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  1. Materials for Lecture • Poling cards • Demos: • J4-01 • J4-22 • J4-51 TESTI N G Animations courtesy of: Sarah Eno

  2. Capacitors Fields near point charges is all well and good, but let’s do something practical! Capacitors are found in all electric circuits. Capacitor Industries, Inc Chicago, IL Sarah Eno

  3. The charges are held together on the plates by their attraction. Capacitors A capacitor is a way of storing charge. The symbol for a capacitor in a schematic for an electrical circuit shows basically what it is: two plates with a gap. (often want to store charge so that it can provide current) Sarah Eno

  4. Storing Charge Let’s think about storing charge… Often, you want to store as much charge as possible, while avoiding large (dangerous) voltages For a fixed voltage, you can increase the charged stored by increasing A or decreasing d Sarah Eno

  5. Capacitance Or the charge you can store per volt is related to the geometry of the plates and the gap Capacitance is the amount of charge you can store per volt, or Q/V. Farad=coulomb/volt Sarah Eno

  6. Increasing Area Sarah Eno

  7. Test Yourself Demo j4-01 • I’m going to charge these plates to 1000 V. I’m going to remove the charger, then I’m going to move them apart. As I move them, will the voltage • Increase • Decrease • Stay the same Sarah Eno

  8. Example What would be the area of a capacitor with a gap of ½ mm to have a capacitance of 1 farad? Sarah Eno

  9. Example Air breaks down and conducts for an electric field strength of 3x106 V/m. How many volts can it hold if it has a gap of 1mm? Capacitors come with voltage ratings. Cheap capacitors can typically hold 50 V. Sarah Eno

  10. The Gap • What if I stick something inside the gap? • Maybe something made of molecules that are electric dipoles… • ceramics • mica • polyvinyl chloride • polystyrene • glass • porcelain • rubber • electrolyte (glyco-ammonium borate, glycerol-ammonium borate, ammonium lactates, etc dissolved in goo or paste) Dielectric material Sarah Eno

  11. Inside: Dipoles Electric Dipole moments in random directions Put a charge on the plates. The charge creates an electric field. Dipole moments try to align with the field. Sarah Eno

  12. 2 3 1 5 6 4 11 7 9 8 10 12 Capacitors • 365 pf, 200V, air variable • 0.25 mF, 3000V, mineral oil • 21000 mF, 25 V, electrolytic • 20 pF, 100 V, air variable • 2 mF, 400 V, polystyrene • 100 mF, 12 V, electrolytic • 10 pf, 200 V, glass/air • 0.1 mF, 10 V, ceramic • 0.1 mF, 1 kV, ceramic • 0.33 mF, 400 V, mylar • 100 pF, 2kV, ceramic • 1000 pF, 200V, silver mica 1) Tune radios, 2) filter HV, 3) power supply filter, 4) tune rf, 5) audio 6) audio, 7) vhf/uhf, 8) audio, 9) audio, 10) audio, 11) high power rf, 12) precision rf Sarah Eno

  13. Test Yourself • Will the field between (and thus the voltage between) the plates be • Larger • Smaller • The same • As without the dielectric? Do j4-22 Sarah Eno

  14. Inside: Fields The field goes down. So, the amount of charge you can put on for 1 volt is larger. So, the capacitance goes up. A certain fraction of the field is “canceled”. E=E0/k. V=V0/k. C=kC0 Sarah Eno

  15. Dielectrics Material k Breakdown field (106 V/m) --------------------------------------------------------------- Air 1.00059 3 Paper 3.7 16 Glass 4-6 9 Paraffin 2.3 11 Rubber 2-3.5 30 Mica 6 150 Water 80 0 Sarah Eno

  16. Example What area would a capacitor with a 0.5 mm gap have to for a capacitance of 1 farad if it had a dielectric constant (k) of 10? Found earlier that without dielectric, need an area of 56x106 m2. So, reduce this by 10 to 56x105 m2 Sarah Eno

