5F10-002
ElectricalResistanceandOhm’sLaw PROMPTSAFTER
STATEMENTOFTHEPROBLEM:ElectricalResistanceandOhm’sLaw
Astudentistryingtodeterminewhatwiretoselectinbuildingacircuitinwhichher9Volt
batteryneedstoprovideasmuchcurrentaspossibletoanelectricmotorthatwilldrivea
pulleyinascienceproject.Thelengthofthewirewillbe65cm.Shecoulduseapieceof
copperwirethatis0.5mmindiameteroraslightlylarger0.75mmaluminumwire.Which
wireshouldshechoose?
STRATEGY
Resistanceisdependentonbothlengthandmaterialtype.Thisisstatedmathematicallyin
R=ρL/A,whereρisthematerial’sresistivity,Listhelength,andAisthecross-sectional
area.Thenthecurrentisdirectlyrelatedto∆V,relatedbytheconstantofproportionalityR.
Ohm’sLawgivesthisrelationshipas∆V=IR.So,wemustexaminethetradeoffbetween
cross-sectionalareaanddifferentresistivityofthematerials.
IMPLEMENTATION
WewillcombinethetwoequationsabovetogetarelationshipforIandthenperformthe
calculationstoseewhichwiretochoose.
CALCULATION
∆V=IR=
! !!
!
and
∆!!
!!
=I=
∆!!! !
!!
Withnumbers:Icopper=
(!)(!.!")(.!"!!"!! )!
!.!"!!"!! (.!")
=162A
Ialuminum=
(!)(!.!")(.!"#!!"!! )!
!.!"!!"!! (.!")
=231A
So,usethealuminumwire.
Anotherpossiblestrategywouldbetocalculatetheresistancesofthecopperandaluminum
wires,thenchoosethewirewiththelowestresistance.Wouldthatmethodwork?WhyorWhy
not?
5F10-002
ElectricalResistanceandOhm’sLaw PROMPTSAFTER
SELF-EXPLANATIONPROMPTS
1. LookingatatableofMaterialReistivities(Table24.1inyourtext,page406)whatmetal
wouldhavebeentheworstchoice,andwhichwouldhavebeentheverybestchoice?
Whatotherproblemswoulduseofthesemetalshavebroughtabout?
2. Whatcanbesaidabouttherelationshipbetween∆VandI?Materialsthatobeythis
relationship,throughouttherangeof∆Vtheyaresubjectedto,arecalled“Ohmic”.
3. ExamineExample24.4inthetext.Howisthisproblemsimilartoordifferentfromthe
aboveexample?(B)Re-readtheparagraphinthetextjustbelowExample24.4.What
objectinyourpocketsometimesexhibitsagooddealoftheresistancetocurrentflow
described?