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24 Electrostatic Potential Energy

Learn how capacitance and dielectrics affect energy storage in capacitors, along with practical application examples and important considerations in circuits. Explore differences between capacitors and batteries for various applications.

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24 Electrostatic Potential Energy

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  1. 0 24 Electrostatic Potential Energy

  2. 0

  3. 0

  4. 0 Example as shown:

  5. Capacitance: Charge Storage per Volt Applied 0 SI Unit: farad [F] = C/V

  6. 0 • Real Parallel-Plate Capacitor • Note: • Uniform Field • Fringing

  7. 0 Parallel Plate Capacitor E is nearly uniform

  8. Cylindrical Capacitor 0 r

  9. 0 r

  10. 0

  11. 0 Work done in Charging a Capacitor = (Q)(Vavg)

  12. 0 Q = VC Vavg = ½ Q/C Work = (Q) x (½ Q/C)= ½ Q2/C = area under curve

  13. Energy Density Inside a Capacitor 0 SI Unit: [J/m3] Ex: Lab Capacitor, C = 1F, V = 6V, vol.=2x10-5 m3. about 35,000 higher than capacitor

  14. Capacitors in “Parallel” Arrangement 0 Ex.

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

  16. 0 equivalent value?

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

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

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

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

  22. 0 Example with:

  23. 0 Rolled Parallel-Plate Capacitor (Can Shape)

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