1. February 14, 2005Capacitors1 Welcome Back Exam returned Wed or Friday.  Problem 1 – We did it in class  Problem 2 - A Web Assign Problem  Problem 3 - Superposition Quiz on Friday (Capacitors) New WebAssign Posted … Wait until Wednesday to try.

2. February 14, 2005Capacitors2 Chapter 25 Capacitors Battery

3. February 14, 2005Capacitors3 Remember distributed Charges

4. February 14, 2005Capacitors4 Infinite Metal Plates -------------- ++++++++++++++++

5. February 14, 2005Capacitors5 Addemup -------------- ++++++++++++++++ E=0

6. February 14, 2005Capacitors6 Not quite infinite …

7. February 14, 2005Capacitors7 Capacitor Composed of two metal plates. Each plate is charged  one positive  one negative Stores Charge Can store a LOT of charge and can be dangerous!

8. February 14, 2005Capacitors8 A Simple Electric Circuit

9. February 14, 2005Capacitors9 Don’t ask questions because I don’t know the answers! Zn Metal Cu Metal Aqueous Solution of

10. February 14, 2005Capacitors10 What’s Next? Zn(solid)  Zn 2+ +2e -  Electrons Hang Around  Zn ion goes into the solution. Cu 2+ (solution) +2e -  Cu depositing on Cu electrode

11. February 14, 2005Capacitors11

12. February 14, 2005Capacitors12

13. February 14, 2005Capacitors13

14. February 14, 2005Capacitors14 Gauss on Capacitors d Air or Vacuum Area A - Q +Q E V=Potential Difference Gaussian Surface Same result from other plate!

15. February 14, 2005Capacitors15 Two Charged Plates (Neglect Fringing Fields) d Air or Vacuum Area A - Q +Q E V=Potential Difference Symbol

16. February 14, 2005Capacitors16 Note d Air or Vacuum Area A - Q +Q E V=Potential Difference + Consider a +q charge at the (-) plate. Move it to the (+) plate Work to do this is W=Fd=qEd also W=q(V f -Vi)=qV Therefore Ed=V E=V/d

17. February 14, 2005Capacitors17 Device The Potential Difference is APPLIED by a battery or a circuit. The charge q on the capacitor is found to be proportional to the applied voltage. The proportionality constant is C and is referred to as the CAPACITANCE of the device. DEFINITION

18. February 14, 2005Capacitors18 UNITS

19. February 14, 2005Capacitors19 Look again

20. February 14, 2005Capacitors20 Continuing… The capacitance of a parallel plate capacitor depends only on the Area and separation between the plates. C is dependent only on the geometry of the device!

21. Diversion on Capacitors

22. February 14, 2005Capacitors22 Two Metal Plates a Capacitor Make.

23. February 14, 2005Capacitors23 More is better!

24. February 14, 2005Capacitors24 Implementation - Variable

25. February 14, 2005Capacitors25 How do you do that?

26. February 14, 2005Capacitors26 Roll it up, Scottie

27. February 14, 2005Capacitors27 Stacked Disks, etc.

28. February 14, 2005Capacitors28 Units of  0 pico

29. February 14, 2005Capacitors29 Simple Capacitor Circuits Batteries  Apply potential differences Capacitors Wires  Wires are METALS.  Continuous strands of wire are all at the same potential.  Separate strands of wire connected to circuit elements may be at DIFFERENT potentials.

30. February 14, 2005Capacitors30 Size Matters! A Random Access Memory stores information on small capacitors which are either charged (bit=1) or uncharged (bit=0). Voltage across one of these capacitors ie either zero or the power source voltage (5.3 volts in this example). Typical capacitance is 55 fF (femto=10 -15 ) Question: How many electrons are stored on one of these capacitors in the +1 state?

31. February 14, 2005Capacitors31 Small is better in the IC world!

32. February 14, 2005Capacitors32 TWO Types of Connections SERIES PARALLEL

33. February 14, 2005Capacitors33 Parallel Connection V V C Equivalent =C E C 1 C 2 C 3

34. February 14, 2005Capacitors34 Series Connection V C 1 C 2 q -q The charge on each capacitor is the same !

35. February 14, 2005Capacitors35 Series Connection Continued V C 1 C 2 q -q V 1 V 2

36. February 14, 2005Capacitors36 For Bunches of Capacitors

37. February 14, 2005Capacitors37

38. February 14, 2005Capacitors38 Example C 1 C 2 V C3C3 C1=12.0  f C2= 5.3  f C3= 4.5  d (12+5.3)pf series

39. February 14, 2005Capacitors39 More on the Big C We move a charge dq from the (-) plate to the (+) one. The (-) plate becomes more (-) The (+) plate becomes more (+). dW=Fd=dq x E x d +q -q E=  0 A/d +dq

40. February 14, 2005Capacitors40 So….

41. February 14, 2005Capacitors41 Not All Capacitors are Created Equal Parallel Plate Cylindrical Spherical

42. February 14, 2005Capacitors42 Spherical Capacitor

43. February 14, 2005Capacitors43 Calculate Potential Difference V (-) sign because E and ds are in OPPOSITE directions.

44. February 14, 2005Capacitors44 Continuing… Lost (-) sign due to switch of limits.

45. February 14, 2005Capacitors45 Real Materials Consist of atoms or molecules bonded together. Some atoms and molecules do not have dipole moments when isolated. Some do. Two types to consider:  Polar  Non-Polar

