Circuit Theory (SKEE 1023)
Transcript of Circuit Theory (SKEE 1023)
INSPIRING CREATIVE AND INNOVATIVE MINDS
Circuit TheoryCircuit Theory(SKEE 1023)(SKEE 1023)
Assoc. Prof. Dr. Mohamed Afendi Mohamed PiahInstitute of High Voltage & High CurrentFaculty of Electrical Engineering, UTM
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M. Afendi M. Piah, PhD
INSPIRING CREATIVE AND INNOVATIVE MINDS
Circuit Theory
Topics
Basic Laws: Ohm’s law; Nodes,Branches and Loops; Kirchhoff’sLaw; Series-parallel resistors;Voltage and Current Division.
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M. Afendi M. Piah, PhD
INSPIRING CREATIVE AND INNOVATIVE MINDS
Circuit Theory
Basic LawsBasic LawsOhm’s law states that the voltage v across a resistor is directly proportionalto the current i flowing through the resistor.
The resistance R of an element denotes its ability to resist the flow ofelectric current, it is measured in ohms ()
Value of R can range from zero to infinity, which are the two extremepossible values of R (0 and ).
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Circuit Theory
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A short circuit is a circuit element with resistance approaching zero.
An open circuit is a circuit element with resistance approaching infinity.
The reciprocal of resistance, known as conductance and denoted by G;
vi
RG
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Conductance is the ability of an element to conduct electric current; it ismeasured in mhos or siemens (S).
shortcircuit
opencircuit
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Circuit Theory
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Nodes, Branches and LoopsNodes, Branches and LoopsTo understand some basic concepts of network topology. A network – as aninterconnection of elements/devices. A circuit is a network providing one or moreclosed path.
A branch represents a single element such as voltage/current source or aresistor.
A node is the point of connection between two or more branches.
A loop is any closed path in a circuit.
M. Afendi M. Piah, PhD
INSPIRING CREATIVE AND INNOVATIVE MINDS
Circuit Theory
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Fundamental theorem of network topology:
b = l + n - 1
b : branchesn : nodesl : independent loops
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Circuit Theory
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Kirchhoff’s LawsKirchhoff’s Laws
Introduced in 1847 by the German physicist Gustav Robert Kirchhoff (1824-1887). The laws are formally known as Kirchhoff’s current law (KCL) andKirchhoff’s voltage law (KVL).
Kirchhoff’s current law (KCL) states that the algebraic sum of currents entering anode (or a closed boundary) is zero.
The sum of the currents entering a node is equal to the sum of thecurrents leaving the node.
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Circuit Theory
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Kirchhoff’s LawsKirchhoff’s Laws
Kirchhoff’s voltage law (KVL) states that the algebraic sum of all voltages arounda closed path (or loop) is zero.
Sum of voltage drops = Sum of voltage rises
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vvvvvvvvvv
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Circuit Theory
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Series Resistors and Voltage DivisionSeries Resistors and Voltage Division
The equivalent resistance of any number of resistors connected in series is thesum of the individual resistances
For N resistors in series, then;
vRR
RvvRR
Rv21
22
21
11 ;
For N resistors in series;
vRRR
RvN
nn
...21
Principle of voltage division
M. Afendi M. Piah, PhD
INSPIRING CREATIVE AND INNOVATIVE MINDS
Circuit Theory
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Parallel Resistors and Current DivisionParallel Resistors and Current Division
The equivalent resistance of two parallel resistors is equal to the product of theirresistances divided by their sum.
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21
21 ; 111
RRRRR
RRR eqeq
For the circuit with N resistors in parallel.
Neq
Neq
GGGGGG
RRRR
...);( econductanc of in terms
1...111
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The equivalent conductance of resistors connected in parallel is the sum of theirindividual conductances.
M. Afendi M. Piah, PhD
INSPIRING CREATIVE AND INNOVATIVE MINDS
Circuit Theory
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Parallel Resistors and Current DivisionParallel Resistors and Current Division
iRR
RiiRR
Ri21
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21
21 ;
Principle of current division
If a current divider has N conductors (G1, G2, …GN) in parallel with the sourcecurrent i, the nth conductor (Gn) will have current;
iGGG
GiN
nn
...21
M. Afendi M. Piah, PhD
INSPIRING CREATIVE AND INNOVATIVE MINDS
Circuit Theory
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Examples and Problems
1. Find currents and voltages in the circuit below.
2. Find vo and io.
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INSPIRING CREATIVE AND INNOVATIVE MINDS
Circuit Theory
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3. Find currents and voltages in the circuit below.
4. Calculate the equivalent resistance Rab.
M. Afendi M. Piah, PhD
INSPIRING CREATIVE AND INNOVATIVE MINDS
Circuit Theory
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5. Find Rab.
M. Afendi M. Piah, PhD
INSPIRING CREATIVE AND INNOVATIVE MINDS
Circuit Theory
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6.
Fig 2.43
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Circuit Theory
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7.
Fig. 2.45
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Circuit Theory
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WyeWye--Delta TransformationsDelta Transformations
• Situations often arise in circuit analysis when the resistors are neither inparallel nor in series.
• Two types of network, i.e. wye and delta.
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Delta to Delta to WyeWye (star) Conversion(star) Conversion
cba
cab
cab
RRRRRRRRR
RYRRRRRRRYR
)(gives; ,)()( Setting
)//()( and )(
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1212
123112
Similarly;
cba
abc
cba
cba
cba
bac
RRRRRRRR
RRRRRRRRR
RRRRRRRRR
)(Therefore;
)(
)(
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2113
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INSPIRING CREATIVE AND INNOVATIVE MINDS
Circuit Theory
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Finally, for delta to Y (star) conversion;
Each resistor in the Y network is the product of the resistors in the twoadjacent branches, divided by the sum of the three resistors.
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INSPIRING CREATIVE AND INNOVATIVE MINDS
Circuit Theory
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WyeWye (star) to Delta Conversion(star) to Delta Conversion
cba
cba
cba
cbacba
RRRRRR
RRRRRRRRRRRRRRR
RRR
;&, of equations theusingBy
2133221
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Therefore;
Each resistor in the network is the sum of allpossible products of Y resistors taken two at atime, divided by the opposite Y resistor.
M. Afendi M. Piah, PhD
INSPIRING CREATIVE AND INNOVATIVE MINDS
Circuit Theory
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The Y and networks are said to be balanced when.
YY
cbaY
RRRR
RRRRRRRR
3or , 3
become formulas conversion ,conditions eUnder thes and , 321
Problem
For the bridge network shown in the figure, find Rab and i.
Ans: 40, 2.5A
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INSPIRING CREATIVE AND INNOVATIVE MINDS
Circuit Theory
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Source TransformationsSource Transformations
If the two networks are equivalent with respect to terminals ab, then V and Imust be identical for both networks. Thus,
RsV
sIRsIsV or ,
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INSPIRING CREATIVE AND INNOVATIVE MINDS
Circuit Theory
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ProblemBy using the method of source transformations, find vx.
M. Afendi M. Piah, PhD