electric circuit note chapter 2.pdf

8/9/2019 ELECTRIC CIRCUIT NOTE CHAPTER 2.pdf

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Chapter 2: Basic laws

ECE 1311: Electric Circuits


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Basic Law OverviewIdeal sources – series and parallelOhm’s law Definitions – open circuits, short circuits, conductance,

nodes, branches, loopsKirchhoff's lawVoltage divider and series resistorsCurrent divider and parallel resistorsWye-Delta transformations


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Ideal Voltage SourceIdeal voltage source in series can be addedIdeal voltage source in parallel = NO GOODRecall: ideal voltage source guarantee the voltage between

two terminals is at the specified potential (voltage)

BOOM


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Ideal Current SourceIdeal current source cannot be connected in seriesIdeal current source in parallel can be addedRecall: ideal current guarantee the current flowing through

source is at the specified valueRecall: Current entering a circuit must be equal to thecurrent leaving the circuit

BOOM


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ResistanceAll material resist the flow of current given by R

• R = resistance of an element in ohms• p = resistivity of material in ohm-meters• l = length of material in meters• A = cross sectional area of material in meter2 A

l R


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Ohm’s Law (1) Ohm’s lawstates that the voltage across a resistor is directlyproportional to the current flowing through the resistor.

Only material with linear relationship satisfy Ohm’s law(note the PSC)

iRv


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Ohm’s Law (2)Two extreme possible values of R: 0 (zero) and (infinite) arerelated with two basic circuit concepts:short circuit and opencircuit.Conductance is the ability of an element to conduct electric

current; it is the reciprocal of resistance R and is measured inmhos or siemens.

The power dissipated by a resistor:

Power absorbed by R is always positive

vi

RG

1

Rv

Rivi p2

2


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Practice 2.1


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Short circuitAn element (or wire) with R = 0 is called a short circuitAn ideal voltage source with V = 0 is equivalent to a shortcircuitSince v = iR and R = 0, v = 0 regardless of iRecall: cannot connect voltage source to a short circuit


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Open circuitAn element with R = is called the open circuitOften represented by a wire with an open connectionAn ideal current source I = 0A is also equivalent to an open

circuitRecall: cannot connect current source to an open circuit


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FormalizationFor this course,networks and circuits will be usedinterchangeablyNetworks are composed of nodes, branches and loops


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Nodes, Branches and LoopsA branch represents a single element such as a voltagesource or a resistor.A node is the point of connection between two or more

branches.A loop is any closed path in a circuit.A network with b branches, n nodes, and l independentloops will satisfy the fundamental theorem of networktopology:

1 nl b


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Practice 2.2

How many branches, nodes and independent loops are there?


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Practice 2.3

How many branches, nodes and loops are there?


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Overview on Kirchhoff’s Law It’s the foundation of circuit analysisThere are two - Kirchhoff’scurrent law (KCL) andKirchhoff’svoltage law (KVL)It tell us how the voltage and current are related within acircuit element are related


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Kirchhoff’s Current Law (1) Kirchhoff’s current law (KCL) states that the algebraicsum of currents entering a node (or a closed boundary) is zero.

i.e. the sum entering a node is equal to the sum leaving anode – based on the law on conservation charge


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Kirchhoff’s Current Law (2)KCL also apply at the boundary


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Practice 2.4Given that essential node is the point between 3 or more branches,


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Kirchhoff’s Voltage Law (1) Kirchhoff’s voltage law (KVL) states that the algebraicsum of all voltages around a closed path (or loop) is zero. Based on the conservation of energy


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Practice 2.5


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Practice 2.6

Apply KVL to find the value I


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Practice 2.7Find v2, v6 and vI


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Practice 2.8Find i0 and v0


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Practice 2.9


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Resistor Circuit OverviewResistors in seriesResistors in parallelVoltage dividers

Current dividersWye-Delta transformation


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Resistors in series


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Resistors in Parallel (1)


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Resistors in Parallel (2)


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Voltage Divider


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Current Divider


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Resistor NetworkKnowing equivalent and parallel equivalents of resistors isnot enough


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Wye-Delta Transformation (1)

)(1 cbacb

R R R R R

R

)(2 cbaac

R R R R R

R

)(3 cbaba

R R R R R

R

1

133221

R

R R R R R R Ra

2

133221

R R R R R R R

Rb

3

133221

R R R R R R R

Rc

Delta -> Y Y -> Delta


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Wye-Delta Transformation (2)


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Practice 2.11


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Practice 2.12

electric circuit note chapter 2.pdf

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