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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?