Chabot College Physics Lab RC Circuits Scott Hildreth

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1 Chabo College Physics Lab Circuis Sco Hildreh Goals: Coninue o advance your undersanding of circuis, measuring resisances, currens, and volages across muliple componens. Exend your skills in making breadboard connecions of elecrical componens, racing connecion errors, diagnosing problems, and resolving hem logically. Verify relaionships beween volage, curren, capaciance, and ime for charging and discharging circuis in series and parallel configuraions. Background: By now you should be comforable making connecions on a circui board, and measuring curren and volage digially using he Vernier equipmen and sandalone mulimeers. This lab aciviy will challenge you o verify he equaions for charging and discharging capaciors in simple DC circui arrangemens. As wih he previous lab, you will: a) Theoreically calculae he rae of charging and discharging simple single, series, and parallel capaciors in an circui, using 10 resisors, a 9V baery, and 0.1 Farad capaciors. b) Consruc models of hese circuis using he PhET Circui Consrucion Ki online, and es your hypoheses abou he currens and volages using his model. c) Experimenally use he Vernier and Pasco circui boards o acually build an circui, and measure he acual values wih he mulimeer, compuer, and oscilloscope. Wrie up: This experimenal wrie up should follow he formal physics laboraory repor forma (available online a hp:// ). Make sure ha you include he roles ha each member of your eam played in he aciviy, clearly labeled picures, daa ables in your appendix, and answers o he QUESTIONS you ll find wihin. The lab repor is due Thursday or Friday, 7/8 April 2016 MATERIALS Compuer running Logger Pro sofware LabPro inerface Vernier Curren & Volage Probe Sysem Addiional Vernier Volage Probes Oscilloscope (opional) 6-8 ses of alligaor clip wires Baeries adjusable low-volage DC power supply Vernier Circui Board Digial Mulimeer w/ (2) volage probes

2 BACKGROUND The charge q on a capacior s plae is proporional o he poenial difference V across he capacior: q V, C where C is he capaciance, measured in he uni of he farad, F, (1 farad = 1 coulomb/vol). If a capacior of capaciance C (in farads), iniially uncharged, is conneced across a resisor R (in ohms) o a poenial V 0 (vols), a ime-dependen curren will flow according o Ohm s law. This siuaion is shown by he (resisor-capacior) circui below when he swich o he baery is closed: R Red C Black Figure 1 As he curren flows, he charge q on he capacior builds up over ime, increasing he poenial across he capacior, which in urn reduces he curren. This process creaes an exponenially decreasing curren flowing hrough he resisor. If you measure he volage drop across he resisor, ha volage will decrease in ime, modeled by: Charging Circui Volage across Resisor R = The rae of he decrease is deermined by he produc, known as he ime consan of he circui. A large ime consan means ha he capacior will discharge slowly. Similarly, he Volage across he capacior C builds up exponenially in ime a a rae deermined by he same ime consan, modeled by: V r ( ) 0 Charging Circui Volage across Capacior C = V c ( ) V0 1 e The same ime consan describes he rae of discharging as well as he rae of charging. The relaionships for discharging circuis are similar o hose above, alhough boh he volage drops across he resisor and capacior decreases, and direcion of he curren and he sign of he volage drop will be reversed: Discharging Circui Volage across Resisor R = V r ( ) V e 0 V e Discharging Circui Volage across Capacior C = V c ( ) 0 V e

3 Resisor Volage Capacior Volage Imporan Noe! Record your eam s skeches, equaions, and answers o he quesions below, clearly and nealy, as par of your overall daa for he experimen. If his is done effecively from he sar, you should NOT have o copy hem over for he repor. PART A: THEORETICAL CALCULATIONS OF CIUITS 1. For an circui wih a single capacior of 0.10 Farads, in series wih a single resisor of 10, and a volage source of 9 V, calculae he ime consan for he circui, and develop he charging and discharging equaions for he volage readings across he resisor and capacior. 2. Skech he graphs of Volage vs. Time for he resisor and he capacior, for boh cases of charging and discharging (four skeches in all!) ime ime 3. If you add a second capacior of equivalen value in series wih he firs, how will his affec he raes of charging and discharging? Develop he new charging and discharging equaions for his siuaion. 4. If you add a second capacior of equivalen value in parallel wih he firs, how will his affec he raes of charging and discharging? PART B: BUILD A MODEL OF YOUR CIUIT NETWORK ONLINE 5. Locae, click on, and SAVE he pre-made PhET files Circuis 1/2/3 ono he deskop of your compuer, from my websie (hp:// ) Now locae and run he PhET simulaor Circui Consrucion Ki AC/DC available online a hp://phe.colorado.edu/en/simulaion/circui-consrucion-ki-ac. We ll use his simulaor o model your circuis. In he upper righ corner, click LOAD, and browse your compuer s files o locae he Circui 1 simulaion file. I should look like he image o he righ; you migh have o add he volage chars from he menu, or adjus he locaions of he volage probes across he componens o correcly read he values.

