Lab report物理实验报告英文.docx
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Labreport物理实验报告英文
Introduction
Capacitoriswidelyusedinavarietyoffieldsasitcanstoreelectricenergy,suchasFiltering,resonantcircuitandmovingphase.Differentcapacitorshavedifferentabilitiestostoreenergy,whichisduetothedifferenceofcapacitance.Capacitance istheabilityofa capacitor tostore charge inan electricfield,itisalsoameasureoftheamountof electricpotentialenergy stored（orseparated）foragiven electricpotential.ThisreportisgoingtoinvestigatethecapacitanceofacapacitormadefromtheexperimentbyusingdifferentDCmethods.Beforethecapacitormadefromtheexperimentismeasured,threeDCmethodswillbetestedtoverifywhetherthesemethodsareefficientbymeasuringthecapacitanceoftheknowncapacitor.Inaddition,aftermeasuringtheunknowncapacitor,thewholecapacitorswillbeconnectedinparallelandthetotalsizeofcapacitancewillbemeasured.
Theory
Capacitancecanbefoundbyusing:
.Thisisfortwoflatplates.Asfortheformula,Cisthecapacitanceofacapacitor,Aistheareaofflatplates,disthedistancebetweenthetwoflatplates,
isthepermittivityofvacuum,
istherelativepermittivity.Permittivityisconstantofproportionalitythatrelatestheelectricfieldinamaterialtotheelectricdisplacementinthatmaterialandrelativepermittivityis theratioofthepermittivityofasubstancetothatoffreespaceorvacuum.Differentmaterialshavedifferentrelativepermittivity,thebehindtableincludestherelativepermittivityofsomedifferentmaterial:
Material
Acetaldehyde
AceticAcid
AceticAcid
Acetone
Acetone
DielectricConstant
21.8
6.2
4.1
20.7
17.7
Source:
（TheEngineeringToolBox,2011.）
Whentwocapacitorsareplacedinseries,thechargeoneachplateisofequalmagnitude,so:
;
hence
（whereQistheamountofchargesonplateandVisthevoltageacrossthecapacitor）.Whenacapacitorischarged（Vacrosscapacitor）:
and
（
istheinitialvoltageaddingonthecapacitor,
isaconstantanditis2.718,Risresistance,Ciscapacitanceand
istheinitialcurrentflowingthroughthecapacitor）.Analogously,whenacapacitorisdischarged,itflows
and
.
Methods
Apparatus:
Powersupply,leads,ruler,calipers,clips,knowncapacitor,aluminumfoil,cling-film,paper,multi-meter,videocamera.
PartA:
usingthreedifferentwaystomeasurethecapacitanceifthegivencapacitor.
Method1ofpartA
Diagram1:
Capacitor
Thismethodismeasuringtheincreasingvoltageofthegivenresistorwhilethecapacitorischarged.Voltageoftheresisterismeasuredbyamulti-meter,whichisatoolthatcanmeasuremanyquantitiessuchasvoltage,current,andresistance.Thegivencapacitorhasanarea（A）of
andthedistance（d）is
.TheVchangesveryfast,sothereneedsaresistertoslowitdownandacameratorecord.Thevoltageofcapacitorcanbefoundbymeasuringthevoltageoftheresister,asvoltageofthecapacitorisequaltotheoutputvoltagesubtractingthevoltageofresistor:
.Whentheloopisconnected,usingthecameratorecordthechangeofvoltage.Afterrecording,drawingagraphoftheV（Vshouldbethevoltageofcapacitoranditisequalto
）andt（thetimeconstant）,thenusingtheequationintheorytofindRCandC.
Table1:
Resultofmethod1ofpartA
t（time）/s
V（voltageofresistor）/v
V（voltageofresistor）/v
V（outputvoltage）/v
0.000
1.127
0.373
1.500
1.000
1.013
0.487
1.500
2.000
0.963
0.537
1.500
3.000
0.893
0.607
1.500
4.000
0.792
0.708
1.500
5.000
0.778
0.722
1.500
6.000
0.714
0.786
1.500
7.000
0.619
0.881
1.500
8.000
0.627
0.873
1.500
9.000
0.578
0.922
1.500
10.000
0.545
0.955
1.500
11.000
0.515
0.985
1.500
12.000
0.479
1.021
1.500
13.000
0.455
1.045
1.500
14.000
0.433
1.067
1.500
15.000
0.406
1.094
1.500
16.000
0.388
1.112
1.500
17.000
0.370
1.130
1.500
18.000
0.350
1.150
1.500
19.000
0.336
1.164
1.500
20.000
0.323
1.177
1.500
21.000
0.307
1.193
1.500
22.000
0.295
1.205
1.500
23.000
0.285
1.215
1.500
24.000
0.272
1.228
1.500
25.000
0.263
1.237
1.500
30.000
0.223
1.277
1.500
37.000
0.178
1.322
1.500
40.000
0.166
1.334
1.500
41.000
0.161
1.339
1.500
46.000
0.143
1.357
1.500
50.000
0.130
1.370
1.500
58.000
0.113
1.387
1.500
64.000
0.103
1.397
1.500
66.000
0.099
1.401
1.500
71.000
0.093
1.407
1.500
77.000
0.068
1.432
1.500
Analysisforthemethod1
Graph1:
thisgraphisdrawnfromtheresultofmethod1.
Graph2:
thestandardgraph.
