@ McGraw-Hill Education 1 Kulshreshtha, D. C. Basic Electrical Engineering McGraw-Hill Education © 2010 PROPRIETARY MATERIAL. © 2010 The McGraw-Hill Companies,

@ McGraw-Hill Education

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Kulshreshtha, D. C. Basic Electrical Engineering McGraw-Hill Education © 2010

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BASIC ELECTRICAL ENGINEERING

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D. C. KULSHRESHTHA,

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@ McGraw-Hill Education

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Kulshreshtha, D. C. Basic Electrical Engineering McGraw-Hill Education © 2010

Chapter 3Network Analysis–

Part I D.C. Kulshreshtha

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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 3

Thought of The DAY

Whatever

THE MIND OF MAN

can CONCIEVE and BELIEVE,

it can

ACHIEVE.

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Topics to be Discussed Electric Circuit, The Resistance

Parameter, The Capacitance

Parameter, The Inductance

Parameter, Energy Sources--Energy Sources--

ClassificationClassification Ideal Voltage Source.Ideal Voltage Source. Ideal Current Source.Ideal Current Source.

Series and Parallel Series and Parallel Combinations.Combinations.

Practical Voltage Practical Voltage Source.Source.

Practical Current Practical Current Source.Source.

Source Transformation.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 SourcesEnergy Sources

ClassificationIndependent Source Or Dependent Source

Voltage Source Or Current Source

DC Source Or AC Source

Ideal Source Or Practical Source

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Independent Ideal Voltage Source

The source has zero internal resistance.

Note that the source determines the voltage, but the current is determined by the load.

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LoadSource


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

The Source has infinite internal resistance (Ri). Next

Source

Load

Note that the source determines the current, but the voltage is determined by the load.


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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PracticalPractical Voltage Source Voltage Source

It is represented by an ideal voltage source in series with an internal resistance (RSV).

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Practical Practical Current SourceCurrent 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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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 15 Next


Equivalence betweenVoltage 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?

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 ?

Ans. Obviously, it should be 4 V

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Click

Click


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 ?

The question seems to be quite tricky! 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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Click

Click


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 SourcesConnected 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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Thursday, April 20, 2023 Ch. 3 Network Analysis- Part I 25 Next


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 :

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mA20

8020

20)100()( Lia

mA20

2080

2)( Lib

V6.1)80)(mA20()( LLL Rivc

mW160 )mA100)(V6.1(IvP L

mW40 V)2)(mA20(

case, second In the

ViP L

Click

Click

Click


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).

V2.5

33

35v

Finally, using voltage divider, we get

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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

jjI

1

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

jjv

1

0

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Polarity of Voltages

NoteNote 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. Select a closed loop.

2. Mark the voltage polarity (+ and -) across each element in the closed loop.

3. Go round the selected loop, and add up all the voltages with + or – signs.

4. 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 :

If you choose to go around the loop anticlockwise, you get

Giving the same result.

V320436 22 RR vv

V320364 22 RR vv

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Click

Click


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) :

2) Knowing vR2 , apply a short-cut (bcdfgb) :

V6

x

x

v

v 01412364

V6

x

x

v

v 0321412

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Click

Click


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 – 2 – 3 – I I – 4 = 0 – 4 = 0 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,

50353

0)(3502

50227

02)(2505

1001005

0510100

1

1

1

1

1

1

III

IIII

III

IIII

III

II

yx

yxy

yx

yxx

yx

x

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;

50

50

100

353

227

1005

1

I

I

I

y

x

Next

Writing the above equations in matrix form,Click

Using Calculator, we solve for Ix and Iy, Click

; and x yI I 3.87 A 0.51 A


Review Electric Circuit, The Resistance

Parameter, The Capacitance

Parameter, The Inductance

Parameter, Energy Sources--Energy Sources--

ClassificationClassification Ideal Voltage Source.Ideal Voltage Source. Ideal Current Source.Ideal Current Source.

Series and Parallel Series and Parallel Combinations.Combinations.

Practical Voltage Practical Voltage Source.Source.

Practical Current Practical Current Source.Source.

Source Transformation.Source Transformation. Dependent Sources. Kirchhoff’s Laws.

Next

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@ McGraw-Hill Education 1 Kulshreshtha, D. C. Basic Electrical Engineering McGraw-Hill Education © 2010 PROPRIETARY MATERIAL. © 2010 The McGraw-Hill Companies,