SP212 Lab: Five Kirchhoff’s Rules and RC Circuits
Version: February 20, 2014
PHYSICS II
LAB 5
SP212
Kirchhoff’sRulesandRCCircuits
Pages10‐11areAppendixesaddedforextrainformation.Pages1‐9onlyaretheLabinstructions.
I. Introduction
A. Today’sLabwillinvestigateKirchhoff’sjunctionlawandKirchhoff’s
voltagelaw,aswellasexperimentwithparallelandseriescircuits.The
finalpartofthelabistostudyacapacitorandresistortogetherina
circuit(RCcircuits).
II. NeededEquipment
A. ProtekDMM,3resistors(eachwithdifferentresistancevalue),multiple
bananaleads,twoD‐cellbatterieswithholders,twolightbulbs,
Tektronixpowersupply(PS),onecylindricalcapacitor,Labprowith3
ammetersandadifferencevoltagemeter,andapencil/pen.
III.TurninyourPre‐lab/homeworkproblemifassigned.
IV. Procedure
A. PreliminaryMeasurements
1. Setup(ifdirectedbyyourinstructor)Totestourthree
ammetersandourvoltageprobetoensurethattheyworkproperlybefore
westarttheexperiment.Yourinstructorwillshowyouhowtodothis
usingtheEquipmentTestProcedure.pdffile.Ifsomethingisn’tworking
correctly,tellyourinstructorandgetanewsensor.
http://intranet.usna.edu/PhysicsDepartment/SP211‐SP212/SP211‐212‐Manual.php Page 1 of 12 SP212 Lab: Five Kirchhoff’s Rules and RC Circuits
Version: February 20, 2014
2. MeasureResistanceUseyourProtekDMMtomeasureandrecordthe
resistanceofeachoftheresistorsonyourlabbench.(Rememberyoucan
lookattheresistorcolorcodetodeterminetheexpectedvalueofthe
resistanceprintedoneachresistor,butthereisatolerance,thisiswhywe
measureitsresistancewhenpossible).
3. Yourinstructorwillremindyouhowtodealwithuncertaintyfromthe
DMMandLogger‐Pro.
Link to the color code and DMM technical manuals; http://intranet.usna.edu/PhysicsDepartment/SP211‐SP212/SP211‐212‐Manual.php B. Kirchhoff’sJunctionRule,akaKirchhoff’sCurrentRule:
1. Buildthecircuitshownbelowforthispart.
2. Usethepowersupplyfortheemf,andsetitsoutputvoltagetobeabout3V.Zero
yourvoltageandcurrentprobes,takesomedata,andthentesttoseeifthe
currentintothejunctionisequaltothecurrentoutofthejunction.Alsotesttosee
ifthepotentialdifferencesacrosstheresistorsarethesame,andiftheyarethe
sameasthepotentialdifferenceacrosstheemf.Attachyourgraphtothe
spreadsheet.
3. Discussion:Inashortparagraphconsistingofcompletesentences,discuss
whetherornotyourmeasurementssupportorrefutetheformulaforadding
resistancesinparallel.AlsodiscusswhetherornottheysupporttheJunctionRule.
Page 2 of 12 SP212 Lab: Five Kirchhoff’s Rules and RC Circuits
Version: February 20, 2014
C. ATwo‐LoopCircuitwithanEMFineachloop:
1. Buildthecircuitshownbelowforthispart.
2. Notethatitisthecircuitfromthepre‐labproblem,withslightlydifferentvalues
forthecircuitelements.Wewanttopredictandmeasurethecurrentsinthis
circuit,andcomparetheresults.
3. Afteryoubuildthecircuit,takedata,andthengentlydisconnecttheD‐celland
powersupplies.TheideaistoavoidrunningtheD‐celldown,buttoleavethe
circuitalmostintact,soyoucantakeanotherdatasetifyouneedto.Enterthe
measuredvaluesoftheemfsintheappropriatecellsinyourspreadsheet.
4. UsingthesameequationsinyourTI‐N’spireCXcalculatorasyouusedtosolvethe
homeworkproblem,modifythevaluesoftheemfsandresistancesasnecessary
andpredictthecurrentsinthethreeresistors.Enterthesepredictionsinthe
appropriatecellsinyourspreadsheet,alongwiththemeasuredresistances(from
preliminarydata)andmeasuredcurrents.