V（voltage）
t（time）/s
Theinitialvoltage（
）is1.45V.
whent=RC,
=1.45V,soV=0.91V,fromthegraph,t=9swhenV=0.91V.Therefore,RCisequalto9,astheresistanceofresistor（R）isgivenandwhichis
.Thecapacitanceofcapacitoris
butheretheresultis
sotheexperimentworksnotwell.Therearesomereasonsresultingtothebigerrorbetweentherealvalueandexperimentvalue.Firstofall,comparingthestandardgraphwiththeresultgraph,Whentimeiszero,thevoltagealsoshouldbezero,however,thevoltageofcapacitorisnotzeroast=0,thisisduetothecapacitorhassomechargesinitbeforetheloopisconnected.Second,asthedataisgottenfromthevideobyeyes,thereexiststhemanmadeerror.Third,thevoltmeteritselfisaresistor,thisalsowillcausetheerror.Inaddition,whentheexperimentisoperated,theloopisnotconnectedverywellandthecapacitorhasbeenused.
Method2ofpartA
Diagram2:
Thismethodismeasuringthecurrentwhilethecapacitorischarging.Thewayofmethod2issameasmethod1andtheresistor,powersupplyandcapacitorarestillthesame.First,usingthecameratorecorddata.Then,drawingagraphaccordingtothesedata.Last,calculatingthecapacitanceaccordingtothegraph.Forthismethod,theformulais
（
istheinitialcurrentflowingthroughthecapacitor）.
Table2:
Resultofmethod2ofpartA
t（time）/s
I（current）/A
0.000
5.510
1.000
2.650
2.000
1.340
3.000
0.687
4.000
0.420
5.000
0.222
6.000
0.140
7.000
0.098
8.000
0.064
9.000
0.043
10.000
0.027
11.000
0.019
12.000
0.014
13.000
0.011
14.000
0.009
15.000
0.007
16.000
0.006
20.000
0.004
26.000
0.002
34.000
0.001
Analysisforthemethod2
Graph3:
thisgraphisdrawnfromtheresultofmethod2.
Therelationshipbetweenthecurrentandtimeis
.Whent=RC,
theinitialcurrent（
）is5.51A,soI=2.03A.Fromthegraph,thetime（t）is1.7swhenI=5.52A.Ast=RC,soRC=1.7,
.Thecapacitanceofcapacitoris
.Comparingtheresultandtherealcapacitance,thismethodworkswell.However,therearestillsomeerrorswhicharecannotbeavoided.Forexample,thedatagottenfromthevideoisnotaccuracy.
Method3ofpartA
Diagram3
Thismethodismeasuringthevoltagewhiledischarging.Similartothemethod1and2,thismethodisalsousingcameratorecordthedataanddrawingagraph,then,usingthegraphandformulatogetthecapacitanceofthecapacitor.
Table3:
Resultofmethod3ofpartA
t（time）/s
V（voltageofcapacitor）/v
0.000
1.145
1.000
0.689
2.000
0.521
3.000
0.441
4.000
0.383
5.000
0.302
6.000
0.282
11.000
0.210
20.000
0.145
37.000
0.092
55.000
0.062
74.000
0.053
90.000
0.041
120.000
0.030
160.000
0.021
200.000
0.012
Analysisforthemethod3
Graph4:
thisgraphisdrawnfromtheresultofmethod3.
Whenacapacitordischarged:
.
=1.145V,Whent=RC,
.Fromthegraph,t=3sasV=0.421V,SORC=3,
.Therealcapacitanceis
comparingtheresultwiththereal,theresultisnotaccuracy.Therearealsosomeerrorsexist,thefirstisthethereissomecurrentflowingthroughthevoltmeterwhichwasignored.Thesecondiswhenthedatarecordedbyeyes,theremustbesomemanmadeerrors.
PartB:
Makingacapacitor
Thispartisdescribingtheprocessofmakingacapacitorbyusingcling-filmandaluminumfoil.Firstofall,puttingcling-filmonthedeskandspreadingit.Second,layingthealuminumfoilonthecling-filmtidily.Then,puttingthecling-filmabovethealuminumfoilagain.Thenext,lettingthealuminumonthetopandmakesurethetwoaluminumcannottoucheachother.Atlast,rollingthemcarefullyandusingmulti-metertotestwhetherthereiscurrentbetweenthetwoaluminumfoilsforonemeteratime.Afterrolling,thecapacitorwasmade.Thelengthofmaterialsis4meterswithawideof0.25meters,sothearea（A）is1metersquare.Thedistance（d）betweentwoaluminumfoilsis
whichismeasuredbyacalipers.Ifthecapacitorneedstostoremorecharge,theareashouldbelargerandthedistanceshouldbesmaller.
PartC:
Measuringthecapacitanceofthecapacitormadeinclass.
Method1ofpartC:
Diagram4:
ThispartisgoingtoEstimatethesizeofthecapacitor（capacitance）whichwasmadeinclassbyusingfourmethods.Thismethodismeasuringthecapacitancebyusingaknowncapacitorandlettheminseries.Theformulais
Thevoltageofcapacitor1gottenfromtheexperimentis3.45v,theoutputvoltageis20v,so
Theresult
.Inaddition,
Ais
anddis
therefore,
.Thisresultisreasonableandtherearesomeerrorsexist.First,whentheloopisconnected,thecapacitorwillbechargedandthedataonvoltmeterwillchange,soreadingtheinitialdataofthevoltmeter（whichwasusedas
）isnotaccuracy.Second,thepowersupplyhasintervalresistance,sothevoltageofcapacitor1isnotequalto
absolutely.
Method2ofpartC:
Diagram5
Capa
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