LAB 05 Capacitors and Capacitive Circuits

Transcription

1 PHYS 155 Unversty Physcs II Lbortory Pre-Lb Fll 2017 CONTENT: 1. Introducton 2. Cpctors A. Cpctnce B. Propertes of Cpctors C. Cpctve Crcuts 3. Pre-lb: A. Actvtes B. Prelmnry Informton LAB 05 Cpctors nd Cpctve Crcuts 1. Introducton Whle n generl physcsts do not judge the mportnce of ther studes bsed on ther potentl pplctons, t s true tht mny tmes scentfc dscoveres hve been fueled by the publc curosty strred by the mzng mchnes tht scence mke possble. Our topc of nterest electromgnetsm s typcl exmple. At the end of the 19 th century, the world ws mesmerzed by the promse of socety runnng on electrcty mrkng the deth of the bulky nd neffcent stem powered engnes. Thence, due to the socetl pressure, the physcsts rcne explntons of how electrc mchnes work hve been grdully trnslted nto technologcl lngos spoken by engneers nd other technologsts desgned to code the purely ppled relm of electromgnetsm. Consequently, there s dlectl contnuum between how physcst nd n engneer descrbe n electrc crcut, but the lnguges they use re somewht dfferent. In our course we re to mostly thnk nd spek s physcsts do bout few electromgnetc devces selected to exemplfy how the respectve physcl prncples cn be used n pplctons: ) Cpctors llustrte the producton nd storge of electrc feld nd energy; b) Resstors control the rte of electrc-energy trnsmsson v electrc currents whch produce mgnetc felds; c) Inductors llustrte the producton nd storge of mgnetc feld nd energy. In the next lb unt we re to tke on the frst devce n the lst: cpctors. 2. Cpctors Whle n our dscussons bout electrc felds nd potentls we hnted bout some of the propertes of cpctors n the lecture n prtculr Prllel-Plte Cpctors n the chpter dedcted to ths subject we re to go nto more detls. Thus, we lerned tht such chrged cpctor cn be used to produce unform electrc feld whch cn be modeled s sequence of equpotentl surfces prllel wth the pltes. Yet, how cn one quntfy the blty of cpctor to produce n electrc feld? How much electrc energy s stored n ths feld? Wht hppens f the electrc propertes of the spce n between the pltes re ltered? How cn one nlyze the functonlty of networks of cpctors? A. Cpctnce + An mmedte use of conductors n electrosttcs s to store chrge by gvng them defnte potentl (for nstnce, usng bttery): such conductor s clled cpctor V + nd ts blty to store chrge proportonl to the potentl s clled cpctnce C E (mesured n frds). For two conductors, V C V V CV C. (1) V Note tht for system of n chrged conductors, the potentls on ech of them wll depend on the chrges on ll conductors through coeffcents tht re purely geometrc. Ths property helps to defne the cpctnce of the system solely ssocted wth the geometry of the conductors nd the electrc permttvty of the embeddng spce. Therefore, to clculte the cpctnce of system of conductors, one hs to compute the dstrbuton of potentl proportonl to the chrge tht produces t nd use t n the defnton of cpctnce: the chrge wll smplfy, levng only the dependence on geometrcl nd nter-plte mterl propertes. Tht s, the cpctnce s chrcterstc of the devce. 1

