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CIRCUIT CIRCUIT VARIABLESVARIABLES

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1.1 Circuit Theory1.1 Circuit Theory

1.2 System of Units1.2 System of Units

1.3 Voltage and Current1.3 Voltage and Current

1.4 Passive Sign Convention1.4 Passive Sign Convention

1.5 Power and Energy1.5 Power and Energy22

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1.1 Circuit Theory1.1 Circuit Theory

nn Electrical engineering covers rather diverse fields Electrical engineering covers rather diverse fields which involve the generation , transmission , and which involve the generation , transmission , and processing of electrical energy and/or signalsprocessing of electrical energy and/or signals

Example : Power systems , Example : Power systems , SignalSignal--processing systems ,processing systems ,Computer systems , Computer systems , Control systems ,Control systems ,Communication systems Communication systems

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nn An electrical circuit is a mathematical model An electrical circuit is a mathematical model that approximates the behavior of an actual that approximates the behavior of an actual electrical system.electrical system.

nn Circuit theory is a special case of Circuit theory is a special case of electromagnetic field theory : the study of static electromagnetic field theory : the study of static and moving electrical charges.and moving electrical charges.

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1.1 Circuit Theory1.1 Circuit Theory

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1.1 Circuit Theory1.1 Circuit Theory

nnBasic assumptionsBasic assumptions1. The electrical signals are transmitted 1. The electrical signals are transmitted

throughout the circuit without time delay.throughout the circuit without time delay.This system is called a lumpedThis system is called a lumped--parameter system.parameter system.

2. No electromagnetic radiation happens. 2. No electromagnetic radiation happens.

3. Only linear circuits are considered in this course. 3. Only linear circuits are considered in this course.

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1.2 System of Units1.2 System of Units

nn The International System of Units (SI) enables The International System of Units (SI) enables engineers to communicate their results efficiently if engineers to communicate their results efficiently if they use the same units of measure. they use the same units of measure.

nn The SI units are based on the following defined The SI units are based on the following defined quantities.quantities.

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Table 1 : The SI UnitsTable 1 : The SI Units

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QuantityQuantity Basic UnitBasic Unit SymbolSymbol

LengthLength metermeter mm

MassMass kilogramkilogram kgkg

TimeTime secondsecond ss

Electric currentElectric current ampereampere AA

1.2 System of Units1.2 System of Units

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Table 2 : Derived Units in SITable 2 : Derived Units in SI

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QuantityQuantity Unit NameUnit Name(Symbol)(Symbol) FormulaFormula

FrequencyFrequency hertz (Hz)hertz (Hz)

ForceForce newton (N)newton (N)

EnergyEnergy joule (J)joule (J)

PowerPower watt (W)watt (W)

ChargeCharge coulomb (C)coulomb (C)

VoltageVoltage volt (V)volt (V)

1s−

2/kg m s⋅

N m⋅

/J s

A s⋅

/J C

1.2 System of Units1.2 System of Units

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Table 2 : Derived Units in SI (cont.)Table 2 : Derived Units in SI (cont.)

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QuantityQuantity Unit NameUnit Name(Symbol)(Symbol) FormulaFormula

ResistanceResistance ohm (ohm (ΩΩ))

ConductanceConductance siemens (S)siemens (S)

CapacitanceCapacitance farad (F)farad (F)

Magnetic fluxMagnetic flux weber (Wb)weber (Wb)

InductanceInductance henry (H)henry (H)

/V A

/A V

/C V

/Wb A

V s⋅

1.2 System of Units1.2 System of Units

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Table 3 : Standardized PrefixesTable 3 : Standardized Prefixes

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PrefixPrefix SymbolSymbol PowerPower

attoatto aa

femtofemto ff

picopico pp

nanonano nn

micromicro μμ

millimilli mm

centicenti cc

1810−

1510−

1210−

310−

610−

910−

210−

1.2 System of Units1.2 System of Units

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Table 3 : Standardized Prefixes (cont.)Table 3 : Standardized Prefixes (cont.)

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PrefixPrefix SymbolSymbol PowerPower

decideci dd

dekadeka dada

hectohecto hh

kilokilo kk

megamega MM

gigagiga GG

teratera TT

110−

10

210

910

610

310

1210

1.2 System of Units1.2 System of Units

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nnVoltage is the energy per unit charge created by Voltage is the energy per unit charge created by the separation of charges. the separation of charges.

nnSI unit : SI unit : volt (volt (VV))

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v = the voltage in volts

ε = the energy in joules

q = the charge in coulombs

1.3 Voltage and Current1.3 Voltage and Current

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Alessandro Antonio Volta1745-1827Germany

???19XX-20XXR.O.C. Taiwan

1.3 Voltage and Current1.3 Voltage and Current

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nnElectric currentElectric current is the rate of charge flow.is the rate of charge flow.nnSI unit :SI unit : ampere (A)ampere (A)

