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Capacitors II

Capacitors II. Today’s plan. Revision and some problems Energy storage in the capacitors Capacitors with dielectric material. - Q. A. r. a. + + + +. + Q. d. - - - - -. b. L. - Q. a. + Q. b. Cylindrical. Spherical. Parallel Plates. Summary of important capacitor geometries.

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Capacitors II

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  1. Capacitors II

  2. Today’s plan • Revision and some problems • Energy storage in the capacitors • Capacitors with dielectric material

  3. -Q A r a + + + + +Q d - - - - - b L -Q a +Q b Cylindrical Spherical Parallel Plates Summary of important capacitor geometries • The definition of the capacitance relatesQto V via C: • The capacitance depends on the geometry: In SI unit system: C has units of “Farads” or F (1F = 1C/V) e o has units of F/m

  4. In a capacitor Charges will occupy the faces facing each other. • Fringing field is prominent if L ~ d • Parallel combination

  5. Series combination

  6. Problem 8

  7. Problem 8

  8. Problem 10

  9. Rule • Identify the points between which Ceq has to be calculated. • Connect the battery and send +Q from +ive and –Q from –ive terminal • Write charges appearing on each plate and potential on each capacitor. • If the plates form an isolated system total charge is zero.

  10. Problem 10 No charge Isolated system Total charge zero

  11. No charge

  12. Problem 10 C1 = C3 = C4 = C5 = C C C y x C C Ceq = C

  13. Electrostatic energy stored in a capacitor Work done by the external agent to charge the capacitor is equal to electrostatic energy stored in the capacitor.

  14. Capacitor is connected to a battery

  15. Battery is doing work against the electric field of plates

  16. Battery is doing work against the electric field of plates

  17. Battery is doing work against the electric field of plates

  18. Battery is doing work against the electric field of plates

  19. At some instance, let the charge on the capacitor is q  V = q/C - ++ - - +

  20. Energy storage • Work done in transferring next piece of charge dq  dW = V dq Equal to electrostatic energy stored in the capacitor

  21. Where does this energy reside?? • In the volume between the plates • More specifically, in the electric field that is present between the plates. Energy density Empty space can contain energy

  22. Capacitors with DielectricEmpirical observation • Capacitance increases • It is good, since hard to make big capacitors.

  23. The role of dielectric

  24. Case 1: Capacitor is not disconnected from battery Now the dielectric slab is inserted - ++ - - +

  25. Capacitor is not disconnected from battery - ++ - - + But

  26. Capacitor is not disconnected from battery - + Charge will increase - ++ - - + - + - + Capacity increases

  27. To be noted…. • Battery maintains a constant V between the plates. • Electric field inside the capacitors must be the same. • Battery moves additional charge q = q´-q • Capacity increases

  28. Case 2: An empty capacitor is charged and then disconnected from the battery.

  29. Case 2: An empty capacitor is charged and then disconnected from the battery. Now filled with dielectric material

  30. Case 1: An empty capacitor is charged and then disconnected from the battery. • Dielectric reduces the strength of the electric field. • E = E0/k (always k >1) V decreases and C increases.

  31. Capacities with the dielectric • Parallel plate capacitor • Spherical capacitor • Cylindrical capacitor

  32. Problem 20 • Find the capacitance of the capacitor

  33. C´

  34. P-14-15 P698 • Show that force per unit area acting on either capacitor plate (Electrostatic pressure) is given by Force by which the plates will attract each other

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