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