4 6. Charge he capacior by closing he swich on he lef. Run he simulaion, noing he resuling graphs of he volages across he resisor and capacior. Pause a any ime using he pause buon below. Do he graphs mach he expeced heoreical resuls? Esimae he volage value a a specific ime from he graphs (like 1/, he ime consan!), and verify your equaions prediced ha value. Record your resuls. Do his for boh graphs. 7. Discharge he capacior by opening he swich on he lef, and closing he swich on he righ. Run he simulaion, noing he resuling graphs of he volages across he resisor and capacior. Pause a any ime using he pause buon below. Do he graphs mach he expeced heoreical resuls? Esimae he volage value a some specific ime from he graphs, and verify your equaions prediced ha value. Record your resuls. Do his for boh graphs. 8. Now model he siuaion wih wo capaciors in series conneced o he same volage and resisor combinaion. LOAD he Circui 2 simulaion. I should look like he screen picure shown. You may have o reconnec he volmeer char leads. 9. Close he lef hand swich o charge he capaciors. Examine he resuling volage graphs. Do hey mach your heoreical predicions? How does he volage drop across each capacior compare o he volage across he baery? You can add anoher char o monior he volage across he resisor. 10. Discharge he capaciors by opening he lef swich and closing he righ swich. Examine he resuling graphs once more, and verify ha hey mach your heoreical predicions. 11. Does i appear ha placing wo capaciors in a circui wih one pahway for charge increases or decreases he amoun of charge sored? You may need o reurn o he original circui from par I o decide. 12. Now model he siuaion wih wo capaciors in parallel conneced o he same volage and resisor combinaion. LOAD he Circui 3 simulaion. I should look like he screen picure shown. You may have o reconnec he volmeer char leads. Repea seps 9 11 above wih his configuraion, and again verify ha he graphs mach your predicions. Does i appear ha placing wo capaciors in a circui wih muliple pahways for charge increases or decreases he amoun of charge sored?

5 PART C: TEST YOUR MODEL EXPERIMENTALLY 13. Connec he circui as shown in Figure 1 a he sar of he lab wih he 10-F capacior and he 100-k resisor. Record he values of your resisor and capacior in your daa able, as well as any olerance values marked on hem. 14. Connec a Differenial Volage Probe o Channel 1 of he LabPro, as well as across he capacior, wih he red (posiive lead) o he side of he capacior conneced o he resisor. Connec he black lead o he oher side of he capacior. 15. Open he Capacior file in he Physics wih Vernier folder. A graph will be displayed. The verical axis of he graph has poenial scaled from 0 o 4 V. The horizonal axis has ime from 0 o 10 s. 16. Charge he capacior for 30 s or so wih he swich in he posiion as illusraed in Figure 1. You can wach he volage reading a he boom of he screen o see if he poenial is sill increasing. Wai unil he poenial is consan. 17. Click o begin daa collecion. As soon as graphing sars, hrow he swich o is oher posiion o discharge he capacior. Your daa should show a consan value iniially, hen decreasing funcion. 18. To compare your daa o he model, selec only he daa afer he poenial has sared o decrease by dragging across he graph; ha is, omi he consan porion. Click he curve fi ool, and from he funcion selecion box, choose he Naural Exponenial funcion, A*exp( C*x ) + B. Click, and inspec he fi. Click o reurn o he main graph window. 19. Record he value of he fi parameers in your daa able. Noice ha he C used in he curve fi is no he same as he C used o sand for capaciance. Compare he fi equaion o he mahemaical model for a capacior discharge proposed in he inroducion, V ( ) V 0 e 20. How is fi consan C relaed o he ime consan of he circui? 21. Make a skech he graph of poenial vs. ime. Choose Sore Laes Run from he Daa menu o sore your daa. You will need his daa for laer analysis. 22. The capacior is now discharged. To monior he charging process, click. As soon as daa collecion begins, hrow he swich he oher way. Allow he daa collecion o run o compleion. This ime you will compare your daa o he mahemaical model for a capacior charging,

6 V ( ) V0 1 e Selec he daa beginning afer he poenial has sared o increase by dragging across he graph. Click he curve fi ool,, and from he funcion selecion box, choose he Inverse Exponenial funcion, A*(1 exp( C*x)) + B. Click and inspec he fi. Click o reurn o he main graph window. 23. Record he value of he fi parameers in your daa able. Compare he fi equaion o he mahemaical model for a charging capacior. 24. Hide your firs runs by choosing Hide Run Run 1 from he Daa menu. Remove any remaining fi informaion by clicking he gray close box in he floaing boxes. Repea he experimen wih a resisor of lower value. How do you hink his change will affec he way he capacior discharges? Rebuild your circui using he 47-k resisor and repea he seps above. SAMPLE DATA TABLE Fi parameers Resisor Capacior Time consan Trial A B C 1/C R () Discharge 1 Charge 1 Discharge 2 Charge 2 C (F) (s) ANALYSIS 1. In he daa able, calculae he ime consan of he circui used; ha is, he produc of resisance in ohms and capaciance in farads. (Noe ha 1F = 1 s). 2. Calculae and ener in he daa able he inverse of he fi consan C for each rial. Now compare each of hese values o he ime consan of your circui. 3. Noe ha resisors and capaciors are no marked wih heir exac values, bu only approximae values wih a olerance. If here is a discrepancy beween he wo quaniies compared in Quesion 2, can he olerance values explain he difference? 4. Wha was he effec of reducing he resisance of he resisor on he way he capacior discharged? OPTIONAL EXTENSIONS Try differen value resisors and capaciors and see how he capacior discharge curves change. Try wo capaciors in parallel. Predic wha will happen o he ime consan. Repea he discharge measuremen and deermine he ime consan of he new circui using a curve fi. Try wo capaciors in series. Predic wha will happen o he ime consan. Repea he discharge measuremen and deermine he ime consan for he new circui using a curve fi.

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