Lect08 - Physics 212 Le cture8 Today's C pt: once C...

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Unformatted text preview: Physics 212 Le cture8 Today's C pt: once C apacitors C apacitors in a circuits, Die ctrics, Ene in capacitors le rgy 40 30 20 10 0 Confused Avg = 3.4 Confident Physics 212 Le cture8, S 1 lide Music Who is the Artist? BB A) B) C) D) E) Michael McDonald Van Morrison Glenn Frey Robert Palmer David Bowie My favoriteVan theMan album Many of m … y My f rie agre that this oneis on thelist of 10 album you m have nds e s ust on a de rt island.. What doe that say about m frie se s y nds?? on Did you know hewrote“Gloria”.. Hedid! FromLast tim : e Re ally.. I ncre dible “S nd in theClowns” e By Van theMan A Classic, Of Course ! Physics 212 Le cture8, S 2 lide Physics 212 Le cture8 Today's C pt: once C apacitors C apacitors in a circuits, Die ctrics, Ene in capacitors le rgy 40 30 20 10 0 Confused Avg = 3.4 Confident Physics 212 Le cture8, S 3 lide S eExamS om tuff xt dne • Examne We sday at 7:00 – – – – C rs m rial through le ove ate cture8 Bring your I D C onflict e at 5:15 – sign up in your grade xam book if you ne d to e If you haveconflicts with both of the contact us im e se m diate ly online.physics.uiuc.edu/courses/phys212/fall09/ExamPrepHe1.html Physics 212 Le cture8, S 4 lide Simple Capacitor Circuit Q V C +Q -Q V C Q=VC Q This “Q” really means that the battery has This moved charge Q from one plate to the other, moved so that one plate holds +Q and the other -Q. 8 Physics 212 Le cture8, S 5 lide Dielectrics V C0 Q0=VC0 V C1=κ C0 Q1=VC1 By adding a dielectric you are just making a By new capacitor with larger capacitance (factor of κ ) new 11 Physics 212 Le cture8, S 6 lide Qtotal Parallel Capacitor Circuit V C1 Q1 = C1V Qtotal C2 Q2 = C2V Key point: V is the same for both capacitors capacitors Key Point: Qtotal = Q1 + Q2 = VC1 + VC2 = V(C1 + C2) Ctotal = C1 + C2 14 Physics 212 Le cture8, S 7 lide Series Capacitor Circuit Q Q=VCtotal +Q -Q +Q -Q V V1 C1 C2 Q V V2 Q Q Q Key point: Q is the same for both capacitors Key point: Q = VCtotal = V1C1 = V2C2 VC Also: V = V1 + V2 Q/Ctotal = Q/C1 + Q/C2 17 1 1 1 = + C2 Ctotal C1 Physics 212 Le cture8, S 8 lide Pre flight 2 Which has lowest total capacitance: C C C C C Ctotal = C 1/Ctotal = 1/C + 1/C = 2/C Ctotal = C/2 70 60 50 40 30 20 10 Ctotal = 2C 18 0 Physics 212 Le cture8, S 9 lide Pre flight 4 Which has lowest total capacitance: C C C C C C Ctotal = C = C/2 C = C/2 Ctotal = Cleft + Cright 70 60 50 40 30 20 10 0 Ctotal = C Same 20 Physics 212 Le cture8, S 10 lide 10 S ilar to Pre im flight 6 Q C2 2 BB V V V C1 Q 1 V C3 Q 3 Ctota l Which of the following is NOT necessarily true: A) B) C) D) E) 24 V0 = V1 Ctotal > C1 V2 = V3 Q2 = Q3 V1 = V2 + V3 Physics 212 Le cture8, S 11 lide 11 Pre flight 6 BB NO YES NO YES NO YES V1 = V2 + V 3 Q2 = Q3 V1 > V2 Q1 Q2 Q2 = + C1 C2 C3 Q1 = Q2 V1 < V2 Q2 = C2C3 Q1 