2 PHYS 155 Unversty Physcs II Lbortory Pre-Lb Fll 2017 Exmple 1: Consder very long cylndrcl r-flled cpctor wth pltes of rd nd b, s n the fgure. Sy tht the pltes re chrged wth unform lner densty λ. In ths cse, the electrc feld produced by ech plte wll be rdl, gven t dstnce r perpendculr on the xs by E rˆ E ˆ rr. (2) λ E 2 0r b λ + Therefore, the potentl dfference between the pltes s: dr b V Erdr ln r ln. (3) b 2 r 2 2 b 0 b 0 0 Consequently, usng defnton (1), the cpctnce per unt length L of the cpctor s: L C 2 0 C. (4) V b L ln b ln 2 0 B. Propertes of Cpctors In electrosttc stutons, cpctors cn be consdered s feld-storge devces. As exemplfed bove, the feld between the pltes depends on the mount of source chrge nd the geometry of the pltes holdng ths chrge. If the feld s known, one cn clculte the potentl dfference between the pltes usng the reltonshp between the feld nd potentl. Moreover, becuse to chrge up the cpctors power supply must do work to trnsfer chrge from one plte to nother, the devce cn be lso consdered s store of electrc energy equl to the negtve of the respectve work. To compute the energy correspondng to certn chrge bult on the pltes of cpctor of cpctnce C, just note tht s the cpctor s beng chrged ech element of chrge dq s trnsported gnst the ncresng potentl dfference. Therefore: 2 q U W Vdq dq 2 2CV. (5) C C 0 0 Bsed on the fct tht the cpctnce depends only on the geometry of the pltes nd the electrc propertes of the mterl nsde, we see tht there re two methods to modfy the cpctnce: 1. Modfyng the geometry, such s decresng the seprton between the pltes to ncrese the cpctnce. In relty, ths method s severely lmted becuse chrge my rc cross pltes due to the ncresng feld. 2. Insertng delectrc between the pltes. A delectrc s n nsultng mterl contnng polrzble molecules. When mmersed n the electrc feld nsde cpctor, the molecules rotte s dpoles nd produce ther own electrc feld opposng the externl one. Thus, the net feld nsde the cpctor s reduced, whle the chrge on the pltes remns the sme. Therefore, the sme mount of energy cn be stored usng reduced potentl dfference between the ptes. The effect of delectrc s to ncrese the cpctnce of the devce by fctor clled delectrc constnt, denoted κ. If the cpctnce wth vcuum between the pltes s C 0, then the nserton of delectrc wll ncrese t to C C 0. (6) C. Cpctve Crcuts Assemblng cpctor n networks cn ether ncrese or decrese the equvlent cpctnce. The net cpctnce of such cpctve crcuts cn be clculted n smple stutons by deconstructng the crcut nto smple combntons of elements n prllel nd seres: 1. In prllel, ll cpctors wll be connected cross the sme potentl dfference, such tht ech wll chrge up ccordng to ther cpctnce. Therefore, the equvlent cpctnce wll be lrger thn tht of ny of the prts: C C C1 C2 C3.... (7) 2. In seres, ll cpctors wll be chned plte-to-plte. Thus, ech cpctor wll hve the sme mount of chrge equl to the net chrge, becuse ny two nterconnected pltes connected wll store zero net chrge, thus overll remnng 2