  17. Example A typical capacitor has a capacitance of 10 mF, a gap of 0.1 mm, and is filled with a dielectric with a dielectric strength of 10. What is the area? Sarah Eno

  18. Energy Stored How much work to move some this charge onto the capacitor? Amount of work to charge from scratch. Sum (integral) up the contributions to bring each charge Sarah Eno

  19. Energy Stored But, Q is hard to measure  Sarah Eno

  20. Simple Circuits Let’s try our first simple circuit Sarah Eno

  21. Capacitors with a Battery An “ideal” battery is a source of constant voltage. Though it is done using properties of metal, ions, etc, you should think of it as containing a fixed E field. Charge on one side is at a higher potential than the other Sarah Eno

  22. Batteries Students have many misconceptions about batteries, which lead to serious difficulties in making predictions about circuits. Batteries are not charged. They do not contain a bunch of electrons, ready to “spit out” Batteries are not current sources. They don’t put out a constant current. Sarah Eno

  23. Ground Zero volt point. Reservoir of electrons. Can take and give electrons easily. Sarah Eno

  24. Circuits Remember: it takes no work to move an charge through a conductor. The potential does not change! (for an ideal conductor… since only a “superconductor” is an ideal conductor, this is only mostly true for copper, gold, etc) Sarah Eno

  25. Test Yourself • When I close the switch will the voltage across the battery • Go down because charge leaves the battery to go to the capacitor • Go up because the battery will get additional charge from the capacitor • Stay the same because the voltage across a battery always stays the same Sarah Eno

  26. Battery + Capacitor Sarah Eno

  27. Example What is the charge on a 1 mF capacitor attached to a 1.5 V battery? How many electrons is that? Sarah Eno

  28. Capacitor Circuits • If you have more than 1 capacitor in a circuit, two basic ways to arrange them • parallel • series Sarah Eno

  29. Parallel Circuits Connected in Parallel • How will the voltage across them compare? • It will half. The voltage from the battery will be divided between the two • It will double. Because there will be two capacitors charged • It will be the same. The voltage is always the same. Sarah Eno

  30. Parallel Circuits How does the charge compare? Sarah Eno

  31. Parallel Twice the charge for the same voltage. Effectively increasing the area of the capacitor Sarah Eno

  32. Parallel If you replaced the 2 capacitors with 1 capacitor, what capacitance would it have to have in order to have the same voltage and the same charge -> effective capacitance of the system Sarah Eno

  33. Series • How will the voltage across them compare? • It will half. The voltage from the battery will be divided between the two • It will double. Because there will be two capacitors charged • It will be the same. The voltage is always the same. The voltage across each is 1/2. That means the charge on each is ½ compared to 1 capacitor circuit. Sarah Eno

  34. Series Its like you have twice the gap. The effective capacitance goes down. Sarah Eno

  35. Series in General Sarah Eno

  36. Check Sarah Eno

  37. Hints for Capacitors • remember the voltage across a battery is fixed • remember voltage does not change along a wire • look for parallel and series combinations, and calculate the equivalent capacitance. Sarah Eno

  38. Example What is the charge on each cap? What is the voltage across each cap? • Look for series and parallel combinations. Calculate equivalent capacitance. Replace. Repeat until have 1 cap. • Then work backwards Sarah Eno

  39. Example Sarah Eno

  40. Example Before the dielectric is added, the capacitance is C0. What is the capacitance afterwards? Picture it as two caps in series, each with a gap d/2 and therefore capacitance 2C0. When add dielectric, each capacitance goes up a factor k Sarah Eno

  41. Test Yourself • Which capacitor has the biggest charge? • 1mF • 0.2 mF • 0.6 mF • They all have the same charge • None of the above Sarah Eno

  42. Example What is the equivalent capacitance? .6 and .2 are in parallel. Add them to get .8 The 1 and the “.8” are in series. Sarah Eno

  43. Fun Another use for capacitance Do j4-51 Sarah Eno

  44. Hints for Capacitor Problems Sarah Eno