PHYS 221 General Physics II

PHYS 221 General Physics II Capacitance, Dielectrics, Lightning Spring 2015 Assigne Reaing: 18.4 18.6 Lecture 5

Recap: PHYS 221 Last Lecture Electric force is conservative Electric potential energy Potential PE elect W elect qex V PE elect q E V x Distance if = x x parallel to E Many meical applications: EKG an EEG measures V between electroes E Phys 221 Spring 2015 Lecture 05 2

Capacitor Capacitor is a evice that stores electrostatic potential energy. A capacitor consists of 2 spatially separate conuctors which can be charge to Q an Q. A Equipotential surfaces Phys 221 Spring 2015 Lecture 05 3

Capacitance The capacitance is efine as the ratio of the charge on one conuctor of the capacitor to the potential ifference between the conuctors. C Q V Capacitance is measure in Faraays represente by the letter F which is equal to (coulomb/volt) Phys 221 Spring 2015 Lecture 05 4

Capacitance between Parallel Plates Calculate the capacitance. We assume, charge ensities on each plate with potential ifference V: A The electric fiel between the plates is uniform an is given by (see Eq. 17.17 in the textbook): E 0 Q 0 A The potential ifference (or voltage) between the plates is V E Q 0 A C Q V 0A Phys 221 Spring 2015 Lecture 05 5

Capacitance between Parallel Plates Calculate the capacitance. We assume, charge ensities on each plate with potential ifference V: A E C Q V Q Q 0 A Nee Q: Nee V: from efinition Use Gauss Law to fin E EA Q o 0 A Phys 221 Spring 2015 Lecture 05 6 Q A V Ex E E Q o A C epens only on the geometry of the capacitor (A,)

Demo Demo: capacitance versus C Q V 0 A Phys 221 Spring 2015 Lecture 05 7

Example What is the capacitance of a parallel plate capacitor mae out of two square plates 10 x10 cm 2 separate by 1 mm wie gap? A=0.01 m 2 C o A =1 mm C C 2 8.85x10 12 ( ) N 2 0.01m2 2 m 10 3 m 88.5x10 12 F 88 pf If we connect 1.5V battery to its plates, how much charge coul be store in this capacitor? Q CV 88 10 12 1.5 C 132 pc Phys 221 Spring 2015 Lecture 05 8

BB i>clicker question BB Does the capacitance C of a capacitor increase, ecrease or remain the same when the charge q on it is ouble? (A) Decreases (B) Remains the Same (C) Increases Phys 221 Spring 2015 Lecture 05 9

Energy Store in a Capacitor Charging capacitor requires work: ΔV must move charges from one plate to another through rising ΔV charging a capacitor involves work: W=1/2 Q ΔV this work is equal to the energy store in a capacitor Energy store in a capacitor: PE cap 1 2 QV Lecture 05 Phys 221 Spring 2015 10

Energy store in a capacitor Energy store in a capacitor: PE cap 1 2 QV Alternative equations for energy store in a capacitor Using Q CV PE cap 1 2 C V 2 Using V Q C PE cap Q2 2C Phys 221 Spring 2015 Lecture 05 11

Where is energy actually store? For a parallelplate capacitor, the capacitance is so the energy store is C 0A PE cap 1 2 C V 2 1 2 0 A V 2 1 2 0 A V 2 The energy per unit volume is: u PE cap A 1 2 0E 2 Energy ensity The electric energy is actually store in the fiel, proportional to E 2. This equation is true in general, for any electric fiel. Phys 221 Spring 2015 Lecture 05 12

Energy Store in a Capacitor (emo) C P.S. Power supply (P.S.) supplies voltage V. PE cap 1 2 CV 2 can prouce a big jolt. Application: efibrillator A fibrillating heart is one in which the cariac muscles go into uncontrolle twitching an quivering. A efibrillator is use to stop this. Phys 221 Spring 2015 Lecture 05 13

BB i>clicker question BB pull q q pull A parallel plate capacitor given a charge q. The plates are then pulle a small istance further apart. What happens to the charge q on each plate of the capacitor? 1) Increases 2) Constant 3) Decreases Remember charge is real/physical. There is no place for the charges to go. Phys 221 Spring 2015 Lecture 05 14

Another Question q q A parallel plate capacitor given a charge q. The plates are then pulle a small istance further apart. Which of the following apply to the situation after the plates have been move? 1)The capacitance increases True False C = ε / pull C ecreases! 2)The electric fiel increases True False E= Q/(ε 0 A) Constant 3)The voltage between the plates increases True V= E pull False Phys 221 Spring 2015 Lecture 05 15

BB pull i>clicker question q A parallel plate capacitor given a charge q. The plates are then pulle a small istance further apart. Which of the following apply to the situation after the plates have been move? The energy store in the capacitor A) increases B) constant C) ecreases q pull BB U= ½ QV Q constant, V increase Plates are attracte to each other, you must pull them apart, so the potential energy of the plates increases. Phys 221 Spring 2015 Lecture 05 16

