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 1. Find E using Gauss’s Law 2. Calculate V = - ∫ E·ds 3. 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. Rectangular Solid Gaussian Surface – Chalk Box front back sides A B ds Ideal Parallel Plate Capacitor: E = 0 outside, E uniform inside

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

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

9. Chapter 26 Capacitance and Dielectrics 26.3 Combinations of Capacitors 1. Parallel 2. Series

11. Capacitors in Parallel d, A 1 d, A 2 C1C1 C2C2 C eq d, A 1 + A 2 For capacitors in parallel, the voltage across each capacitor is the same because the is no V along the connecting conductors. For many capacitors in parallel the reciprocal of the equivalent capacitance is the sum of all the individual capacitances C eq = C 1 + C 2 + C 3 + … C 1 =  0 A 1 /d C eq =  0 (A 1 + A 2 )/d = C 1 + C 2 C 2 =  0 A 2 /d

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

13. Capacitors in Series d 1, A C1C1 C2C2 C eq d 1 + d 2, A For capacitors in series, the same charge exists across each capacitor because charge is conserved. For many capacitors in series the reciprocal of the equivalent capacitance is the sum of all the reciprocals of the individual capacitances 1/C eq = 1/C 1 + 1/C 2 + 1/C 3 + … d 2, A 1/C 1 = d 1 / 0 A1/C 2 = d 2 / 0 A1/C eq = (d 1 +d 2 )/ 0 A = 1/C 1 + 1/C 2

14. Charge is conserved

16. P26.17(p.746) V ab = 15V

17. P26.19 (p.747) C 1 = 6.00F V = 20.0V C 2 = 3.00F

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

19. P26.27 (p.747)

20. 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? A. same B. half C. double D. quadruple E. quarter What stays constant? What do we have to assume?

21. P26.29 (p.748)

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

23. Chapter 26 Capacitance and Dielectrics 26.5 Capacitors with Dielectrics C = C 0 C 0 is the capacitance in a vacuum  is the dielectric constant for the material

25. P26.29 (p.748)

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