46. February 14, 2005Capacitors46 Polar Molecule E

47. February 14, 2005Capacitors47 Polar Materials

48. February 14, 2005Capacitors48

49. February 14, 2005Capacitors49 Apply an Electric Field Some LOCAL ordering Large Scale Ordering

50. February 14, 2005Capacitors50 Adding things up.. - E + Net effect REDUCES the field

51. February 14, 2005Capacitors51 Non-Polar Material

52. February 14, 2005Capacitors52 Non-Polar Material Effective Charge is REDUCED Electric Field in the dielectric is reduced

53. February 14, 2005Capacitors53 Effect of Capacitor Material Dielectric Effective Charge is REDUCED Electric Field in the dielectric is reduced

54. February 14, 2005Capacitors54 We can measure the C of a capacitor (later) C 0 = Vacuum or air Value C = With dielectric in place C=  C 0 Definition

55. February 14, 2005Capacitors55 Dielectric Constant

56. February 14, 2005Capacitors56 How to Check Charge to V 0 and then disconnect from the battery. C0C0 V0V0 Connect the two together V C 0 will lose some charge to the capacitor with the dielectric. We can measure V with a voltmeter (later). Q

57. February 14, 2005Capacitors57 Checking the idea.. V Note: When two Capacitors are the same (No dielectric), then V=V 0 /2.

58. February 14, 2005Capacitors58 Some  values Material Dielectric Strength Breakdown KV/mm Air13 Polystyrene2.624 Paper3.516 Pyrex4.714 Strontium Titanate 3108

59. February 14, 2005Capacitors59 Messing with Capacitor + V - + V - +-+-+-+- The battery means that the potential difference across the capacitor remains constant. For this case, we insert the dielectric but hold the voltage constant, q=CV since C  kC 0 q k  kC 0 V THE EXTRA CHARGE COMES FROM THE BATTERY! Remember – We hold V constant with the battery.

60. WHERE IS THIS NEW CHARGE? Hang on … we will get there. But there is more capacity so there is more charge for the same applied voltage

61. February 14, 2005Capacitors61 Another Case We charge the capacitor to a voltage V 0. We disconnect the battery. We slip a dielectric in between the two plates. We look at the voltage across the capacitor to see what happens.

62. February 14, 2005Capacitors62 Case II – No Battery +-+-+-+- q0q0 qq q=C 0 V o When the dielectric is inserted, no charge is added so the charge must be the same. V0VV0V

63. February 14, 2005Capacitors63 Another Way to Think About This There is an original charge q on the capacitor. If you slide the dielectric into the capacitor, you are adding no additional STORED charge. Just moving some charge around in the dielectric material. If you short the capacitors with your fingers, only the original charge on the capacitor can burn your fingers to a crisp!

64. February 14, 2005Capacitors64 q0q0

65. February 14, 2005Capacitors65 A Reminder of days past

66. February 14, 2005Capacitors66 A Closer Look at this stuff.. Consider this capacitor. No dielectric. Applied Voltage via a battery. C0C0 ++++++++++++ ------------------ V0V0 q -q

67. February 14, 2005Capacitors67 Remove the Battery ++++++++++++ ------------------ V0V0 q -q The Voltage across the capacitor remains V 0 q remains the same as well. The capacitor is fat (charged), dumb and happy.

68. February 14, 2005Capacitors68 Slip in a Dielectric Almost, but not quite, filling the space ++++++++++++ ------------------ V0V0 q -q - - - - + + + -q’ +q’ E0E0 E E’ from induced charges Gaussian Surface

69. February 14, 2005Capacitors69 A little sheet from the past.. ++++++ ------ q -q -q’ +q’ 0 2xE sheet 0

70. February 14, 2005Capacitors70 Some more sheet… (original field)

71. February 14, 2005Capacitors71 A Few slides back Case II – No Battery +-+-+-+- q0q0 qq q=C 0 V o When the dielectric is inserted, no charge is added so the charge must be the same. V0VV0V

72. February 14, 2005Capacitors72 From this last equation

73. February 14, 2005Capacitors73 A Bit more…..

74. February 14, 2005Capacitors74 Important Result (We already know) Electric Field is Reduced by the presence of the material. The material reduces the field by a factor .  is the DIELECTRIC CONSTANT of the material

75. February 14, 2005Capacitors75 Another look +-+- VoVo

76. February 14, 2005Capacitors76 Add Dielectric to Capacitor Original Structure Disconnect Battery Slip in Dielectric +-+- VoVo +-+- +-+- V0V0 Note: Charge on plate does not change!

77. February 14, 2005Capacitors77 What happens? +-+-  i   i  oooo Potential Difference is REDUCED by insertion of dielectric. Charge on plate is Unchanged! Capacitance increases by a factor of  as we showed previously

78. February 14, 2005Capacitors78 SUMMARY OF RESULTS

79. February 14, 2005Capacitors79 APPLICATION OF GAUSS’ LAW

80. February 14, 2005Capacitors80 New Gauss for Dielectrics

81. February 14, 2005Capacitors81 The Insertion Process With A Battery +-+- VoVo -------- F