1. 1 24 Electrostatic Potential Energy

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4. 4 Example as shown:

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

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

7. 7 Parallel Plate Capacitor E is nearly uniform

8. 8 Cylindrical Capacitor r

9. 9 r

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

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

13. 13 Energy Density Inside a Capacitor Ex: Lab Capacitor, C = 1F, V = 6V, vol.=2x10 -5 m 3. SI Unit: [J/m 3 ] about 35,000 higher than capacitor

14. 14 Capacitors in “Parallel” Arrangement Ex.

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

16. 16 equivalent value?

17. 17 Dielectric Constant K reduces E and V (E = E o /K) C = KC o C = Capacitance with Dielectric C o = “Empty” Capacitor

18. 18 Ex. K’s vacuum: 1 exactly air: 1.00059 paper: 3.7 water: 80 barium titanate: 1200 potassium tantalate niobate (0 °C): 34,000

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

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

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

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29. 29 Example with:

30. 30 Rolled Parallel-Plate Capacitor (Can Shape)