ChapterChapter 27.27. CurrentCurrent andand ResistanceResistance AAA PowerPointPowerPointPowerPoint PresentationPresentationPresentation bybyby PaulPaulPaul E.E.E. Tippens,Tippens,Tippens, ProfessorProfessorProfessor ofofof PhysicsPhysicsPhysics SouthernSouthernSouthern PolytechnicPolytechnicPolytechnic StateStateState UniversityUniversityUniversity © 2007 Objectives:Objectives: AfterAfter completingcompleting thisthis module,module, youyou shouldshould bebe ableable to:to:
•• DefineDefine electricelectric currentcurrent andand electromotiveelectromotive forceforce.. •• WriteWrite andand applyapply OhmOhm’’ss lawlaw toto circuitscircuits containingcontaining resistanceresistance andand emf.emf. •• DefineDefine resistivityresistivity ofof aa materialmaterial andand applyapply formulasformulas forfor itsits calculation.calculation. •• DefineDefine andand applyapply thethe conceptconcept ofof temperaturetemperature coefficientcoefficient ofof resistanceresistance.. ElectricElectric CurrentCurrent
ElectricElectric currentcurrent II isis thethe raterate ofof thethe flowflow ofof chargecharge QQ throughthrough ++ +Q A aa crosscross--sectionsection AA inin aa unitunit ofof A timetime tt.. tt Q 1C WireWire I 1 A t 1 s --
OneOneOne ampereampereampere AAA isisis chargechargecharge flowingflowingflowing atatat thethethe rateraterate ofofof oneoneone coulombcoulombcoulomb perperper secondsecondsecond... ExampleExample 1.1. TheThe electricelectric currentcurrent inin aa wirewire isis 66 A.A. HowHow manymany electronselectrons flowflow pastpast aa givengiven pointpoint inin aa timetime ofof 33 s?s? q IqIt; t II == 66 AA qq == (6(6 A)(3A)(3 s)s) == 1818 CC RecallRecall that:that: 11 ee- == 1.61.6 xx 1010-19 C,C, thenthen convert:convert: - 1e 20 18 C 18 C-19 1,125 x 10 electrons 1.6 x 10 C
In 3 s: 1.12 x 1020 electrons ConventionalConventional CurrentCurrent ImagineImagine aa chargedcharged capacitorcapacitor withwith QQ == CVCV thatthat isis allowedallowed toto discharge.discharge. + - + - Electron flow: The direction + - Electron flow: The direction - Electron ofof ee flowingflowing fromfrom –– toto +.+. e- flow + ConventionalConventional current:current: TheThe motionmotion ofof +q+q fromfrom Conventional flow ++ toto –– hashas samesame effect.effect.
ElectricElectric fieldsfields andand potentialpotential areare defineddefined inin termsterms ofof +q+q,, soso wewe willwill assumeassume conventionalconventional currentcurrent (even(even ifif electronelectron flowflow maymay bebe thethe actualactual flow).flow). ElectromotiveElectromotive ForceForce AA sourcesource ofof electromotiveelectromotive forceforce (emf)(emf) isis aa devicedevice thatthat usesuses chemical,chemical, mechanicalmechanical oror otherother energyenergy toto provideprovide thethe potentialpotential differencedifference necessarynecessary forfor electricelectric current.current.
PowerPower lineslines BatteryBattery WindWind generatorgenerator WaterWater AnalogyAnalogy toto EMFEMF
High Constriction Low High Resistor Low pressure pressure potential potential + - R I Switch Water Valve Flow E
Water Pump Source of EMF
TheThe sourcesource ofof emfemf (pump)(pump) providesprovides thethe voltagevoltage (pressure)(pressure) toto forceforce electronselectrons (water)(water) throughthrough electricelectric resistanceresistance (narrow(narrow constriction).constriction). ElectricalElectrical CircuitCircuit SymbolsSymbols
ElectricalElectrical circuitscircuits oftenoften containcontain oneone oror moremore resistorsresistors groupedgrouped togethertogether andand attachedattached toto anan energyenergy source,source, suchsuch asas aa battery.battery. TheThe followingfollowing symbolssymbols areare oftenoften used:used: Ground Battery Resistor + -
+ - + - -+ -+ - ElectricElectric ResistanceResistance SupposeSuppose wewe applyapply aa constantconstant potentialpotential differencedifference ofof 44 VV toto thethe endsends ofof geometricallygeometrically similarsimilar rodsrods of,of, say:say: steel,steel, copper,copper, andand glass.glass.
Steel Copper Glass
Is Ic Ig
4 V 4 V 4 V TheThe currentcurrent inin glassglass isis muchmuch lessless thanthan forfor steelsteel oror iron,iron, suggestingsuggesting aa propertyproperty ofof materialsmaterials calledcalled electricalelectrical resistanceresistance R.R. OhmOhm’’ss LawLaw OhmOhm’’ss lawlaw statesstates thatthat thethe currentcurrent II throughthrough aa givengiven conductorconductor isis directlydirectly proportionalproportional toto thethe potentialpotential differencedifference VV betweenbetween itsits endend points.points. Ohm' s law: I V OhmOhm’’ss lawlaw allowsallows usus toto definedefine resistanceresistance RR andand toto writewrite thethe followingfollowing formsforms ofof thethe law:law: VV IVIRR; ; R I ExampleExample 2.2. WhenWhen aa 33--VV batterybattery isis connectedconnected toto aa light,light, aa currentcurrent ofof 66 mAmA isis observed.observed. WhatWhat isis thethe resistanceresistance ofof thethe lightlight filament?filament? V 3.0 V R I 0.006 A
RR == 500500 R = 500 + - R TheThe SISI unitunit forfor electricalelectrical I 6 mA resistanceresistance isis thethe ohmohm,, V = 3 V 1 V 1 Source of 1 A EMF LaboratoryLaboratory CircuitCircuit SymbolsSymbols
A + V Emf Rheostat -
Source of Voltmeter Source of Ammeter Rheostat EMF FactorsFactors AffectingAffecting ResistanceResistance
1.1. TheThe lengthlength LL ofof thethe material.material. LongerLonger materialsmaterials havehave greatergreater resistance.resistance. LL 2L2L 11 22 2.2. TheThe crosscross--sectionalsectional areaarea AA ofof thethe material.material. LargerLarger areasareas offeroffer LESSLESS resistance.resistance.
