Phys1112: DC and RC circuits
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1 Name: Group Members: Dae: TA s Name: Phys1112: DC and RC circuis Objecives: 1. To undersand curren and volage characerisics of a DC RC discharging circui. 2. To undersand he effec of he RC ime consan. Apparaus: PASCO volage-curren sensor, power supply (10V), wo alligaor clips o connec he capacior, five long banana wires, µf bipolar capacior, 100 Ω and 250 Ω resisor, PASCO inerface wih PASCO sofware, mulimeer. Bipolar capacior: Correc funcioning of he bipolar capacior requires connecing higher poenial o he posiive (red) erminal of he capacior and lower poenial o he negaive erminal of he capacior. Par A: RC circui - Discharging a capacior In he previous experimen we measured currens and volages in a series and parallel circui involving resisors (ligh bulbs). In a circui wih only resisors and baeries, he curren hrough and volage across each resisor do no change wih ime. However, if he circui involves a capacior, hen he curren and volage across circui elemens do change wih ime. In his experimen we invesigae curren and volage in a series circui involving a resisor and a capacior referred o as an RR circui. 1. The amoun of charge ha mus be moved from one side of he capacior o he oher o esablish a volage, V, for a capacior wih capaciance, C, is given by. Calculae he amoun of charge ha will be moved from one side of he capacior o he oher if we hook a 10 V baery up o he μf capacior. Show your work and pay aenion o unis. Q = 2. The capacior is charged o 10 V and hen conneced o a 100 Ω resisor in he circui shown o he righ. If he volage across he capacior is 10 V, volage will be across he resisor righ afer he circui is conneced? +Q -Q VR = RC circui The loop rule for circuis may be useful here. The oal change in volage (or he oal poenial difference) mus be zero whenever we go around a closed loop. 1
2 3. Using he volage across he resisor, calculae he amoun of curren ha mus be flowing hrough he resisor (and in he res of his single loop circui) immediaely afer we connec he circui as shown. Remember ha he volage across he resisor is given by VR=IR. Show your work. +Q -Q I = Draw arrows on he figure o he righ o show he direcion ha he curren is flowing. 4. Curren is he rae a which charge is flowing. As he curren flows in he direcion you indicaed, will he amoun of charge on he lef plae of he capacior increase, decrease, or say he same? Explain. 5. As he curren flows in he direcion you indicaed, will he amoun of charge on he righ plae of he capacior increase, decrease, or say he same? Explain. 6. So as he curren flows in he direcion you indicaed, will he volage across he capacior increase, decrease, or say he same? Explain. 7. Using wha you deermined abou he change in he volage across he capacior, will he volage across he resisor increase, decrease, or say he same? Explain. 8. Using wha you deermined abou he change in he volage across he resisor, will he curren flowing in he circui increase, decrease, or say he same? Explain. Check your answers wih your TA before you proceed. TA iniials 2
3 9. Since curren is he rae a which charge is flowing, if he curren in he circui decreases, wha does ha mean abou he rae a which he charge (and volage) on he capacior changes? 10. Skech your predicions for he graphs of volage across he resisor versus ime and curren in he circui versus ime for he RC circui. VR I Par B: Discharging a capacior - Volage vs. ime and curren vs. ime Now we will make he following circui, charge he bipolar capacior o 10V, and hen invesigae volage and curren in he discharging. Do no connec he circui o he power supply ye. Wai for TA s approval before you do ha. Use a 100 Ω resisor and blue cylindrical μf bi-polar capacior (noe + and signs). You will be using PASCO volage curren sensor o measure volage and curren across he resisor and capacior. Selec he daa sampling frequency o be 5 Hz ha means he sensor collecs volage and curren daa 5 imes per second. Ammeer 10V 25000μF R V Volmeer Have your TA check your circui se up before coninuing. TA iniials 3
4 100Ω Once he circui is conneced, open Capsone sofware and click on he wo-graph emplae. Choose he verical axis o be volage in one graph. Choose curren o be he verical axis in he oher graph. Boh should have horizonal axis as ime. If he verical axis does no show volage/curren opions ha means eiher he sensor is fauly or here is no a good connecion o he inerface. Now connec he power supply and charge he capacior. (In he picure, black wire would be conneced o he negaive erminal of he power supply). Sar recording daa while he power supply is conneced and hen disconnec he power supply. Record daa for abou seconds and sop recording. You should have a nice volage vs. ime graph and a curren vs. ime graph. If necessary pracice doing his several imes unil you are saisfied wih he graph. Keep he bes run and delee he ohers. 11. Skech he curves you measured below. For he skeches, make =0 he ime when you disconneced he power supply. VR I 4
5 12. How does he shape of he measured volage vs. ime and curren vs. ime graphs compare wih your predicions in Quesion 10? 13. How would you describe he slope of each curve and how hey are changing as ime increases? As migh have guessed from he shape of he curren and volage curves, he discharge process follows an exponenial decay curve. The volage across he capacior ( V C ) a ime is expeced o be given by V C = V 0 e /RR, where V 0 is he iniial volage of he capacior a = 0. Since V 0 is he volage a one specific ime, i is a consan in his equaion. So he only variable on he righ side of he equaion is. 14. The exponen of he exponenial funcion conains RR for he given circui, which is called he ime consan. Use he unis of R and C o find unis of RR. Wrie ohms in erms of vols and amps and wrie farads in erms of vols and coulombs. Simplify unil you ge somehing simple. Show your work below. Unis of RC are Are hese unis consisen wih he name ime consan? Par C: Deermining he effec of changing he resisance 15. If we used a larger resisor in he circui, would he curren be larger, smaller, or he same jus afer we disconnec he power supply? 16. Based on your answer o Quesion 15, do you predic ha he discharge of he capacior will be faser, slower, or he same if we use a larger resisor? Explain why. 5
6 17. Now wih he power supply disconneced, change he resisance o 250 Ω. Follow he seps above o collec and ge he curren and volage graphs for he discharge of he capacior. Display boh volage vs. ime curves (100 Ω and 250 Ω) on he same graph. Also display boh curren versus ime curves on one graph. Selecing boh runs from he hird iem from he lef of Graph menu can do his. Skech he curves you measured for boh he 100 Ω and he 250 Ω resisor below. For each skech, adjus he curve so ha =0 is he ime ha you disconneced he power supply. Make sure you are accurae abou wheher he wo volages curves sar a he same value. Also make sure you are accurae for he curren curves. Make sure and indicae which curve is for 100 Ω and which is for 250 Ω. VR I 18. Is he discharge faser, slower or he same wih 250 Ω as i was wih 100 Ω? Does his mach your predicion? If no, explain why i behaves differen han you hough i would. 19. Is he iniial curren larger, smaller or he same wih 250 Ω as i was wih 100 Ω? Does his mach your predicion? If no, explain why i behaves differen han you hough i would. 6
7 Par D: Conclusions 20. Would he capacior discharge more quickly or more slowly if we had used a capacior wih a smaller value of capaciance? Explain. 21. Why does he capacior charge almos insanly when he power supply is conneced? 22. Why does he capacior discharge more slowly when he swich is opened compared o charging? 7
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