physics lab9

physics lab9 - Lab9:RCCircuits1 StaciWilliams

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Unformatted text preview: Lab9:RCCircuits1 StaciWilliams NicoleHarty,KevinSchesing,CaitlinKubota Section015 Theory: Thevoltageacrossaresistorisproportionaltothecurrentthroughtheresistorand thevoltageacrossacapacitorisproportionaltothetimeintegralofthecurrentinto thecapacitor.Thevoltageacrossaninductorisproportionaltothetimederivative ofthecurrentthroughtheinductor Capacitors A capacitor is a 2 terminal circuit element that stores energy in its electric field, consisting of two parallel plates separated by a small gap, which is usually filled withanonconductingdielectricmaterial.IfapositivecurrentIentersoneplateofa capacitoradexitstheotherplateapositivechargeQbuildsuponthefirstplateand anegativechargeQbuildsuponthesecondplate.AvoltageVcdevelopsacrossthe capacitor and the charge Q and voltage Vc are linearly related by the equation Q=CVcwhereCisaconstantcalledthecapacitance.Theunitsofcapacitanceifthe farad (F), and the capacitance depends on the geometry of the capacitor and the dielectricpropertiesoftheinsulatorbetweentheplates,andcapacitorshaveagiven maximumvoltage. RCCircuits AseriesRCcircuithasagivenvoltagesourceV(t)andhasavoltageacrossaresistor andcapacitordesignatedbyVrandVcandthecurrentaroundtheloopbyI,andIis positiveinthedirectionoftheloopbyKirchoff'slaw.Kirchoff'slawstatesthatthe voltage change around any loop must be zero, Vr+Vc=V and letting Vr=IR it equateswithaconstantvoltageQ=(Q0CV)e^t/RC+CVwhereQ0ishechargeof thecapacitorattimezero.ThequantityRCisthetimeconstantanditisexponential whenVisconstant.Beginningattimezerotheparamtersofthecircuitexponentially approachtheconstantvalues.VcapproachesVandIapproaches0.Inatime3RCthe paramtersarewithin95%ofthefinalvalue.ThevoltageacrossthecapacitorisQ/C, andthecurrentisdQ/dt,andthevolatageisVr=IR.Whenavoltageisswitched,the charge on and the voltage across the capacitor do not change instantaneously. Vc andQarecontinuousbutdonotdifferentiableattheswitchingpoint QuestionsandInformation: ThevoltageacrossaresistorwillbelabeledVRandKrichoff'slawtellsthatvoltage changes around the loop always equate to 0 and is represented by VR+VC=V. By integrating the equation becomes Q(QoCV)^t/RC +CV and the charge at time t=0, RC will be the time constant of the circuit. Time dependence is exponentially relatedwhenVisconstant.VCapproachesVandIapproaches0,andanimportant pointisthatwhenthevoltageisswitched,thechargesacrossthecapacitorwillnot switchrightaway. 4.1T..RC,PositiveOnlySquareWave FortheparametesusedtheassumptiontatT..RCisvalid,andtheeresultsarewhat weexpected. 4.2T>>RC,SymmetricSquareWave Theresultsagainwerewhatweexpected,butontegraphthevalueispulsatingas thedataisbeinggraphed. 4.3T<<RC,PositiveOnlySquareWave RC=100*0.330=33sec. T=33.72milliseconds Thetimeperiodbtainedisafactorofthetimeconstant. Itdoesseemreasonabletomeasurestraightlines. Fig.3haslinesthathaveasteeperslopethanthegraphweobtained,asoursappears more linear. 4.4T<<RC,SymmetricSquareWave Approximatingwithstraightlinesisreasonable. ComparedtoFig.4,ourlinesseemmorelinear. 4.5T~RC,SymmetricSquareWave Theresultsobtainedwerewhatwasexpected ErrorAnalysis Theexperiementseemedtogoasplanned,soanyoftheerrorthatmighthavebeen experiencedwouldhavebeenprobablyduetosystematicerrorduetotheuseof computergraphingtoolsandanalogreaders.TheperiodTthatweobtainediavery closetotheexpectedvalueaswell. Conclusion Theexperiementwentasplanned,andhelpedtoillustratehowRCcircuitswork. 4.1Graph 4.2Graph 4.3Graph 4.4Graph 4.5Graph ...
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This note was uploaded on 05/08/2010 for the course PHYS v12 taught by Professor Adler during the Spring '10 term at NYU.

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