C1 (C2 + C3 ) Q1 = Q2 V1 < V2 Q1 = Q2 V1 < V2 25 Q1 = Q2 V1 < V2 (A) (B) (C) (D) Physics 212 Le cture8, S 12 lide 12 Energy in a Capacitor Energy In pre-lecture 7 we calculated the work done to move charge Q from one In plate to another: plate C V +Q U = 1/2QV = 1/2CV2 =1/2Q2/C -Q Since Q = VC This is potential energy waiting to be used… This 26 Physics 212 Le cture8, S 13 lide 13 Me ssing w/ Capacitors cte ry • I f conne d to a batte V stays constant V1 = V Q1 = C1V1 = κ CV = κ Q V κ C1 = κ C dn • I f isolate the total Q stays constant Q1 = Q κ C1 = κ C V1 = Q1/C1 = Q/κ C = V / κ Physics 212 Le cture8, S 14 lide 14 Pre flight 8 BB 60 “Q is fixe in this caseand wehavejust incre d thecapacitanceon d ase C The fore thevoltagediffe nceon C m belowe 2. re , re 2 ust r.” “Die ctrics incre C le ase apacitance The do not incre or de ase .y ase cre pote ntial diffe nce re ” “The dielectric increases the energy stored so it must also increase the voltage” 50 40 30 20 10 0 33 Physics 212 Le cture8, S 15 lide 15 Me ssing w/ Capacitors AC T Two ide ntical paralle platecapacitors areconne d to ide l cte ntical batte s. The a die ctric is inse d rie n le rte be e theplate of capacitor C . C parethee rgy store in thetwo capacitors. twe n s 1 om ne d V C0 V C1 κ =2 BB BB A) U1 < U0 B) U0 = U1 Com pareusing U = 1/ 2C 2 V C) U1 > U0 U1/U0 = κ 35 Pote ntial Ene goe UP rgy s UP Physics 212 Le cture8, S 16 lide 16 Pre flight 10 BB BB A B C 50 “We know that U = 0.5*(Q^2)/C as in our case Q did not We change and C has increased in C2 due to the dielectric, therefore U1>U2” therefore “Charge doesn't change so neither does U. .” “When a dielectic is placed in a capacitor, the When capacitance increases, which means that the potential energy increases” potential 33 40 30 20 10 0 Physics 212 Le cture8, S 17 lide 17 Pre flight 12 BB V m bethesam ! ust e Q: 50 40 Q1 Q2 = C1 C2 U1 = U2 = 1CV2 21 1C V2 22 C1 Q1 = Q2 C2 U1 = C1 U2 C2 30 20 10 0 U: Physics 212 Le cture8, S 18 lide 18 C alculation V C0 x0 V κ x0/4 BB capacitanceC and width x0 is 0 An air-gap capacitor, having conne V.to a batte of cte ry voltage d once • C ptual Analysis: Q C≡ V What change whe thedie ctric adde s n le d? (A) Only C (B) only Q (C) only V (D) Cand Q (E) V and Q Cchange s Q change s Physics 212 Le cture8, S 19 lide 19 Adding die ctric change thephysical capacitor le s V doe not changeand Cchange s s 38 C alculation V C0 x0 V κ x0/4 BB An air-gap capacitor, having capacitanceC0 and width x0 is conne V.to a batte of cte ry voltage d trate • S gic Analysis: – – C alculatene capacitanceC w Apply de finition of capacitanceto de rm Q te ine To calculateC le first look at: , t’s To Vle ft κ Vright (A) Vleft < Vright (A) 40 (B) Vleft = Vright (C Vleft > Vright ) The conducting plate is an equipotential !! Physics 212 Le cture8, S 20 lide 20 C alculation V C0 x0 An air-gap capacitor, having capacitanceC0 and width x0 is conne V.to a batte of cte ry voltage d BB V κ x0/4 Can conside capacitor to betwo capacitance C and C2, in paralle r s, 1 l κ What is C ? 