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i = the current in amperes

q = the charge in coulombs

t = the time in seconds

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Note : Data taken from W.F. Cooper , Electrical Safety EngineeriNote : Data taken from W.F. Cooper , Electrical Safety Engineering 2ng 2ndnd. . (London (London ﹕﹕Butterworth , 1986) ; and C.D. Winburn , Practical, Butterworth , 1986) ; and C.D. Winburn , Practical, Electrical Safety (Monticello , N.Y. : Marcel Dekker ,Electrical Safety (Monticello , N.Y. : Marcel Dekker , 1988)1988)

Barely perceptibleBarely perceptible 3 ~ 5 mA3 ~ 5 mA

Extreme painExtreme pain 30 ~ 50 mA30 ~ 50 mA

Muscle paralysisMuscle paralysis 50 ~ 70 mA50 ~ 70 mA

Heart stoppageHeart stoppage 500 mA500 mA

nn Physiological reactions to current levels in humansPhysiological reactions to current levels in humans

1.3 Voltage and Current1.3 Voltage and Current

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AndreAndre--Maria AmpereMaria Ampere17751775--18361836ScotlandScotland 1616

1.3 Voltage and Current1.3 Voltage and Current

???19XX-20XXR.O.C. Taiwan

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1.4 Passive Sign Convention1.4 Passive Sign Convention

nn The circuit elements (or components) considered in The circuit elements (or components) considered in this course can be twothis course can be two--terminal, threeterminal, three--terminal, or terminal, or fourfour--terminal components.terminal components.

nn They are ideal mathematical models and may not They are ideal mathematical models and may not be realized in the physical world.be realized in the physical world.

nn However, actual devices and systems can be However, actual devices and systems can be modeled by using these ideal elements.modeled by using these ideal elements.

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nn twotwo--terminal elementterminal element (example: resistor)(example: resistor)

RV

nn threethree--terminal elementterminal element (example: npn transistor)(example: npn transistor)

+

-

+

-beV

ceV

1.4 Passive Sign Convention1.4 Passive Sign Convention

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nn fourfour--terminal elementterminal element (example: coupling inductors)(example: coupling inductors)

1v 2v1L 2L

1.4 Passive Sign Convention1.4 Passive Sign Convention

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nn For a twoFor a two--terminal element, the reference voltage terminal element, the reference voltage polarity and the reference current direction can be polarity and the reference current direction can be arbitrarily assigned.arbitrarily assigned.

nn If passive sign convention is chosen, then the If passive sign convention is chosen, then the current reference direction is automatically chosen current reference direction is automatically chosen to be in the direction of the reference voltage drop to be in the direction of the reference voltage drop across the element.across the element.

nn Hence, only one reference is required.Hence, only one reference is required.2020

1.4 Passive Sign Convention1.4 Passive Sign Convention

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v+

-

v+

-

i

1.4 Passive Sign Convention1.4 Passive Sign Convention

Choose voltage polarity reference

Choose current direction reference

Implies the current reference direction

Implies the voltage polarity reference

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1.5 Power and Energy1.5 Power and EnergynnThe output capacity of an electrical system is often The output capacity of an electrical system is often

expressed in terms power or energy.expressed in terms power or energy.nnPower is work done per unit timePower is work done per unit timennSI unit : watt(w)SI unit : watt(w)

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p = the power in watts

ε = the energy in joules

t = the time in seconds

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nnFrom definitions of From definitions of vv and and ii

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1.5 Power and Energy1.5 Power and Energy

p = the power in wattsv = the voltage in voltsi = the current in amperes

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nnIf passive sign convention is adopted , thenIf passive sign convention is adopted , then

pp>0 , this power is dissipated in (or being >0 , this power is dissipated in (or being delivered to) the component or circuit.delivered to) the component or circuit.

pp<0 , this power is being extracted (or generated) <0 , this power is being extracted (or generated) from the component or circuit.from the component or circuit.

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1.5 Power and Energy1.5 Power and Energy

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nnEnergy can be calculated by integrating the Energy can be calculated by integrating the corresponding powercorresponding power

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1.5 Power and Energy1.5 Power and Energy

ε = the energy in joulesp = the power in wattst = the time in second

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SummarySummarynn Objective 1Objective 1：：Understand and be able to use SI Understand and be able to use SI

units and the standard prefixes for units and the standard prefixes for powers of 10.powers of 10.

nn Objective 2Objective 2：：Know and be able to use the Know and be able to use the definitions of definitions of vv andand ii..

nn Objective 3Objective 3：：Know and be able to use the Know and be able to use the definitions of definitions of pp and and εε..

nn Objective 4Objective 4：：Be able to use the passive sign Be able to use the passive sign convention and interpret the meaning convention and interpret the meaning of the algebraic sign of of the algebraic sign of pp.. 2626

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Assignment : Chapter ProblemsAssignment : Chapter Problems

nn ProblemProblem 1.171.171.19(a)1.19(a)1.231.231.301.30

nn Due within one week.Due within one week.

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