1 24 Electrostatic Potential Energy

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4 Example as shown:

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

6 Real Parallel-Plate Capacitor Note: Uniform Field Fringing

7 Parallel Plate Capacitor E is nearly uniform

8 Cylindrical Capacitor r

9 r

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

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

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 Capacitors in “Parallel” Arrangement Ex.

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

16 equivalent value?

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

18 Ex. K’s vacuum: 1 exactly air: 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 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 Summary Electrostatic potential energy Capacitance: field, energy, voltage, charge Capacitors in circuits Dielectrics /

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29 Example with:

30 Rolled Parallel-Plate Capacitor (Can Shape)