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Kulshreshtha, D. C.
@ McGraw-Hill Education
Basic Electrical Engineering
McGraw-Hill Education © 2010
BASIC ELECTRICAL ENGINEERING
D. C. KULSHRESHTHA,
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Kulshreshtha, D. C.
@ McGraw-Hill Education
McGraw-Hill Education © 2010
Basic Electrical Engineering
Chapter 3
Network Analysis–Part I

D.C. Kulshreshtha
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Thought of The DAY
Whatever
THE MIND OF MAN
can CONCIEVE and BELIEVE,
it can
ACHIEVE.
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Ch. 3 Network Analysis- Part I
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Topics to be Discussed







Electric Circuit,
The Resistance
Parameter,
The Capacitance
Parameter,
The Inductance
Parameter,
Energy Sources-Classification
Ideal Voltage Source.
Ideal Current Source.
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




Series and Parallel
Combinations.
Practical Voltage
Source.
Practical Current
Source.
Source Transformation.
Kirchhoff’s Laws.
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Electric Circuit

It is a closed path, composed of active and
passive elements.

Active Element : It supplies energy to the
circuit.
Passive Element : It receives energy and then
1) either converts it to heat,
as in a Resistance (R).
2) or stores it in
(a) Electric Field, as in a Capacitor (C).
(b) Magnetic Field, as in an Inductor (L).

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Energy Sources

Classification
Independent Source
Voltage Source
DC Source
Ideal Source
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Or
Or
Or
Or
Dependent Source
Current Source
AC Source
Practical Source
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Independent Ideal Voltage Source
Source
Load
Note that the source determines the voltage, but the
current is determined by the load.
The source has zero internal resistance.
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



The voltage source is said to be idle if the output
terminals are open such that i = 0.
When turned off (killed or made inactive), so that v =
0, it is equivalent to a short circuit.
Reference Marks : One terminal is marked plus and the
other minus. (Oversimplification; one mark can be
omitted.)
When actual polarity is opposite to the reference
marks, the voltage is a negative number.
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Independent Ideal Current Source
Source
Load
Note that the source determines the current, but the
voltage is determined by the load.
The Source has infinite internal resistance (Ri).
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



The current source is said to be idle if the output
terminals are shorted together, such that v = 0.
When turned off (killed or made inactive), so that i = 0,
it is equivalent to an open circuit.
Reference Marks : An arrow is put.
When actual direction of current is opposite to the
reference (arrow) direction, the current is a negative
number.
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Do you observe duality ?
The roles for the current and voltage are
interchanged in the two sources.
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Practical Voltage Source
It is represented by an ideal voltage source in series
with an internal resistance (RSV).
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Practical Current Source
It is modelled as an ideal current source in parallel
with an internal resistance (RSI).
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Source Transformation


A practical current source can be converted
into its equivalent practical voltage source,
and vice versa.
This conversion is valid only for the external
load connected across the terminals of the
source.
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Ch. 3 Network Analysis- Part I
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Equivalence between
Voltage Source and Current Source

Two sources would be equivalent if they produce
identical values of VL and IL, when they are
connected across the same load.
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Series and Parallel Combinations




What would be the net emf of the combination
if two ideal voltage sources of 2 V and 4 V are
connected in series so as to aid each other?
Click
Ans. 6 V
What would be the net emf of the combination
if two ideal voltage sources of 4 V and 4 V are
connected in parallel ? 4 V or 8 V ?
Click
Ans. Obviously, it should be 4 V
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




What would be the net emf of the combination if two
ideal voltage sources of 2 V and 4 V are connected in
parallel ? 2 V or 4 V or 3 V ?
Click
The question seems to be quite tricky!
Click
Ans. The question is wrong. The question contradicts
itself.
Ideal Voltage Sources in parallel are permissible only
when each has the same terminal voltage at every
instant of time.
What is its dual ?
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Ideal Voltage Sources
Connected in Series
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Ideal Current Sources
Connected in Parallel
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Practical Current Sources
Connected in Series
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Practical Voltage Sources
Connected in Parallel
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Example 1 : Reduce the network shown in figure
to its simplest possible form by using source
transformation.
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Solution
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Example 2

