C and C are needed to determine dielectric constant of

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1 TALLINN NIERSITY OF TEHNOLOGY, INSTITTE OF PHYSIS PARALLEL PLATE APAITOR Objctiv Dtrmiig capacitac of a capacitor ad dilctric costat of th isulatig matrial Equipmt dd Exprimt stad with rfrc capacitor ad capacitor with ukow capacitac, dilctrical plats, lctrostatic voltmtr or stadard multimtr, callipr or micromtr 3 Thory I cas th spac btw capacitors plats is filld with homogous dilctric matrial, its capacitac ca b calculatd, as follows: S εε, () d whr S is plats surfac, d distac btw plats, ε dilctric costat of th dilctric F (plat) ad ε prmittivity costat i SI-systm uits ( ε 8,85 ) m Figur Formula () is ot applicabl wh th spac btw capacitor's plats is ot filld uiformly with a homogous dilctric matrial (lik air) Lt us cosidr a cas wh a dilctric plat with thickss d is placd btw ad i paralll to th plats of a capacitor with air dilctric (fig ) apacitac of a capacitor ca b calculatd as follows:, () d' + d ε whr is capacitac of th capacitor without a dilctric plat Lt us driv dilctric costat of th dilctric plat from formula (): ε (3) d d' It follows from (3) that capacitacs ad ar dd to dtrmi dilctric costat of th isulatig matrialε

2 TALLINN NIERSITY OF TEHNOLOGY, INSTITTE OF PHYSIS apacitac of ukow capacitor i this xprimt is dtrmid as follows Rfrc capacitor with kow capacitac ad chargd to som voltag is coctd paralll to th ukow capacitor Masurig chag of pottial o capacitors (coctd i paralll) is ough to calculat capacitac of capacitor octio diagram of xprimt is show o fig losig cotacts of switch K chargs rfrc capacitor up to th voltag of a D supply oltag btw rfrc capacitor plats is masurd with voltmtr with vry big itral rsistac Evry voltmtr has a (parasitic) capacitac (show with dashd li o fig ) This capacitac is coctd i paralll to ad is chargd up to aswll Total charg of capacitors ad q + ) ca b xprssd as ( (4) Figur Prssig switch K cocts th ukow capacitor i paralll to capacitor Sic cotacts of switch K ar ow op (forcd by a sprig), total charg of th systm rmais costat Du to rdivisio of charg btw capacitors voltag falls from valu to valu so that or, takig i accout formula (4): q + + ) (, O ca driv ( + ) ( + + ) + (5) + + Part of th systms charg rmaiig o plats of ukow capacitor is utralisd wh switch K is dprssd sic it shorts th capacitor (s figur ) Rmaiig charg o capacitors + ca b xprssd: q ( + ) Prssig switch K agai forcs part of charg q from capacitor to flow to capacitor agai charg of capacitor + is rducd to valu q ( + ) Hr

3 TALLINN NIERSITY OF TEHNOLOGY, INSTITTE OF PHYSIS or, takig i accout formula (5): (6) I a similar way o ca calculat voltag pulsd by switch K tims: + displayd by voltmtr if capacitor O ca driv capacitac of ukow capacitor as follows: is ( + ) (7) Formula (7) is corrct oly i cas charg of dcrass oly du to chargig ad dischargig of capacitor oditio is tru wh uwatd but always prst rsistac R (figur ) which is total rsistac of isolatio of capacitor, switchs K, K ad wirig is big ough I that cas (durig masurmts) charg comig through rsistor R, is may tims smallr tha charg goig to capacitor I prst xprimt stad valu of R is sufficit ad causs ad additioal rror o biggr tha % if masurmts of ar prformd quickr tha i 5 miuts Elctrical diagram o xprimt stad is show o figur 3 is rfrc capacitor, capacitor with ukow capacitac ad capacitac of voltmtr Figur 3 4 Exprimtal procdur Rcord th data of masurig dvics ad valus of, ad d Ask istructor to chck coctios ad giv a xact task 3 oct a lctrostatic voltmtr (or stadard multimtr istructor tlls which o) to th stad Switch th stad ON Wh usig a multimtr tur its mod switch to 3

4 TALLINN NIERSITY OF TEHNOLOGY, INSTITTE OF PHYSIS 4 harg rfrc capacitor up to voltag (o mor tha, ) by prssig switch K (figur 3) If voltag is highr tha,, ask istructor to adjust it Writ valu to tabl 5 Prss ad rlas switch K This cocts paralll to th ukow capacitor, which has air as dilctric ad capacitac is Radig of voltmtr falls somwhat, writ it dow Obsrvig voltmtr radigs ad prssig ad rlasig switch K rach th situatio wh voltag radig is at last /3 of th origial radig out prssig/dprssig vts of switch K togthr with voltmtr radigs ad rcord thm to corrspodig colums of row of tabl 6 Rpat th xprimt at last 5 tims alus of, ad may b diffrt i diffrt xprimts 7 Rpat th xprimt with o plat isrtd to ukow capacitor (its capacitac is th ) Th rpat xprimt with plats isrtd alu of ukow capacitor is Rcord all masurmt data to corrspodig rows of tabl apacitac of masurd (ukow) capacitor Dtrmiig capacitac of ukow capacitor Exp rim,, r 5 5 5,pF ( ) i i ± ± ± Tabl oltmtr: d d,,,, d 8 s formula (7) to calculat for vry masurmt: i, ma for vry capacitor ad its A-typ modifir ucrtaity o lvl,95 9 Masur thickss of dilctric plats d i 5 diffrt placs alculat d ad it's ucrtaity o 4

5 TALLINN NIERSITY OF TEHNOLOGY, INSTITTE OF PHYSIS lvl,95 sig valus,, d ad d ad formula (3) calculat dilctric costat of plats ε You kow that: ad Fid th combid ucrtaity c( ε) for ε kowig that d d Kowig ow valu of ε, dtrmi matrial of th dilctric plat 3 Sic you dtrmid total capacitac of capacitors coctd i paralll also i cas thr was air btw lctrods of o of thm ad dilctrical plat i aothr, o ca writ: ( ε + ) assumig that d d To chck corrctss of valu ε calculatd, mak crtai that last formula is valid Assum ad 5 Qustios ad tasks Dfi th cocpt of capacitac What paramtrs affct it? Dfi th cocpt of dilctric costat of th isulatig matrial usig th oulomb' law 3 Substatiat th formula for calculatig capacitac of paralll-plat capacitor 4 How is charg distributd wh two capacitors ar coctd i paralll? 5 What ar th bfits of multipl chargig mthod of ukow capacitor, usd i this xprimt wh compard to oly o charg cycl (i this cas is dtrmid from formula (7) whr )? 6 Why must th total rsistac R show o figur b as big as possibl? 7 A mpty (uchargd) capacitor is coctd to a capacitor chargd to som voltag What happs to systms total rgy? 8 Numbr of tims of prssig ad dprssig switch K to discharg capacitor to giv voltag lvl is biggr i systm with o dilctric plats btw lctrods of masurd capacitor is biggr wh compard to a stup with dilctric plats Why? 9 Plats of a capacitor ar shord with suprcoductig wir What happs to rgy stord i th capacitor? 6 Litratur Halliday, D Rsick, R, Walkr, J Fudamtals of Physics 6th d Nw York, Joh Wily & Sos, Ic,,