Equivalent Capacitors a V b Q 1 Q 2 C 1 C 2 Q 3 C3 a V b Q C a V b Q Q Q Q Q Q C a b Q Q Phys 221 Spring 2015 Lecture 05 17

Capacitors in Parallel Capacitors connecte in parallel can be replace with an equivalent capacitor that has the same total charge, Q an the same applie potential V. a V b Q 1 Q 2 a V C C 1 2 b Parallel Combination: Q1 Q2 V C C 1 2 Q Q C 2 1 C Q C 2 1 Equivalent Capacitor: C C C 1 2 Q Q1 Q2 Q1( C1 C2) C V V CV 1 Phys 221 Spring 2015 Lecture 05 18

Capacitors in Series Capacitors are in series when a potential ifference that is applie across their combination is the sum of the resulting potential ifferences across each capacitor. a Q Q Q Q C 1 C 2 b Phys 221 Spring 2015 Lecture 05 19 a Q The charge on C 1 must be the same as the charge on C 2 since applying a potential ifference across ab cannot prouce a net charge on the inner plates of C 1 an C 2. RHS: LHS: Q V ab C Q Vab V1V2 C Q C 1 2 Q C b 1 1 1 C C C 1 2

Example 1 a b C 3 C 1 C 2 a C b How o we start?? Realize to first group C 1 an C 2 Recognize C 3 is in series with the parallel combination on C 1 an C 2. i.e. 1 1 1 C C C C 3 1 2 C ( C C ) C 3 1 2 C C C 1 2 3 Phys 221 Spring 2015 Lecture 05 20

Question What is the relationship between V 0 an V? V 0 Q Q (Area A) V Q Q (Area A) /3 /3 conuctor (a) V = (2/3)V 0 (b) V = V 0 (c) V = (3/2)V 0 Phys 221 Spring 2015 Lecture 05 21

Dielectrics Empirical observation: Inserting a nonconucting material between the plates of a capacitor changes the VALUE of the capacitance. Definition:The ielectric constant of a material is the ratio of the capacitance when fille with the ielectric to that without it. Phys 221 Spring 2015 Lecture 05 22

Dielectrics Empirical observation: Inserting a nonconucting material between the plates of a capacitor changes the VALUE of the capacitance. Definition: The ielectric constant of a material is the ratio of the capacitance when fille with the ielectric to that without it. C C 0 k values are always > 1 (e.g., glass = 5.6; water = 78) (the water ha better be very pure an nonconucting) They INCREASE the capacitance of a capacitor (goo, since it is har to make big capacitors) They permit more energy to be store on a given capacitor than otherwise with vacuum (i.e., air) Phys 221 Spring 2015 Lecture 05 23

Effect of Dielectrics on the Electric Fiel real charge real charge E E' electric fiel ue to the ipoles; it opposes applie E E fiel 0 E ' resultant fiel E 0 Phys 221 Spring 2015 Lecture 05 24

Demo: Dielectrics & Capacitance E 0 V V E E Phys 221 Spring 2015 Lecture 05 25

Dielectric Strength *The maximum value of the electric fiel that a ielectric material can tolerate before breaking own. * It limits the voltage that can be applie to a capacitor. The maximum voltage is calle the breakown potential. Phys 221 Spring 2015 Lecture 05 26

Dielectric Properties material κ ielectric strength (kv/mm) air (1 atm) 1.00059 3 paraffin 2.1 2.5 10 glass (Pyrex) 5.6 14 mica 5.4 10 100 polystyrene 2.55 24 H 2 O (20 0 C) 80? titania ceramic 130 strontium titanate 310 8 Phys 221 Spring 2015 Lecture 05 27

Dielectric Combinations 1 2 A A /2 /2 A/2 A/2 1 2 Phys 221 Spring 2015 Lecture 05 28

Energy store in electric fiel Energy in a capacitor is store in the electric fiel U=PE Since we know the energy of a capacitor, we can calculate energy store in electric fiel an the energy ensity (U/Volume) Electric fiel energy ensity: u 1 2 0 E 2 Electric fiel energy is proportional to E 2 This equation is true in general, for any electric fiel This formula can be easily verifie for a plane capacitor Phys 221 Spring 2015 Lecture 05 29

Energy store in electric fiel Energy in a capacitor is store in the electric fiel Since we know the energy of a capacitor, we can calculate energy store in electric fiel 1 U C V 2 cap 2 U cap U cap 1 2 1 2 0A 0 E 2 AE 2 Volume insie a capacitor Electric fiel energy ensity: Ucap 1 2 u 0E A 2 Phys 221 Spring 2015 Lecture 05 30