LabQuest 24. Capacitors
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1 Capaciors LabQues 24 The charge q on a capacior s plae is proporional o he poenial difference V across he capacior. We express his wih q V = C where C is a proporionaliy consan known as he capaciance. C is measured in he uni of he farad, F, (1 farad = 1 coulomb/vol). If a capacior of capaciance C (in farads), iniially charged o a poenial V 0 (vols) is conneced across a resisor R (in ohms), a ime-dependen curren will flow according o Ohm s law. This siuaion is shown by he (resisor-capacior) circui below when he swich is closed. Figure 1 As he curren flows, he charge q is depleed, reducing he poenial across he capacior, which in urn reduces he curren. This process creaes an exponenially decreasing curren, modeled by V ( ) = V e 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. 0 OBJECTIVES Measure an experimenal ime consan of a resisor-capacior circui. Compare he ime consan o he value prediced from he componen values of he resisance and capaciance. Measure he poenial across a capacior as a funcion of ime as i discharges. Fi an exponenial funcion o he daa. One of he fi parameers corresponds o an experimenal ime consan. Physics wih Vernier 24-1
2 LabQues 24 MATERIALS LabQues LabQues App Differenial Volage Probe connecing wires Vernier Circui Board or 10 µf non-polarized capacior 47 kω and 100 kω resisors 2 C- or D-cell baeries wih holder single-pole, double-hrow swich PRELIMINARY QUESTIONS 1. Consider a candy jar, iniially wih 1000 candies. You walk pas i once each hour. Since you don wan anyone o noice ha you re aking candy, each ime you ake jus 10% of he candies remaining in he jar. Skech a graph of he number of candies remaining as a funcion of ime. 2. How would he graph change if insead of removing 10% of he candies, you removed 20%? Skech your new graph. PROCEDURE 1. Connec he circui as shown in Figure 1 above wih he 10 µf capacior and he 100 kω resisor. Record he values of your resisor and capacior in your daa able, as well as any olerance values marked on hem. 2. Connec he Differenial Volage Probe o LabQues and choose New from he File menu. If you have an older sensor ha does no auo-id, manually se up he sensor. 3. Connec he clip leads on he Differenial Volage Probe 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. 4. Monior he inpu o deermine he maximum volage your baery produces. a. Charge he capacior for 10 seconds wih he swich in he closed posiion (see Figure 1). b. Wach he reading on he screen and noe he maximum value reached. You will need his value in a laer sep. 5. Se up LabQues for riggering and daa collecion. In his mode you will no have o manually synchronize daa collecion and he capacior discharge. Insead, LabQues will wai for he volage o reach a cerain level before collecing daa. a. On he Meer screen, ap Rae. Change he daa-collecion rae o 20 samples/second and he daa-collecion lengh o 4 seconds. b. Tap Triggering and selec Enable Triggering. c. Change he Triggering seings so ha daa collecion sars when volage is decreasing. d. Ener a rigger level of 90% of he maximum volage you observed in Sep 4. This means ha daa collecion will begin when volage decreases across his rigger level. e. Use 0 as he number of poin colleced before daa collecion is riggered. f. Selec OK. 6. Verify ha he swich has been in he closed posiion illusraed in Figure 1 for 10 seconds, ensuring ha he capacior is charged Physics wih Vernier
3 Capaciors 7. Sar daa collecion. Wai a momen, and hrow he swich o is oher posiion o discharge he capacior. LabQues will wai for he measured volage o reach he rigger level before collecing daa. Afer daa collecion is complee, a graph of volage vs. ime will be displayed. 8. Nex, fi he exponenial funcion y = A*exp(-Cx)+B o your daa. a. Choose Curve Fi from he Analyze menu. b. Selec Naural Exponen as he Fi Equaion. c. 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 How is fi consan C relaed o he ime consan of he circui, which was defined in he inroducion? d. Selec OK. 9. Prin or skech he graph of volage vs. ime. 10. Repea Seps 1 9 wih a 47 kω resisor. DATA TABLE Fi parameers Resisor Capacior Time consan Trial A B C 1/C R (Ω) Discharge 1 Discharge 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 1 Ω F = 1 s). 2. Compare he fi equaion o he mahemaical model for a capacior discharge proposed in he inroducion, V ( ) = V e Inerpre he fi parameers A and C. Wha aspecs of your experimen do hey measure? Wha are heir unis? 3. From he fi parameer C, calculae and ener in he daa able 1/C for each rial. Compare each of hese values o he ime consan of your circui. 4. Noe ha resisor and capacior are no marked wih heir exac values, bu only approximae values wih a olerance. Ask your insrucor he olerance of he resisors and capaciors you 0 Physics wih Vernier 24-3
4 LabQues 24 are using. If here is a discrepancy beween he wo quaniies compared in quesion 2, can he olerance values explain he difference? 24-4 Physics wih Vernier
5 EXTENSIONS Capaciors 1. Make a plo of ln(v) vs. ime for he capacior discharge. Wha is he meaning of he slope of his plo? How is i relaed o he consan? 2. Wha percenage of he iniial poenial remains afer one ime consan has passed? Afer wo ime consans? Three? 3. Use a Curren Probe and Differenial Volage Probe o simulaneously measure he curren hrough he resisor and he poenial across he capacior. How will hey be relaed? 4. Insead of a resisor, use a small flashligh bulb. To ligh he bulb for a percepible ime, use a large capacior (approximaely 1 F). Collec daa. Explain he shape of he graph. 5. Try differen value resisors and capaciors and see how he capacior discharge curves change. 6. Try wo 10 µf 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. 7. Try wo 10 µf 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. Physics wih Vernier 24-5
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