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Fundamental of Electrical circuits

Fundamental of Electrical circuits. Course Des c ription:. Electrical units and def i nitio n s : V olta g e, current, po w e r , en e rg y , circu i t el e ments: r esistors, ca p acitors, i n ductors, i n de p en d ent and de p en d ent sources.

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Fundamental of Electrical circuits

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  1. Fundamental of Electrical circuits

  2. Course Description: Electricalunitsanddefinitions:Voltage,current, power,energy,circuitelements: resistors, capacitors, inductors,independentanddependentsources. CircuitTheory and analysismethods: Kirchhoff’sLaws,voltageandcurrent divider,nodeandmeshanalysis,TheveninandNorton theorem,maximumpowertransfer,superposition theorem. SinusoidalSteady StateAnalysis:sinusoidproperties, complexnumber representations,phasors, circuit theory andanalysis methodinAC circuits.

  3. Textbook: WilliamH.Hayt,Jr.,JackE.Kemmerly,Steven M.Durbin“EngineeringCircuitAnalysis”, Eighth edition,McGraw-Hill.

  4. Chapter 1: Introduction Circuittheory: Afieldasdiverseas electricalengineering Electriccircuits:commonfor EE.: Amathematicalmodel,whichapproximates thebehaviorofanactualelectric system

  5. Overview: • Linearcircuitanalysis: • Resistivecircuitanalysis:introduceanumber ofvery powerfultechniques,suchasnodal analysis,meshanalysis,superposition,etc. • time-domainanalysis:allowcapacitors and inductorsto beincludedinacircuit. • frequency-domainanalysis:transform differentialequationsintomoreeasilymanaged algebraicequations.

  6. Relationship: RelationshipofCircuitAnalysistoEngineering: Learninghowtoanalyzeaproblem. Tolearnhowto •Tobemethodical •Todeterminethegoalofaparticularproblem •Towork withtheinformationgivento develop aplanofattack •Toimplementtheplantoobtainasolution •Toverify thattheproposedsolutionisaccurate

  7. AnalysisandDesign: This textisfocusedondevelopingour abilitytoanalyzeandsolveproblem. Developingourdesignskillscomesless naturallyto usthandevelopingouranalytical skills.

  8. Computer-Aided Analysis: Moderncircuitanalysissoftwareis rapidly increasinginitslevelofintegration. Weneedtohaveasolidunderstandingof howcircuits workinorderto developanability todesignthem.

  9. Problem-Solving: Asuggested problem- solvingflowchart

  10. Problem-Solving: • Developtheskillstosuccessfullyattackthe • unsolvedproblems • Identifywhat’s givenandwhat’s to befound • Sketcha circuitdiagramorothervisualmodel • label,reference,redrawtosimpleform • simplified • Thinkofseveralsolutionmethods andaway of choosingamongthem • Calculateasolution • paperandpencil • calculator • Useyourcreativity • Test yoursolution

  11. Chapter 2: BasicComponentsandElectricCircuits

  12. Objectives: • Definitionofbasicelectricalquantitiesandassociatedunits • Therelationshipbetweencharge, current, voltage,andpower • Thepassivesignconvention • Dependentand independentvoltageand currentsources • ThebehavioroftheresistorandOhm’slaw

  13. Unitsand Scales: • In order to state the value of some measurable quantity, we must • give both a number and a unit, such as “3 meters. • The most frequently used system of units is the International • System of Units (abbreviated SI in all languages). TABLE :2.1 SI BaseUnits The fundamental unit of work or energy is the joule (J). One joule = in SI base units) The fundamental unit of power is the watt (W), defined as 1 J/s.

  14. Unitsand Scales: TABLE2.2 SI Prefixes

  15. Charge: • There are two types of charge: • positive (corresponding to a proton) and • negative (corresponding to an electron). • the fundamental unit of charge is the coulomb (C). • It is defined in terms of the ampere by counting the total charge that • passes through an arbitrary cross section of a wire during an interval of • one second; one coulomb is measured each second for a wire carrying • a current of 1 ampere (Fig. 2.1). • In this system of units, a single electron has a charge of • and a single proton has a charge of • A quantity of charge that does not change with time • is typically represented by Q. • The instantaneous amount of charge • (which may or may not be time-invariant) • is commonly represented by q(t), or simply q.

  16. Current: • Electrical current is the time rate of flow of electrical charges through a • conductor or circuit element. • Current is symbolized by Ior i, and so • The unit of current is the ampere (A), It is commonly abbreviated as an • “amp,”. • One ampere equals 1 coulomb per second. (A=C/s). • The charge transferred between time tₒand t • may be expressed as a definite integral: • The total charge transferred • over all time is thus given by

  17. Current:

  18. Current: Twodifferentmethodsoflabelingthesamecurrent. (a,b)Incomplete,improper,and incorrectdefinitionsofacurrent. (c)thecorrectdefinitionofi1(t).

  19. Current:

  20. Voltage: • An electrical voltage (or a potential difference) exists between two • terminals is a measure of the work required to move charge • through the element. • The unit of voltage is the volt (V), and 1 volt is the same as 1 J/C. • Voltage is represented by V or v. • A voltage can exist between a pair of electrical terminals whether a • current is flowing or not. • Voltages are assigned polarities that indicates the direction of • energy flow. • The voltage is indicated by a plus-minus pair of algebraic signs.

  21. Voltage: (a,b) Theseareinadequatedefinitionsof avoltage.(c)Acorrectdefinitionincludes bothasymbolforthevariableand aplus- minussymbolpair. (a,b) TerminalBis5Vpositivewith respecttoterminalA; (c,d) terminalAis5Vpositivewith respecttoterminalB.

  22. Power: • It is represented by P or p. • Its unit is watts (W) • Passive sign convention • If a positive current is entering a positive terminal of • an element, then the energy is supplied to the element • (or the element absorbs the power). • If a positive current is entering a negative terminal of • an element, then the energy is supplied by the element • (or the element generates the power).

  23. Power: Computethe powerabsorbedbyeachpart.

  24. Power: Computethe powerdelivered byeachpart.

  25. Energy calculation:

  26. Sources: Symbolforanindependentcurrent source. Symbolforindependent voltage source:(a)DCvoltagesource; (b)battery;(c)acvoltagesource. Thefourdifferenttypes ofdependentsources: current-controlled currentsource; (CCC) voltage-controlled currentsource; (VCC) voltage-controlledvoltagesource; (VCV) current-controlledvoltagesource. (CCV)

  27. Dependant sources

  28. Example: Inthecircuitbelow,ifv2 isknowntobe 3V,findvL.

  29. Example: Findthepowerofeachelementinthecircuitbelow.

  30. Networkand Circuits: Theinterconnectionoftwoormore simplecircuitelementsformsandelectricalnetwork.Ifthenetworkcontainsatleastone closedpath,itis alsoanelectriccircuit.

  31. Ohm’sLaw: Ohm’s law states that the voltage across conducting materials is directly proportional to the current flowing through the material • where the constant of proportionality R is called the resistance. The unit of • resistance is the ohm, which is 1 V/A and customarily abbreviated by a • capital omega, Ω.

  32. Ohm’sLaw: passiveelement:R,L,C activeelement: sources

  33. Example:

  34. Homework: Determinethe powerbeingabsorbedbyeach ofthecircuitelementsshown

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