Chapter 24 Capacitance

1. Chapter 24Capacitance

2. Topics • Capacitance • Storage of Electrical Energy • Capacitors, Batteries and Circuits • Dielectrics

3. Capacitance The capacitance of a device is defined by Q is the charge stored V is the potential difference within the system The unit is the farad (F) = Coulomb/Volt But since the farad is such a huge unit we usually use mF = 10-6 F or pF = 10-12 F

4. Capacitance Spherical Conductor The potential on the surface of a spherical conductor of radius R is Therefore, its capacitance is

5. +Q -Q Capacitance Capacitors A capacitor is a device that stores charge –Q on one conductor and charge +Q on the other conductor The stored charge creates an electric field, and therefore, a potential difference between the conductors

6. Capacitance Parallel Plate Capacitors If two conducting plates of area A are separated by a small distance d the electric field between them will be approximately constant and of magnitude

7. Capacitance Parallel Plate Capacitors Since the electric field is constant, the potential difference between the plates is simply so the capacitance is

8. Capacitance Cylindrical Capacitors A coaxial cable of length L is an example of a cylindrical capacitor R2 R1

9. Storage of Electrical Energy Work must be done to move positive charge from a negatively charged conductor to one that is positively charged. Or to move negative charge in the reverse direction.

10. Storage of Electrical Energy In moving charge dq, the electrical potential energy of the capacitor is increased by Therefore,

11. Energy Density of Electric Field Electric field Electric potential Potential energy

12. Energy Density of Electric Field The energy densityue This expression holds true for any electric field

13. Capacitors, Batteries and Circuits The potential is the same throughout a conductor when it is in electrostatic equilibrium; that is, when the charge has stopped moving

14. Capacitors in Parallel At equilibrium, the potential across each capacitor is the same, namely, 12 V same potential same potential

15. The two capacitors are equivalent to a single capacitor with capacitance

16. Capacitors in Series At equilibrium, the sum of the potentials across both capacitors will be equal to 12 V

17. The potential across C1 + that across C2 is equal to the potential difference between points a and b

18. Dielectrics A non-conducting material is called a dielectric Michael Faraday 1791 – 1867 Michael Faraday discovered that the capacitance increases when the space between conductors is replaced by a dielectric wikimedia

19. Dielectrics Electric field strength in the presence of a dielectric is where k (kappa) is called the dielectric constant of the inserted material E0 is the field before the dielectric is inserted. is called the permittivity

20. Maximum electric field strength

21. Molecular View of Dielectric

22. Molecular View of Dielectric -sb +sb The polarized molecules of the dielectric tend to align themselves parallel to the electric field due to the charges on the conductors - - - - - - - - + + + + + + + +

23. Molecular View of Dielectric The bound chargesb induced on the surface of the dielectric creates an electric field opposed to the electric field of the free charge sf on the conductors, thereby reducing the field between them

24. Summary • Capacitance C = Q / V (farad) • Capacitors • In parallel C = C1 + C2 • In series 1/C = 1/C1 + 1/C2 • Stored energy U = ½ QV • Energy density ue = ½ e0 E2 • Effect of dielectric E = E0 / k