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Chapter 26 Capacitance and Dielectrics

Chapter 26 Capacitance and Dielectrics. Concept Question 1. Chapter 26 Capacitance and Dielectrics 26.1 Definition of Capacitance C = Q/ V Ability to separate charge increases with V Units: 1 F arad = 1 C oulomb/1 V olt. Chapter 26 Capacitance and Dielectrics

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Chapter 26 Capacitance and Dielectrics

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  1. Chapter 26 Capacitance and Dielectrics

  2. Concept Question 1

  3. Chapter 26 Capacitance and Dielectrics 26.1 Definition of Capacitance C = Q/V Ability to separate charge increases with V Units: 1 Farad = 1 Coulomb/1 Volt

  4. Chapter 26 Capacitance and Dielectrics • 26.2 Calculation of Capacitance • Find E using Gauss’s Law • Calculate V = -∫E·ds • Apply C = Q/V • Q will always divide through and C will depend only on materials and geometric properties of the capacitor

  5. Small pieces of thread align with the electric field between oppositely charged plates of a capacitor

  6. Ideal Parallel Plate Capacitor: E = 0 outside, E uniform inside Rectangular Solid Gaussian Surface – Chalk Box front sides A ds back B

  7. Concept Question 2 A. B. C. D.

  8. A B Fig 26-6b, p.801

  9. Chapter 26 Capacitance and Dielectrics • 26.3 Combinations of Capacitors • Parallel • Series

  10. Capacitors in Parallel For capacitors in parallel, the voltage across each capacitor is the same because the is no V along the connecting conductors. Ceq d, A1 C1 d, A1 + A2 d, A2 C2 Ceq = 0(A1+ A2)/d = C1 + C2 C1 = 0A1/d C2 = 0A2/d For many capacitors in parallel the reciprocal of the equivalent capacitance is the sum of all the individual capacitances Ceq = C1 + C2 + C3 + …

  11. E = 0 inside a conductor once the charges stop moving.

  12. Capacitors in Series For capacitors in series, the same charge exists across each capacitor because charge is conserved. Ceq C2 C1 d1, A d1 + d2, A d2, A 1/C1 = d1/0A 1/C2 = d2/0A 1/Ceq = (d1+d2)/0A = 1/C1 + 1/C2 For many capacitors in series the reciprocal of the equivalent capacitance is the sum of all the reciprocals of the individual capacitances 1/Ceq = 1/C1 + 1/C2 + 1/C3 + …

  13. Charge is conserved Charge is conserved

  14. Vab = 15V P26.17(p.746)

  15. C1 = 6.00F C2 = 3.00F V= 20.0V P26.19 (p.747)

  16. Chapter 26 Capacitance and Dielectrics 26.4 Energy Stored in a Charged Capacitor U = QV/2 = CV2/2 = Q2/2CDifferent ways of expressing of the same quantity

  17. P26.27 (p.747)

  18. CT3: A parallel-plate capacitor is charged and then disconnected from the battery. By what fraction does the stored energy change when the plate separation is doubled? • same • half • double • quadruple • quarter What stays constant? What do we have to assume?

  19. P26.29 (p.748)

  20. Concept Question 4 A. B. C. Hint: The increase in potential energy equals the work of the external agent.

  21. Chapter 26 Capacitance and Dielectrics 26.5 Capacitors with Dielectrics C = C0C0 is the capacitance in a vacuum  is the dielectric constant for the material

  22. P26.29 (p.748)

  23. = 2aq Line of action = qE a Moment arm asin a

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