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CHAPTER25
CURRENT,RESISTANCEAND
ELECTROMOTIVEFORCE
BASICCONCEPTS
CURRENTandCURRENTDENSITY
RESISTANCEandRESISTIVITY
BATTERYINTERNALRESISTANCE
ENERGYANDPOWERINCIRCUITS
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CURRENTISTHEMOVEMENTOFCHARGE
INAMATERIAL
Insomecasestheobjectsthataremovingarepositive.
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Inothercases,forexampleinmetals,the
objectsarenegative(electrons).
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Currentisthetimerateofpassageofthe
charge.
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Considerthattherearenmovingchargedparticlespervolume
And
TheaveragedriftvelocityisvdThenintimedt
TheparticlesmoveadistanceofvddtInthevolume,Avddt, showninthefiguretherewillbenAvddtparticles.
Eachparticlehasachargeq.
Thusintimedtthecharge,dQ,thatwill
passthroughthecylinderis
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Currentis
Currentdensity(currentperunitcross
sectionoftheconductor)is
Notethatcurrentdensityisavector
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RESISTIVITY
Resistivity, ,isacharacteristicofa
material.
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RESISTIVITYResistivity, ,changeswithtemperature.
Where isthevalueat200C.
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Forametal:
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ForSemiconductor:
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Somematerialslooseallresistivity
Superconductors:
Discoveredin1911byH.Kammerlingh
Onnes.
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RESISTANCEResistanceisacharacteristicofanobject.
Resistance,R,isrelatedtoResistivity, ,by
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Thelongertheobjectthehigherthe
resistance.
Thelargerthecrosssectionthesmallerthe
resistance.
If isconstantthetotalcurrentthrougha
conductorisproportionaltothevoltage
acrossit.
Or
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Theconstantofproportionalityisthe
resistance,R.
Or
ThisisOhmsLaw.
IfaresistorobeysOhmsLawitisanOhmic
resistor.
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ObeysOhmsLaw:
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SemiconductorsarenotOhmic:
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POWERDISIPATEDWITHCURRENTFLOW.
Remember
q
V
Changeinenergy
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And
Therefore
UseOhmsLaw
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Or
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CALCULATERESISTANCE
AcopperrodwithcrosssectionAhasa
lengthLwhatisitsresistance? Workfor
and .
FromTable25.1
Therefore
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Moredifficult:Example25.4
Acylinderwithresistivity haslengthL,
innerradiusaandouterradiusb. Calculate
theresistanceforcurrentflowfromthe
innertotheouterwalls.
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Where isthepathlengthofthecurrent
flow.
And isthecrosssectionforcurrentflow.
Now
Considerathinshellwithinthecylinderwall
withradius ,thickness andlength .
Theareaoftheshellis .
Thepaththecurrentflowsis .
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Then
Integratetoget .
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CIRCUITS
Circuitelements:
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Othersymbolswillbeaddedafterwe
discussmagnetism.
InternalResistance
Twopoints:
Ifnocurrentisinacircuitelementthereis
nopotentialdropacrosstheelement.
Batterieshaveinternalresistance.
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Thefigureisofa12Vbatterywithno
currentinthecircuit.
Thevoltmeterwillread12V.
Butifthereiscurrent:
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Thevoltmeterwillreadlessthan12V.
Whatisthecurrentinthecircuit?
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Whatwillthevoltmeterread?