24 Electrostatic Potential Energy 1 2 3 Example

24 Electrostatic Potential Energy 1

2

3

Example as shown: 4

Capacitance: Charge Storage per Volt Applied SI Unit: farad [F] = C/V 5

Real Parallel-Plate Capacitor Note: • Uniform Field • Fringing 6

Parallel Plate Capacitor E is nearly uniform 7

Cylindrical Capacitor r 8

r 9

10

Work done in Charging a Capacitor = (Q)(Vavg) 11

Q = VC Vavg = ½ Q/C Work = (Q) x (½ Q/C)= ½ Q 2/C = area under curve 12

Energy Density Inside a Capacitor SI Unit: [J/m 3] Ex: Lab Capacitor, C = 1 F, V = 6 V, vol. =2 x 10 -5 m 3. about 35, 000 higher than capacitor 13

Capacitors in “Parallel” Arrangement Ex. 14

Capacitors in “Series” Arrangement Q=0 Ex. 15

equivalent value? 16

Dielectric Constant K • • reduces E and V (E = Eo/K) C = KCo C = Capacitance with Dielectric Co = “Empty” Capacitor 17

Ex. K’s • • • vacuum: 1 exactly air: 1. 00059 paper: 3. 7 water: 80 barium titanate: 1200 potassium tantalate niobate (0 °C): 34, 000 18

Supercapacitors • • porous structure surface areas much greater charge separation distance < 1 nm very high capacitance 19

Batteries Capacitors slow/special charging simple/fast charging limited # cycles with over 500, 000 decreasing utility cycles at 100% short life 10 to 12 year life high energy density low energy density poor low temp. performance good low temp. perf. 20

Summary • • • Electrostatic potential energy Capacitance: field, energy, voltage, charge Capacitors in circuits Dielectrics / 21

22

23

24

25

26

27

28

Example with: 29

Rolled Parallel-Plate Capacitor (Can Shape) 30