3 PHYS 155 Unversty Physcs II Lbortory Pre-Lb Fll Pre-lb only the unblnced chrges t the ends of the chn. The potentl dfference cross the chn wll be equl to the sum of voltges cross ndvdul cpctors, such tht the equvlent cpctnce wll be smller thn tht of ny of the prts, s gven by (8) C C C C C A. Actvtes As you red the ntroductory mterl provded bove: Mke sure you understnd wht cpctors re n generl, beyond the fmlr exmple of prllel pltes cpctors Retn tht cpctnce s chrcterstc of the devce, ndependent of the ppled potentl Prctce fndng the cpctnce of smple cpctors, by studyng Exmple 1 nd tryng to pply the method to prllel plte cpctor nd sphercl cpctor (Exmples 1 nd 2 n the pre-lb ssocted wth LAB03 my come n hndy). Understnd how the energy stored by cpctor depends on the ppled potentl nd the chrge on the pltes. Sketch smple seres nd prllel combntons of cpctors, to lern how to dentfy them n lrger crcuts. 2. Strtng wth ths experment, n some of the lb unts we wll use more elborte dt cquston system bsed rther verstle nterfce whch cn be hndled drectly from PASCO computer pplcton clled Cpstone. You my downlod on your computer fully functonl trl verson of ths progrm from Our deprtment holds collectve serl, but we shll use t only f our lbs run pst the trl perod. So mke sure tht you brng n t lest one lptop computer per group wth ths progrm nstlled. Hence, ths week the Lb Form s not pdf document, but ".cb" one the extenson hndled by the Cpstone pp. Just downlod t nd tke look t t. The.cb fle provdes n ctve envronment where you cn collect, store nd sve dt, dscuss your results, nd nswer questons. Accordngly, the lb report wll be the respectve.cb fle fter runnng the experment nd fllng n the requred tsks. B. Prelmnry nformton The subject of our next lb s Cpctors nd Cpctve Crcuts. In ths bref experment, you wll: Prctce how to use the Cpstone pplcton n conjuncton wth the dt cquston system. Observe vrous propertes of prllel-plte cpctor wth moble pltes. Observe the effect of delectrc upon the cpctnce Anlyze the mpct of surroundng cpctnce nterferng wth cpctve mesurements. In ths context, you wll note tht the surroundng cpctnce C s contrbutes s cpctor n prllel wth the system cpctor C, such tht the potentl dfference cross the chrged system ncludng prllel-plte cpctor would be V C C s A 0 C d s. (9) Tht s, the surroundng would mpct the dependence of the potentl dfference on the system cpctnce. 3

4 PHYS 155 Unversty Physcs II Lbortory Pre-Lb Fll 2017 C. uz 5 Nme: Bsed on the pre-lb redng, nswer the followng questons on the Blckbord ste ssocted wth our PHYS 155 lecture. The numbers n squre brckets ndcte the ponts llotted for the respectve queston. 1. [2] Whch of the followng s flse bout electrc cpctors? ) Ther cpctnce depends on the potentl dfference cross the pltes. b) They cn store electrc feld. c) They cn store electrc energy. d) They cn store net mount of electrc chrge e) The electrc feld nsde cn be non-unform. 2. [2] Wht hppens wth the cpctnce of cpctor f ts plte seprton s doubled? ) It doubles rrespectve of the type of cpctor. b) It doubles only f the cpctor s prllel-plte. c) It doubles only f the cpctor s cylndrcl. d) It decreses rrespectve of the type of cpctor prllel-plte, cylndrcl or sphercl. e) It hlves rrespectve of the type of cpctor prllel-plte, cylndrcl or sphercl. 3. [2] If the potentl dfference ppled to cpctor s doubled, wht hppens wth the energy stored? ) It won t chnge. b) It doubles. c) It qudruples. d) It hlves. e) It qurters. 4. [2] The shown cpctve crcut, ncludng three dentcl cpctors C, s chrged usng bttery whch s then removed. If the rghtmost cpctnce s doubled, wht hppens wth the potentl dfference cross the crcut? ) It won t chnge. b) Increses by 2/3 c) Increses by 1/3 d) Decreses by 2/3 e) Decreses by 1/3 5. [2] Ths week you wll perform n experment nvolvng n nstructonl cpctor wth movble prllel pltes. Note tht the system s senstve to the cpctve nterference of ts surroundngs, such s wres nd power sources, whch ct lke cpctor n prllel. Usng the defnton of cpctnce (C = /V) nd the expresson for prllel-plte cpctnce (C = ε 0 A/x), you my esly verfy tht not countng the surroundngs the potentl dfference V cross the cpctor should vry lnerly wth the plte seprton x. How bout f the surroundng cpctnce s counted n? ) V wll stll vry lnerly wth d. b) V wll ncrese wth x t smller nd smller rte. c) V wll ncrese wth x t lrger nd lrger rte. d) V wll frst ncrese nd then decrese wth x. e) V wll frst decrese nd then ncrese wth x. (No quz for ths lb unt) 4

5 PHYS 155 Unversty Physcs II Lbortory Pre-Lb Fll