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Capacitors

Capacitors. A device storing electrical energy. – – – – – – –. + + + + + + +. –q. +q. Capacitor. A potential across connected plates causes charge migration until equilibrium. Charge stored q = C D V C = capacitance Unit = C/V = henry = H. D V. A. C 2. N m 2.

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Capacitors

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  1. Capacitors A device storing electrical energy

  2. – – – – – – – + + + + + + + –q +q Capacitor A potential across connected plates causes charge migration until equilibrium Charge stored q = CDV C = capacitance Unit = C/V = henry = H DV

  3. A C2 N m2 e0 = 8.8510–13 Parallel Plate Capacitance Plate area A, separation d d Capacitance = Ae0/d

  4. + – DV • Conductor • Capacitor or • Resistor Circuit Element Symbols • Potential Source

  5. DV + – C + – DV At Equilibrium • Capacitor charges to potential DV • Capacitor charge Q = CDV

  6. DQ slope = 1/C DV area = W Q Energy in a Capacitor • C = Q/DV so DV = Q/C • Work to push charge DQ W =DVDQ = (Q/C)DQ

  7. DV Q/C Q Energy in a Capacitor • Work to charge to Q is area of triangleW = 1/2 Q(Q/C) = 1/2 Q2/C • Work to charge to DVW = 1/2 DV (CDV) = 1/2C(DV)2 CDV

  8. Series Parallel Combining Capacitors and

  9. Parallel Components • All have the same potential difference • Capacitances add • (conceptually add A’s)

  10. Series Capacitors • All have the same charge separation • Reciprocals are additive • (conceptually add d’s)

  11. e0 = 8.8510–13 C2 N m2 Gauss’s Law • Electric flux through a closed shell is proportional to the charge it encloses. FE = Qin/e0

  12. R q q 1 q kq e04pr2 if k = = = e0A 4pe0 4pe0 r2 r2 Field around a Point Charge Shell Area = 4pr2 FE = q/e0 = EA +q E = =

  13. s 1 sA FE = , so E = e0 2 e0 Field Around Infinite Plate With uniform charge density s = Q/A = E(2A)

  14. –q –q +q 1/2 s/e0 0 0 +q s/e0 1/2 s/e0 Infinite ||-Plate capacitor Individually Together

  15. Field E = = s Q e0 Ae0 Qd • Potential DV = Ed = Ae0 Q Ae0 Ae0 • Capacitance Q/DV = = Qd d Parallel Plate Capacitance • Plate area A, plate separation d

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