5. Discussion:DoyourmeasurementssupportorrefuteKirchhoff'sRulesfor
analyzingcircuits?Pleasewriteacomprehensiveandcomprehensibleparagraph
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Version: February 20, 2014
D. An RC Circuit (Skip to E if you completed this section in Lab 4.)
1. Measuretheresistanceofyour39‐OhmresistorwithyourProtekDMM.Look
uptheuncertaintycode;itmaybedifferentfromthatfortheAmprobeDMM
usedinthesuppliedexampledata.
2. Thecapacitanceofthelargebluecapacitorisgiveninthespreadsheet
template,alongwithitsuncertainty.
3. Measurethetimeconstantofthiscircuit.
i. Tomakethemeasurement,followtheseinstructions:
ii. Buildthecircuitshownbelow.
For the resistor in the circuit, R, we will use a 39  resistor. PS is Tektronix power supply (5V
(far left hand side)).
Finally C is the 25,000 F (0.025 F) capacitor similar to the one shown on above.
iii. ProgramLoggerProbysettinguponevoltageandonecurrentsensor,
settingthedurationoftheexperimentto20seconds,anddatarateto
20samples/second.
iv. Startwiththeswitchinthedischargeposition.Makesurethe
capacitoriscompletelydischargedbyleavingtheswitchinthe
dischargepositionforalongtime.Zero all sensors.
v. Thenbegincollectingdata,andthenthrowtheswitchtothecharging
position.
vi. Afterthecapacitoriscompletelycharged,fliptheswitchtothe
dischargeposition,andcompletethedatarun.
Page 4 of 12 SP212 Lab: Five Kirchhoff’s Rules and RC Circuits
Version: February 20, 2014
vii. Fitexponentialstothecharginganddischargingcurves,andfindthe
timeconstantforeachcurvefromthefits.Averagetheresultsforyour
bestestimateofthemeasuredvalueofthetimeconstant,andusethe
standarddeviationasyourestimateoftheexperimentaluncertainty.
viii. Afterattachingyourgraphtothespreadsheet,annotateit:
1. Giveitatitle,includingthenumberandnameoftheexercise,
andnumberandnameoftheexperimentandpart.
2. Writethefinalresultofthemeasurement,withuncertaintyon
yourgraph.
3. Label,asIhavedoneinthesampledata,whenchargingand
dischargingaretakingplace.
4. Pointoutanythingelsethatisofinterestorimportanceto
yourreader.
4. Calculatethetheoreticaltimeconstantvalueforthiscircuitandcalculatethe
uncertaintyinyourpredictedvalue.τ=RC
5. Discussion:Compareyourmeasuredvalueforthetimeconstantwiththe
theoretically‐predictedvalue,thatis,explainwhetherornotthetwovalues
agree.Writeincompletesentences.Inadditiontocomparingpredictedand
measuredvaluesforthetimeconstant,explainthesignsandshapesofeachof
thefourcurvesinyourgraph.Usecomplete,grammaticallycorrectsentences
structuredintoacoherentparagraph.
E. Resistors in Series (If time permits)
1. Setupthe22‐Ohmand39‐OhmresistorinseriesandusetheProtekDMM
tomeasuretheresistanceoftheseriescombination.
2. Calculatethetheoreticalvalueoftheseriescombinationusingyour
measuredvaluesfortheindividualresistancesofthe22‐Ohmand39‐Ohm
resistorstocalculatethetheoreticalresistanceyoushouldgetwhenyou
connecttheminseries.Don’tforgettheuncertainty!
3. Compare your results to the theory;doesitlookliketheoverall
resistanceinseriesisthesumoftheindividualresistances?Inother
words,doesyourexperimentmatchtheory?
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Version: February 20, 2014
F. Kirchhoff’sLoopRule,akaKirchhoff’sVoltageRule(If time permits):
1. Buildthecircuitshownbelow.
2. Usethepowersupplyfortheemf,andsetitsoutputvoltagetobeabout3V.The
exactvaluedoesn’tmatter;youwillmeasureitwhenyoutakethedata.When
usingtheLabProtomeasurevoltagesandcurrents,theuncertaintyshouldbe
calculatedas2%ofthemeanvalue,plusthestandarddeviation
3. Zerotheprobesintheusualway,andcollectdata.
4. Usethemeasuredcurrent,alongwiththemeasuredresistances,tocalculatethe
potentialdifferencesacrosseachoftheresistors.Then,testtoseewhetherthe
sumofthepotentialdifferencesequalszerowhenyouwalkaroundthiscircuit.