AA 2A2A 22 11 FactorsFactors AffectingAffecting RR (Cont.)(Cont.) 3.3. TheThe temperaturetemperature TT ofof thethe material.material. TheThe higherhigher temperaturestemperatures usuallyusually resultresult inin higherhigher resistances.resistances.
RR >> RRo RRo 4.4. TheThe kindkind ofof materialmaterial.. IronIron hashas moremore electricalelectrical resistanceresistance thanthan aa geometricallygeometrically similarsimilar coppercopper conductor.conductor.
RRi >> RRc Copper Iron i c ResistivityResistivity ofof aa MaterialMaterial
TheThe resistivityresistivity isis aa propertyproperty ofof aa materialmaterial thatthat determinesdetermines itsits electricalelectrical resistanceresistance RR..
RecallingRecalling thatthat RR isis directlydirectly proportionalproportional toto lengthlength LL andand inverselyinversely proportionalproportional toto areaarea AA,, wewe maymay write:write: L RA R or A L
TheThe unitunit ofof resistivityresistivity isis thethe ohmohm--metermeter ((m)
ExampleExample 3.3. WhatWhat lengthlength LL ofof coppercopper wirewire isis requiredrequired toto produceproduce aa 44 mm resistor?resistor? AssumeAssume thethe diameterdiameter ofof thethe wirewire isis 11 mmmm andand thatthat thethe resistivityresistivity ofof coppercopper isis 1.721.72 xx 1010-8 .mm ..
D22(0.001 m) A AA == 7.857.85 xx 1010-7 mm2 44 L RA (0.004 )(7.85 x 10-7 m 2 ) R L -8 A 1.72 x 10 m
RequiredRequired lengthlength is:is: L = 0.183 m TemperatureTemperature CoefficientCoefficient ForFor mostmost materials,materials, thethe resistanceresistance RR changeschanges inin proportionproportion toto thethe initialinitial resistanceresistance Ro andand toto thethe changechange inin temperaturetemperature tt.. ChangeChange inin R Rt resistance:resistance: 0 TheThe temperaturetemperature coefficientcoefficient ofof resistance,resistance, isis thethe changechange inin resistanceresistance perper unitunit resistanceresistance perper unitunit degreedegree changechange ofof temperature.temperature. R 1 ; Units: 0 Rt0 C ExampleExample 4.4. TheThe resistanceresistance ofof aa coppercopper wirewire isis 4.004.00 mm atat 20200CC.. WhatWhat willwill bebe itsits resistanceresistance ifif 0 o heatedheated toto 8080 CC?? AssumeAssume thatthat == 0.0040.004 /C/C .. o o o RRo == 4.004.00 mmtt == 8080 CC –– 2020 CC == 6060 CC 00 RRtR 0 ; (0.004/ C )(4 m )(60 C )
RR== 1.031.03 mm RR == RRo ++ RR
RR == 4.004.00 mm + 1.03 mm
RR == 5.035.03 mm ElectricElectric PowerPower ElectricElectric powerpower PP isis thethe raterate atat whichwhich electricelectric energyenergy isis expended,expended, oror workwork perper unitunit ofof time.time. ToTo chargecharge C:C: WorkWork == qVqV Work qV q V q PI and tt t SubstituteSubstitute qq == ItIt ,, then:then: I V VIt P P = VI t CalculatingCalculating PowerPower
UsingUsing OhmOhm’’ss law,law, wewe cancan findfind electricelectric powerpower fromfrom anyany twotwo ofof thethe followingfollowing parameters:parameters: currentcurrent II,, voltagevoltage VV,, andand resistanceresistance RR..
OhmOhm’’ss law:law: VV == IRIR V 2 PVIPIR; 2 ; P R ExampleExample 5.5. AA powerpower tooltool isis ratedrated atat 99 AA whenwhen usedused withwith aa circuitcircuit thatthat providesprovides 120120--V.V. WhatWhat powerpower isis usedused inin operatingoperating thisthis tool?tool?
PP == VIVI == (120(120 V)(9V)(9 A)A) PP == 10801080 WW
ExampleExample 6.6. AA 500500--WW heaterheater drawsdraws aa currentcurrent ofof 1010 A.A. WhatWhat isis thethe resistance?resistance?
2 P 500 W PIRR; RR == 5.005.00 I 22(10 A) SummarySummary ofof FormulasFormulas
Q 1C ElectricElectric I 1 A current:current: t 1 s
Ohm’sOhm’s LawLaw VV IVIRR; ; R I 1 volt Resistance: 1 ohm 1 ampere SummarySummary (Cont.)(Cont.)
L RA ResistivityResistivityResistivity ofofof R or materials:materials:materials: A L
TemperatureTemperature coefficientcoefficient ofof resistance:resistance: R 1 R Rt0 ; Units: 0 Rt0 C
V 2 ElectricElectric PVIPIR; 2 ; P PowerPower P:P: R CONCLUSION:CONCLUSION: ChapterChapter 2727 CurrentCurrent andand ResistanceResistance