source. The current
supplied by this voltage source, when short circuited is put across the terminal A and B will
be equal to Vs/Rin.
A current source supplying this current is Is = Vs/Rin and having the same resistance
across , It will represent the current source.
sss IRV
s
s
sR
VI
R
viRiv ssss or
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KIRCHOFF’s CURRENT LAW
At any junction point in an electrical circuit, the total current into the junction equals the
total current out of the junction.
(“What goes in must come out.”)
In the diagram at right,
I1 + I2 = I3
OR
Where N is the total number of branches connected to a
node.
Example 1 (KCL) Determine I, the current flowing out of the voltage source.
Use KCL
1.9 mA + 0.5 mA + I are entering the node.
I
3 mA is leaving the node.
3ma .5ma
1.9ma
I
Kirchhoff’s Voltage Law
In any complete path in an electrical circuit, the sum of the potential increases equals the
sum of the potential drops.
(“What goes up must come down.”)
nodenode
1
0
leaveenter
N
n
n
ii
i
mAI
mAmAmAI
mAImAmA
6.0
)5.09.1(3
35.09.1
7
Example 2 (KVL)
Find the voltage across R1. Note that the polarity of the voltage has been assigned in the
circuit schematic.
First, define a loop that include R1.
If the outer loop is used:
Follow the loop clockwise.
rises drops
M
1m
v v
0 v
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By convention, voltage drops are added and voltage rises are subtracted in KVL.
Summary
The currents at a node can be calculated using Kirchhoff’s Current Law (KCL).
The voltage dropped across components can be calculated using Kirchhoff’s Voltage Law
(KVL).
Ohm’s Law is used to find some of the needed currents and voltages to solve the problems.
VV
VVV
R
R
2
035
1
1
9
THEVNIN’S THEOREM :- This theorem provides a mathematical technique for replacing
a two terminal network by a voltage source Vt, and resistance Rt connected in series. The
voltage source Vt ( called Thevenin’s equivalent voltage), this is the open circuit voltage
that appears across the load terminals when the load is removed or disconnected and
resistance Rt, called the Thevenin’s equivalent resistance, is equal to the resistance of
network looking back into the load terminals.
The steady state current will be I = Vt/(Rt +RL) This is in the case of DC network
Let us consider a circuit shown here below, which consists of a source of EMF
E volts and internal resistance r ohms connected to an external circuit consists of resistance
R1 and R2 Ohms in series. AB across which a resistance R2 ohms is connected the network
acts as source of open circuit voltage Voc ( also called Thevenin’s equivalent voltage Vt
and internal resistance Rin ( also called Thevenin’s resistance Rt)
For determination of open circuit voltage Voc ( Vt) Disconnect the load resistance RL from
the terminals A B to provide open circuit
Now current through resistance R2,
I = E
R1 + R2 +r
For determination of internal resistance Rin or Rt of the network under consideration,
remove the voltage source from the circuit, leaving behind only its internal resistance r , as
shown in in figure. Now view the circuit inwards from open terminal A and B. It is found
that in circuit below now consists resistance R2 only, and the other consists of resistance R1
and r in series.
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Thus the equivalent resistance Rt as viewed from open terminals A and B
Rt = R2(R1+r)
R2 +R1+r
When load resistance Rl is connected across terminal A and B, the network behaves as a
source of Voltage Vt and terminal resistance Rt and the current flowing through the load
resistance Rl is given as
I1 = Vt = ER2 ( R1+R2+r)
Rt+Rl R2 (R1 +r) + Rl
R1 +r +R2
= ER2
R2 (R1+r) + Rl ( R1+R2 +r)
The current in any passive circuit element ( which may be called Rl ) in a network is the
same as would be obtained if Rl were supplied with a voltage source Voc or Vt in series
with an equivalent resistance Rin or Rt . Voc being the open circuit voltage at terminal
from which Rl has been removed and Rin or Rt being the resistance that would be measured
at these terminals, after all sources have been removed and each have been replaced with its
internal resistance.
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SUPERPOSITION THEOREM
The superposition principle states that the voltage across (or current through) an element in
a linear circuit is the algebraic sum of the voltages across (or currents through) that element
due to each independent source acting alone.
Steps to apply superposition principle
1. Turn off all independent sources except one source. Find the output (voltage or
current) due to that active source using nodal or mesh analysis.
Turn off voltages sources = short voltage sources; make it equal to zero voltage
Turn off current sources = open current sources; make it equal to zero current
2. Repeat step 1 for each of the other independent sources.
3. Find the total contribution by adding algebraically all the contributions due to
the independent sources.
Dependent sources are left intact.
2mA Source Contribution
I’0 = -4/3 Ma
12
4 ma Source Contribution
I’’0 = 0
12 voltage source contribution
I’’’0 = -4 mA
Final result
I’0 = -4/3 mA
I’’0 = 0
I’’’0 = -4 mA
I0 = I’0+ I’’0+ I’’’0 = -16/3 mA
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STAR DELTA TRANSFORMATION:- Three resistances connected nose to tail as
shown in figure are said to be Delta connected or mesh connected.
Three resistances connected together at a common point O are said to be connected in
star.
The replacement of delta or mesh by the equivalent star system is known as
DELTA STAR TRANSFORMATION
The two system will be equivalent or identical if the resistance measured between any
pair of lines is same in both the system when the third line is open the resistance
between point B and C
RBC = R3║ (R1 + R2)
= R3 (R1 + R2)
R3+ R1+ R2
Where as In Star
RBC = RB + RC
Since two system are identical, resistance between terminals B and C in both system