1 = C 1 κ C 2 (A) C = C (B) C = 3/ 4C (C C = 4/ 3C )1 1 0 0 (A) 1 0 (D) C = 1/ 4C0 1 43 I n ge ral. For paralle platecapacitor: C= ε 0 A/d ne l A = 3/ 4A0 C = 3/4 (ε 0A0/d0) 1 d = d0 le C = 3/ 4C A die ctric (κ ) of width x0/4 i 1 0 inse hysics 212thegap8, Slide 21 rte into Lecture as shown Pd 21 C alculation V C0 x0 An air-gap capacitor, having capacitanceC0 and width x0 conne V.to a batte of cte ry voltage d V κ x0/4 BB κ What is C ? 2 = C 1 κ C 2 C = 3/ 4C 1 0 (A) C = κ C0 2 (B) C = 3/ 4 κ C 2 0 (C) C = 4/ 3 κ C 2 0 (D) C = 1/ 4 κ C0 2 I n ge ral. For paralle platecapacitor fille with die ctric: C= κ ε 0 A/d ne l d le A = 1/ 4A0 d = d0 45 C= ¼(κ ε 0A0/d0) C = 1/ 4 κ C 2 0 A die ctric (κ ) of width x0/4 le Physics 212 Le gapS show cture lide 22 inse d into the 8, as 22 rte C alculation V C0 x0 An air-gap capacitor, having capacitanceC0 and width x0 is conne V.to a batte of cte ry voltage d V κ BB x0/4 κ What is C ? What C = C 1 κ C 2 C = 3/ 4C 1 0 C = 1/ 4 κ C 2 0 (A) C = C 1 + C 2 (B) C C = C 1 (+)κ C 2 1 1 C = + C1 C2 −1 C= paralle com l bination of C and C2: C= C + C2 1 1 C= C (3/ 4 + 1/ 4 κ ) 0 46 A die ctric (κ ) of width x0/4 is le inse Physics 212 LectureasSlide 23 rte into thegap 8, shown. d 23 C alculation V C0 x0 An air-gap capacitor, having capacitanceC0 and width x0 is conne V.to a batte of cte ry voltage d BB V κ x0/4 κ C = C 1 κ C 2 C = 3/ 4C 1 0 C = 1/ 4 κ C 2 0 C= C (3/ 4 + 1/ 4 κ ) 0 What is Q? C≡ Q V Q = VC 3 1 Q f = VC 0 + κ 4 4 50 A die ctric (κ ) of width x0/4 is le inse Physics 212 LectureasSlide 24 rte into thegap 8, shown. d 24 Different Problem V Q0 x0 An air-gap capacitor, having capacitance C0 and width x0 is conne d to a cte batte of disconne and the ry n batte is voltageV d. ry cte C0 V κ BB BB 1/4x0 (A) Vf < V (B) Vf = V (C) Vf > V Q = Q0 = C0V Q stays sam : no way to add or subtract stays e We know C: (property of capacitor) We C = C0 (3/4 + 1/4 κ ) Vf = Q/C = V/(C0 (3/4 + 1/4 κ )) Physics 212 Lecture 8, Slide 0 5 25 2 A die ctric (κ ) of width 1/4x le Different Problem V Q0 x0 An air-gap capacitor, having capacitanceC0 and width x0 is conne d to a batte of voltage cte ry V and the d. ry is disconne n batte cte BB C0 V κ 1/4x0 Vf = Q/C = V/(C0 (3/4 + 1/4 κ )) How did energy stored in capacitor change How when dielectric inserted? when (A) U increased (B) U stayed same (C) U decreased U = ½ Q2/C Q remained same C increased U decreased A die ctric (κ ) of width 1/4x0 is le Physics 212 Lecture 8, Slide 26 inse d into thegap as shown. 26 rte ...
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This note was uploaded on 04/04/2011 for the course PHYSICS 212 taught by Professor Mestre during the Spring '11 term at University of Illinois at Urbana–Champaign.

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