5. Discussion:Inashortparagraphconsistingofafewcompletesentences,discuss
whetherornotyourmeasurementssupportorrefutetheformulaforadding
resistancesinseries.AlsodiscusswhethertheysupportorrefuteKirchhoff’sloop
rule.
G. ResistorsinParallel(If time permits):
1. SimilarlytoPartB1,predictandmeasuretheresistanceresultingfromthe
parallelcombinationofyour22‐Ohmand39‐Ohmresistors
2. Compare your results to the theory;doesitlookliketheoverall
resistanceinparallelis
1
1

R R
1
?Inotherwords,doesyourexperiment
1
 ...
2
matchtheory?
Page 6 of 12 SP212 Lab: Five Kirchhoff’s Rules and RC Circuits
Version: February 20, 2014
H. BulbsinSeriesandBatteriesinSeries(If time permits):
1. Quicklysetupthesamesetupyousawlastweektohelprefreshyourmemory
abouthowbrightthebulbwas.
2. Thenconnecttwobulbsinserieswithtwobatteriesinseriesasshowninthenext
diagram.
3. Discussion:Remove one banana lead while answering these questions to
avoid draining the battery needlessly. Inashortparagraphconsistingofafew
completesentences,comparethe brightness of these bulbs with the
brightness of a single bulb in the same circuit (as observed in step 1).
4. Discussion:Whathappensifyouremoveonebulb?Why?
I. BulbsinParallelandBatteriesinSeries(If time permits)::
1. Connecttwobulbsinparallel.Connecttheparallelcombinationofbulbstotwo
batteriesinseriesasshowninthenextdiagram.
2. Discussion: Remove one banana lead while answering these questions to
avoid draining the battery needlessly. Inashortparagraphconsistingofafew
completesentences,discussthebrightnessofthesebulbswiththebrightnessof
thebulbsinPartH2.
3. Discussion:Whathappensifyouremoveonebulb?Why?
Page 7 of 12 SP212 Lab: Five Kirchhoff’s Rules and RC Circuits
Version: February 20, 2014
4. Discussion:Whatwouldhappenifyouconnectedyourtwobulbsinparalleltotwo
batteriesinparallelasshowninthenextdiagram?
Perhaps if there is time remaining, your instructor will let you come back and connect this circuit to see if your prediction was accurate. However, for now, after answering the above discussion questions move on to the next section. V. LabReporttohandin:
1.
Annotated Graph and discussion from Part B.
2.
Spreadsheet, Graph, and discussion from Part C.
3.
Spreadsheet, Graph, and discussion from Part D
(if completed during this lab instead of lab 4.)
4. Spreadsheet and discussion from Parts E and Part G
(if directed by your instructor).
5.
Spreadsheet, Annotated Graph and discussion from Part F
(if directed by your instructor).
6.
Discussions from Part H and I
(if directed by your instructor).
Don’tforgetuncertainties,units,annotationsanddiscussions.
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Version: February 20, 2014
VI.
Clean‐Up(ensureallequipmentisoffandallwiresare
disconnected!)
A. GoldenRule:“Dountoothersasyoudesirethemtodountoyou.”
ThisappliesasmuchhereinthelabasitdoesintheFleet.AsfutureNavalOfficers,
howcanyouexpectyourenlistedsailorstomaintainacleanworkareaifyour
stateroom,workareas,messarea,etcisa“pigsty?”Soasofficersitisimperativethat
wecleanupafterourselvesnotonlytofollowtheGoldenRule,butalsotoleadby
examplefortheenlistedpersonnelunderourcharge.
1. EndofLabCheckout:Beforeleavingthelaboratory,pleasetidyuptheequipmentat
theworkstationandquitallrunningsoftware.
2. Thelabstationshouldbeinbetterconditionthanwhenyouarrivedandmore
importantly,shouldbeofanappearancethatyouwouldbePROUDtoshowtoyour
legalguardiansduringa“ParentsWeekend.”
3. Haveyourinstructorinspectyourlabstationandreceivetheirpermissiontoleavethe
LabRoom.
4. YouSHALLfollowthisprocedureduringeverylabforSP212!
Many thanks to Dr. Huddle, Dr. Katz, Dr. Mungan, and Dr. Fontanella for their assistance in producing this Laboratory procedure; specific references can be supplied on request. LCDR Timothy Shivok Page 9 of 12 SP212 Lab: Five Kirchhoff’s Rules and RC Circuits
Version: February 20, 2014
AppendixA
List of Objectives for this lab. Attheendofthisactivity,youshould:
1. BeabletodeterminetheequivalentresistanceofResistorsinseries.Thenobserve
thattheexperimentalresultsmatchtheory.
