PHYS 142 Poling cards Materials for Lecture CH

PHYS 142 Poling cards Materials for Lecture CH 26 TESTING Demos: http: //www. physics. umd. edu/deptinfo/facilities/lecdem. htm J 4 -01 J 4 -22 J 4 -51 Animations courtesy of: http: //webphysics. davidson. edu/Applets. html Sarah Eno 1

PHYS 142 Capacitors CH 26 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 2

PHYS 142 Capacitors CH 26 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. The charges are held together on the plates by their attraction. (often want to store charge so that it can provide current) Sarah Eno 3

PHYS 142 Storing Charge CH 26 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 4

PHYS 142 Capacitance CH 26 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 5

PHYS 142 Increasing Area Sarah Eno CH 26 6

PHYS 142 Test Yourself CH 26 Demo j 4 -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 1) Increase 2) Decrease 3) Stay the same Sarah Eno 7

PHYS 142 Example CH 26 What would be the area of a capacitor with a gap of ½ mm to have a capacitance of 1 farad? Sarah Eno 8

PHYS 142 Example CH 26 Air breaks down and conducts for an electric field strength of 3 x 106 V/m. How many volts can it hold if it has a gap of 1 mm? Capacitors come with voltage ratings. Cheap capacitors can typically hold 50 V. Sarah Eno 9

PHYS 142 The Gap CH 26 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 10

PHYS 142 Inside: Dipoles CH 26 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 11

PHYS 142 Capacitors 2 3 1 5 4 7 8 9 6 10 11 12 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 CH 26 1) 365 pf, 200 V, air variable 2) 0. 25 m. F, 3000 V, mineral oil 3) 21000 m. F, 25 V, electrolytic 4) 20 p. F, 100 V, air variable 5) 2 m. F, 400 V, polystyrene 6) 100 m. F, 12 V, electrolytic 7) 10 pf, 200 V, glass/air 8) 0. 1 m. F, 10 V, ceramic 9) 0. 1 m. F, 1 k. V, ceramic 10) 0. 33 m. F, 400 V, mylar 11) 100 p. F, 2 k. V, ceramic 12) 1000 p. F, 200 V, silver mica 12

PHYS 142 Test Yourself CH 26 Will the field between (and thus the voltage between) the plates be 1) Larger 2) Smaller 3) The same 4) As without the dielectric? Do j 4 -22 Sarah Eno 13

PHYS 142 Inside: Fields CH 26 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=E 0/k. V=V 0/k. C=k. C 0 Sarah Eno 14

PHYS 142 Dielectrics Material CH 26 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 15

PHYS 142 Example CH 26 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 56 x 106 m 2. So, reduce this by 10 to 56 x 105 m 2 Sarah Eno 16

PHYS 142 Example CH 26 A typical capacitor has a capacitance of 10 m. F, a gap of 0. 1 mm, and is filled with a dielectric strength of 10. What is the area? Sarah Eno 17

PHYS 142 Energy Stored CH 26 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 18

PHYS 142 Energy Stored CH 26 But, Q is hard to measure Sarah Eno 19

PHYS 142 Simple Circuits CH 26 Let’s try our first simple circuit Sarah Eno 20

PHYS 142 Capacitors with a Battery CH 26 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 21

PHYS 142 Batteries CH 26 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 22

PHYS 142 Ground CH 26 Zero volt point. Reservoir of electrons. Can take and give electrons easily. Sarah Eno 23

PHYS 142 Circuits CH 26 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 24

PHYS 142 Test Yourself CH 26 When I close the switch will the voltage across the battery 1) Go down because charge leaves the battery to go to the capacitor 2) Go up because the battery will get additional charge from the capacitor 3) Stay the same because the voltage across a battery always stays the same Sarah Eno 25

PHYS 142 Battery + Capacitor Sarah Eno CH 26 26

PHYS 142 Example CH 26 What is the charge on a 1 m. F capacitor attached to a 1. 5 V battery? How many electrons is that? Sarah Eno 27

PHYS 142 Capacitor Circuits CH 26 If you have more than 1 capacitor in a circuit, two basic ways to arrange them • parallel • series Sarah Eno 28

PHYS 142 Parallel Circuits CH 26 Connected in Parallel How will the voltage across them compare? 1) It will half. The voltage from the battery will be divided between the two 2) It will double. Because there will be two capacitors charged 3) It will be the same. The voltage is always the same. Sarah Eno 29

PHYS 142 Parallel Circuits CH 26 How does the charge compare? Sarah Eno 30

PHYS 142 Parallel CH 26 Twice the charge for the same voltage. Effectively increasing the area of the capacitor Sarah Eno 31

PHYS 142 Parallel CH 26 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 32

PHYS 142 Series CH 26 How will the voltage across them compare? 1) It will half. The voltage from the battery will be divided between the two The voltage across each is 1/2. That means the charge on each is ½ compared to 1 capacitor circuit. 2) It will double. Because there will be two capacitors charged 3) It will be the same. The voltage is always the same. Sarah Eno 33

PHYS 142 Series CH 26 Its like you have twice the gap. The effective capacitance goes down. Sarah Eno 34

PHYS 142 Series in General Sarah Eno CH 26 35

PHYS 142 Check Sarah Eno CH 26 36

PHYS 142 Hints for Capacitors CH 26 • 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 37

PHYS 142 Example CH 26 What is the charge on each cap? What is the voltage across each cap? 1) Look for series and parallel combinations. Calculate equivalent capacitance. Replace. Repeat until have 1 cap. 2) Then work backwards Sarah Eno 38

PHYS 142 Example Sarah Eno CH 26 39

PHYS 142 Example CH 26 Before the dielectric is added, the capacitance is C 0. What is the capacitance afterwards? Picture it as two caps in series, each with a gap d/2 and therefore capacitance 2 C 0. When add dielectric, each capacitance goes up a factor k Sarah Eno 40

PHYS 142 Test Yourself CH 26 Which capacitor has the biggest charge? 1) 1 m. F 2) 0. 2 m. F 3) 0. 6 m. F 4) They all have the same charge 5) None of the above Sarah Eno 41

PHYS 142 Example CH 26 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 42

PHYS 142 Fun CH 26 Another use for capacitance Do j 4 -51 Sarah Eno 43

PHYS 142 Hints for Capacitor Problems Sarah Eno CH 26 44