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


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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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

1

Conductance is the ability of an element to conduct electric current; it ismeasured in mhos or siemens (S).

shortcircuit

opencircuit



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.



Circuit Theory

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Fundamental theorem of network topology:

b = l + n - 1

b : branchesn : nodesl : independent loops



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.

52431 iiiii



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

41532

54321

0

vvvvvvvvvv



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



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.

21

21

21 ; 111

RRRRR

RRR eqeq

For the circuit with N resistors in parallel.

Neq

Neq

GGGGGG

RRRR

...);( econductanc of in terms

1...111

321

21

The equivalent conductance of resistors connected in parallel is the sum of theirindividual conductances.



Circuit Theory

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Parallel Resistors and Current DivisionParallel Resistors and Current Division

iRR

RiiRR

Ri21

12

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



Circuit Theory

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Examples and Problems

1. Find currents and voltages in the circuit below.

2. Find vo and io.



Circuit Theory

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3. Find currents and voltages in the circuit below.

4. Calculate the equivalent resistance Rab.



Circuit Theory

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5. Find Rab.



Circuit Theory

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6.

Fig 2.43



Circuit Theory

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7.

Fig. 2.45



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.



Circuit Theory

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Delta to Delta to WyeWye (star) Conversion(star) Conversion

cba

cab

cab

RRRRRRRRR

RYRRRRRRRYR

)(gives; ,)()( Setting

)//()( and )(

3112

1212

123112

Similarly;

cba

abc

cba

cba

cba

bac

RRRRRRRR

RRRRRRRRR

RRRRRRRRR

)(Therefore;

)(

)(

21

3234

2113



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.



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

321

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.



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



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 ,



Circuit Theory

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ProblemBy using the method of source transformations, find vx.


circuit theory (skee 1023)

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