2. BeabletodeterminetheequivalentresistanceofResistorsinparallel.Thenobserve
thattheexperimentalresultsmatchtheory.
3. DevelopaneasewithKirchhoff’sfirstrule,akaKirchhoff’sCurrentLaw(KCL)or
junctionrule,includingbeingabletosolveforvariouscurrents.
4. Observethatthealgebraicsumofallthecurrentsenteringanodemustbeequalto
thealgebraicsumofallthecurrentsexitinganode.
5. DevelopaneasewithKirchhoff’ssecondrule,akaKirchhoff’sVoltageLaw(KVL)or
looprule,includingbeingabletosolveforvariousvoltagesand/orcurrents.
6. Observeagain,thatthealgebraicsumofallthevoltagedropsandvoltagesourcesina
closedloopmustadduptozero.
7. Developaneasewithsimultaneousequations(inyourcalculatororpreferablyby
hand)andsolveacomplexcircuitinvolvingtwoemfsourcesandparallelresistors.
Thenobservethattheexperimentalresultsmatchtheory.
8. ObservetheeffectsbatteriesandlightbulbsinSeriesorParallelarrangements.
9. Observethevoltageacrossthecapacitorandcurrentthroughtheresistoras
functionsoftimeinasimpleRCseriescircuitwhenthecapacitorischarging.
10. Observethevoltageacrossthecapacitorandcurrentthroughtheresistoras
functionsoftimeinasimpleRCseriescircuitwhenthecapacitorisdischarging.
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Version: February 20, 2014
AppendixB
Additional introductory material A. Inthelaboratoryfour,duringtheSimpleCircuitsportion,Kirchhoff'ssecond
rule,thelooprule,wasintroduced.Intoday'slaboratory,wewillreviewthe
secondruleandstudyKirchhoff'sfirstrule,thejunctionrule.Theserules
representfundamentalprinciplesthatapplytoanycircuit.Theyare
fundamentalbecausethefirstruleisanalternativestatementofconservation
ofchargeandthesecondruleisbasedonconservationofenergy.
B. Inthefirstpartofthislab,wewillstudyresistorsconnectedinseriesandin
thesecondpartwewillstudyresistorsconnectedinparallel.Combinationsof
resistorsaresometimesknownasresistornetworks.Oneoftheimportant
characteristicsofaresistornetworkistheequivalentresistance,Req.Reqcan
bethoughtofastheresistanceofasingleresistorthatcanreplacethe
network.Ineachcase,inordertostudyKirchhoff'srules,wewilladdasource
ofemftotheresistornetworkandmeasurethevoltagesandcurrents
associatedwiththeresultantcircuit.
C. In another part of this lab, we will study a circuit containing more than one emf
source and multiple resistors.
Discussion
A. Inclass,welearnedtocalculatetheequivalentresistanceofseriesresistors.
Req = R1 + R2 + R3 + ... B. Wealsolearnedtocalculatetheequivalentresistanceofparallelresistors.
C. Additionally,welearnedbothKCLandKVL:
a. Thatthealgebraicsumofallthecurrentsenteringanodemustbeequaltothe
algebraicsumofallthecurrentsexitinganode.
b. Thatthealgebraicsumofallthevoltagedropsandvoltagesourcesinaclosed
loopmustadduptozero.
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Version: February 20, 2014
D. RCCircuitsThefinalpartofthelabistostudyacapacitorandresistortogetherinacircuit.
TheoryWhenaresistor,capacitorandemf,ε,areconnectedinseries(theswitchinposition1,
tocharge),thecapacitorchargesaccordingto
ThequantityRC isknownasthetimeconstant.Consequently,thevoltageacrossthe
capacitoris
Finally,theassociatedchargingcurrentis
Ifthebatteryisthenremovedfromthecircuit(bymovingtheswitchtoposition2,to
discharge)andthecapacitorremainsconnectedacrosstheresistor,thecapacitordischarges
accordingto
wherethevoltageacrossthecapacitoris
andthecurrentduringdischargeis
Wewillmeasurethevoltageacrossthecapacitorandthecurrentintheresistorforboththe
chargingcapacitorandthedischargingcapacitor.
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