Resistance, Ohm’s Law, and the Temperature of a Light Bulb ...

1 Resistance, Ohm's Law, andtheTemperature ofaLightBulbFilamentNamePartnerDateIntro ductionCarbonresistorsarethekindtypicall yusedin aremadefroma smallcylinderofgraphite,surroundedbya protective ,orleads,areattachedtotheendsofthegraphi tecylinderandheldin the lamentofa lamentusuallyconsistsofa thintungstenwirewithitstwo endsconnectedtoseparatepartsofthemetalba seofthelightbulb. Like most(butnotall)solidmaterials,graphitean dtungstenareohmic,whichmeansthatresistor smadefromthemobey Ohm's Law, V=IR;where Vis thepotentialdifferenceacrosstheresistor, Iis thecurrent owingthroughtheresistor,andRistheresista nceoftheresistor.

2 TheunitforresistanceistheOhm,abbreviated withtheGreekomega, (1 = 1V/A). Carbonresistorstypicallyrangefromabout10 toabout10M .Figure1:Schematicdiagramofa 's Lawsaysthat VandIareproportional,onemightexpectthata graphof V(verticalaxis) (horizontalaxiswillbea straightlinethroughtheoriginwithslopeequ altotheconstantR. Insomecases,however, sucha graphwillnotresultina thatlargercurrentstendtoheatupa resistor, andformostmaterialsa changeintemperaturecausesa changeinresistance,R. Thistemperaturedependenceoftheresistance appearsasa changingslopeina ,youwillusethechangingresistanceofa lightbulb rsttwo coloredbandsgive the rsttwo ,considera resistorwiththecoloredbandsred(=2),black (=0),orange(=3),andgold(=5%).)

3 Thevalueoftheresistanceforthisresistoris 20 103 = 20k witha toleranceof5%= 1 k . SotheresistancewouldberecordedasR = 20 1 k .Table1 ,ThirdEdition, "loose"resistorsat yourworkstation(they bothhave thesamecolorcode),recordthecolorsoftheba ndsandthecorrespondingresistancevaluewit htoleranceinthespacebelow. :HeatDissipationinResistorsAlthoughbotho fyourresistorshave thesamecolorcode,they "burnout" convenienttimeduringthelabperiod(notnece ssarilynow),toucheachresistortoseewhicho neis warmerandrecordyourobservationsinthespac ebelow.

4 Thetwo resistorsarecarryingthesamecurrent?Activ ity3:DigitalMultimetersandResistanceMeas urementsDigitalmultimeters(DMMs)areelect ronicdevicesthatcanbeusedtomake a threeDMMsatyourstation have andtodeterminehow they V , COM, ,asexplainedbelow. regionsmarkedV, A, ,(andperhapsothers)formeasuringvoltage,c urrent, DMMcanbeusedasanohmmeter ,youwilluseit theresistoryouwishtomeasurewithanohmmete ris wiredintoacircuit,it ,connectanotherintotheV terminal,andturntherotatingdialintothe getmaximumaccuracy, youshouldturnthemeterdialto thelowest rangepossiblewith-outcausingover ow.

5 Recordtheresistanceandmeterrangeinthespa cebelow. ofthesemetersis approximately1%,andusethisinrecordingthe uncertainty. DoesthevalueofresistancemeasuredwiththeD MMagreewiththecolorcodevaluetowithinexpe rimentaluncertainties? inthespacebelow. Doesthemeasuredvalueagreewiththevaluepri ntedontheresistortowithinexperimentalunc ertainties? measuretheresistanceofthelightbulb. Recordthevalueandthemeterrangeyouusedtom easureit inthespacebelow. Don't :Usinga DMMasa measurevoltage,theleadsshouldbeattachedt otheCOMandV terminals, ,theV terminalis coloredred(forpositive).

6 Regardlessofcoloring, circuit,thenumberdisplayedbythemeterwill bethepotentialdifferencebetweenthosetwo cally, themeterwillreadthepotentialatthepositiv e terminalminusthepotentialat thenegative Figure2 ,becauseanincorrectlywiredcircuitis likelytogive spuriousresultsandmayburnouta Now connecttheDMMtothecircuitsoastomeasureVA - VB. To getmaximumaccuracy thedialshouldbesettothelowestvoltagerang ethatdoesnotcauseover ow. Recordthevoltageandthemeterrangethatyoua reusinginthespacebelow. Don't forgettheuncertainty.

7 (I'mnotgoingtosaythisanymore.) youreversetheleadstothemeter?Tryit,recor dandexplaintheresults,thenreturntheleads totheirpreviouscon 's Law, if a resistorweretohave zeroresistance,thepotentialdifferenceacr ossit wouldbezero, (Leave the rstDMMinplace.) + power SupplyResistorBulbABCDF igure2:A seriescircuitwitha resistor, lightbulb, :Usinga DMMasanAmmeterAnammeteris a ,anammetermeasuresthecurrent owingthroughthemeteritself,butit canbeusedtomeasurethecurrent owingthrougha resistorina toinsertthemeterintothecircuitinsucha waythatallthecurrent owingthroughtheresistorofinterestalsogoe sthroughthemeter.

8 Forexample,if theconnectionbetweenpointsB andC inthecircuitinFigure2 is replacedwithtwo leadsanda meterasshowninFigure3,thenany currentgoingthroughtheresistormustalsogo throughthemeter. Similarly, allthecurrentthat owsthroughthemetermustalsogothroughtheli ghtbulb. Byinsertingtheammeterintothecircuitinthi sway, usethesecondmeterasanammeter, remove thewireconnectingB toC andreplaceit thenumber5 +AVPower SupplyResistorBulbCDABF igure3:A seriescircuitwitha resistor, lightbulb,andpowersupply. Thevoltmetermeasuresthepotentialdifferen ceacrosstheresistorandtheammetermeasures thecurrent negative, reversetheleadstothemeter.

9 Recordthecurrentandusanarrow onthediagraminFigure3 :I-VGraphsfora Resistoranda , VR, thepotentialdifferenceacrossthelightbulb , VB, andthecurrentinthecircuit,I, fordifferentpowersupplysettingsinapproxi mately2 Vincrementsbetween0 and30V. Recordyourdataina tableinthespacebelow. Make a notebesideyourtabletoindicatethepointat graphofthepotentialdifferenceacrossthere sistor, VR, (verticalaxis)versusthecurrent,I, (horizontalaxis).Doestheresistorappearto beohmic? Also,doa graphofthepotentialdifferenceacrosstheli ghtbulb, VB, (verticalaxis)versusthecurrent,I, (horizontalaxis).

10 Doesthelightbulbappeartobeohmic? alreadymeasuredthetemperatureofthelightb ulbwhenit is ndthehightemperatureresistanceofthe lamentby ttingthedataintheregionwherethebulbis ,doa resistoris givenbyR=R0[1 + (T T0)];whereRistheresistanceattemperatureT ,R0istheresistanceattemperatureT0, and isthetemperaturecoef cientofresistance(seeyourtext).Useyourda tatoestimatethetemperatureofthelightbulb lamentwhenit is +AVVP ower SupplyResistorBulbABCDF igure4:Aseriescircuitwitha resistor, lightbulb,andpowersupply.