electromagnetism - question regarding inverse relation of resistance with area of cross section -...

4/4/2015 electromagnetismQuestionregardinginverserelationofresistancewithareaofcrosssectionPhysicsStackExchange

http://physics.stackexchange.com/questions/67608/questionregardinginverserelationofresistancewithareaofcrosssection 1/2

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Questionregardinginverserelationofresistancewithareaofcrosssection

Itissaidthatresistanceisinverselyproportionaltoareaofcrosssection.Butgreaterareawillhavegreaterelectricflux,andgreaterelectricfluxwillhavegreatermagneticflux,andgreaterthemagneticfluxwillhavegreatereddycurrent,whichisoppositetothecurrentflowing.Sothiswillopposethecurrenthenceresistanceincreases.AmIright?

electromagnetism electrostatics resistance

editedJun10'13at18:51Qmechanic 44.1k 6 61 138

askedJun10'13at17:22kuldeepsingh11 1

3Answers

Eveniftheclaimwerecorrect,youwouldnotbe youwouldbe whilethestatementyouaremakingwouldbe .)

true righttrue

Buttheexplanationyouareofferingisn'tright.Thereasonwhytheresistancegoeslike issimplythatforaconstantcurrent ,thecurrentperunitareacurrentdensityis andaccordingtothemicroscopic ,it'sthecurrentdensitythatdictatesthevoltageperunitlengthofthewire(alsoknownastheelectricfield):

ComparingthisequationwiththeusualOhm'slaw ,weseethat

Becauseyou'reonlychanging while arekeptfixed,youseethat .Magneticfieldsdon'tplayanyrolehereatallwhileelectricfieldsdoplayrolebutwenevercalculateany"electricflux"toconstructtherightjustification.

1/AI j = I/A

Ohm'slaw J = E

| | = V

E

1

I

A

V = RI

R =

A

A , V 1/A

answeredJun10'13at17:39LuboMotl110k 7 162 323

welltheresistanceyouaretalkingaboutistheresistancewhichtheflowofcurrentexperiencesbecauseofcollisionofelectronswithfixedkernels.thevalueofthisresistanceisinverselyproportionaltoareaofconductor

answeredJun13'13at19:22manuja1 1

Let'sanalyseeachsegmentofyourpost:

Itissaidthatresistanceisinverselyproportionaltoareaofcrosssection.

Yes,thatistrueforanconductorwhenotherphysicalparametersarefixed(length,resistivity,temperature)

Butgreaterareawillhavegreaterelectricflux...

Yes.

...andgreaterelectricfluxwillhavegreatermagneticflux...

TheElectriccurrentintheconductorwillcauseamagneticfieldthatwrapsaroundtheconductor,thefield(orfluxdensity)willbeproportionaltothecurrent.

4/4/2015 electromagnetismQuestionregardinginverserelationofresistancewithareaofcrosssectionPhysicsStackExchange

http://physics.stackexchange.com/questions/67608/questionregardinginverserelationofresistancewithareaofcrosssection 2/2

...andgreaterthemagneticfluxwillhavegreatereddycurrent,whichisoppositetothecurrentflowing.

Thatwouldbethecase ifthemagneticfluxchanges,whichinturnmeansthatthecurrentandvoltagehastochangewithtime.Inotherwords:itdoesnotmatterforDC.IwillignorethevariousformsoffluctuatingcurrentandonlyfocusonsinusoidalAC.

only

TheeddycurrentsinhighfrequencyACcauseavarietyofeffects,themostrelevantofwhich,inthiscaseofasingleconductoris' '.Buteveninthatcase,theresistanceisinverselyproportionaltodiameter(decreaseswithincreaseinarea):

Skineffect

whereiscalledtheskindepth.Theskindepthisthusdefinedasthedepthbelowthesurfaceoftheconductoratwhichthecurrentdensityhasfallento1/e(about0.37)ofcurrentdensityatsurface.

Sothiswillopposethecurrenthenceresistanceincreases.AmIright?

Yes,resistancedoesincreasewhenyoutakeintoaccounttheeffectofeddycurrentincertainsituations(fluctuatingvoltagelikehighfreqAC) justDCwithouteddycurrents.Butifyouimpliedthatlargerareadoesnotdecreaseresistance,youarewronginthiscase.

comparedto

answeredJul13'13at22:44mehfoos923 1 4 15