In the given figure,
(a) If RL = 80 Ω, find current iL.
(b) Transform the practical current source into a
practical voltage source and find iL if RL = 80 Ω
again.
(c) Find the power drawn from the ideal source in
each case.
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Solution :
20
(a) iL  (100) 
 20 mA
20  80
(b) iL 
2
 20 mA
80  20
Click
(c) vL  iL  RL  (20 mA )(80 )  1.6 V
Click
P  vL  I  (1.6 V)(100 mA )  160 mW
Click
In the second case,
P  iL  V  (20 mA )( 2 V)  40 mW
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Benchmark Example 3

Take the benchmark example of the circuit
given in figure. Using source transformation,
determine the voltage v across 3-Ω resistor.
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Solution :
Transforming the 4-A current source into a
voltage source,
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Combining the two voltage sources,
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Again transforming the voltage source into
current source,
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Combining the two current sources we get Fig.
(e). Transforming this current source into
voltage source (Fig. f )
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Combining the two resistances, we get Fig.
(g).
Finally, using voltage
divider, we get
3
v  5
 2.5 V
33
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Kirchhoff’s Laws

(1) KCL : Algebraic sum of currents
meeting at a junction of conductors in a
circuit is zero.
 It is simply a restatement of the principle
of conservation of charge.
b
I
j 1
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j
0
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
(2) KVL :The algebraic sum of voltages
around a closed circuit or a loop is zero.

It is simply a restatement of the principle of
conservation of energy.
k
v
j 1
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j
0
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Polarity of Voltages
Note that polarity of the voltage (emf) across a
battery does not depend upon the assumed
direction of current.
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Applying KVL
1.
2.
3.
4.
Select a closed loop.
Mark the voltage polarity (+ and -) across
each element in the closed loop.
Go round the selected loop, and add up
all the voltages with + or – signs.
Any one of the following two rules can be
followed :
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(i) Rule 1 : While travelling, if you meet a
voltage rise, write the voltage with positive sign ;
if you meet a voltage drop, write the voltage with
negative sign.
(ii) Rule 2 : While travelling, write the voltage
with positive sign if + is encountered first; write
the voltage with negative sign if – is encountered
first.
We shall be following Rule 1, as it has a strong
analogy with the physical height (altitude) of a
place.
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Example 5 : Use KVL to find vR2 and vx.
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For finding vR2, we write KVL eqn. going
around loop abgha clockwise :
Click
 36  vR 2  4  0  vR 2  32 V
If you choose to go around the loop
anticlockwise, you get
Click
 4  36  vR 2  0  vR 2  32 V
Giving the same result.
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There are two ways to determine vx
1) We can consider this voltage as the voltage
across the gap from d to f. Writing KVL
(habcdfgh) :
Click
 4  36  12  14  vx  0
vx  6 V
2) Knowing vR2 , apply a short-cut (bcdfgb) :
Click
 12  14  vx  32  0
vx  6 V
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Important Note about KVL



The assumed direction of current through a
resistor and the polarity of voltage across it
are always in conformity.
The end into which the current enters is
marked positive.
Passive-element sign convention.
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Example 6 : Find the current supplied by
the 60-V source in the network.
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Solution :


We need not find the currents I1, I2 and I3.
Instead, we reduce the network.
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Example 7 : Determine the value of
current I.
2–3–I–4=0
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or
I = -5 A
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Example 8
Using KCL and KVL, determine the currents ix
and iy in the network shown.
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Solution : Using KCL, the currents in other branches
are marked as shown. Writing KVL equations for the
loops 1, 2 and 3,
100  10 I1  5I x  0

5I x  0 I y  10 I1  100
5I x  50  2( I1  I x )  2 I y  0

7 I x  2 I y  2 I1  50
 2 I y  50  3( I1  I x  I y )  0

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3I x  5I y  3I1  50
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Writing the above equations in matrix form,
5
7

3
0
2
5
10 

 2
 3
 I x  100 
  

 I y    50 ;
 I   50
 1
Using Calculator, we solve for Ix and Iy,
I x  3.87 A;
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and
Click
Click
I y  0.51 A
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Review







Electric Circuit,
The Resistance
Parameter,
The Capacitance
Parameter,
The Inductance
Parameter,
Energy Sources-Classification
Ideal Voltage Source.
Ideal Current Source.
Friday, May 12, 2017






Series and Parallel
Combinations.
Practical Voltage
Source.
Practical Current
Source.
Source Transformation.
Dependent Sources.
Kirchhoff’s Laws.
Ch. 3 Network Analysis- Part I
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