Capacitance

1. C Capacitance Chapter 18 – Part II

2. Two parallel flat plates that store CHARGE is called a capacitor. The plates have dimensions >>d, the plate separation. The electric field in a parallel plate capacitor is normal to the plates. The “fringing fields” can be neglected. Actually ANY physical object that can store charge is a capacitor.

3. V A Capacitor Stores CHARGE Apply a Potential Difference V And a charge Q is found on the plates Q

4. Unit of Capacitance = F

5. Thin Film Structure

6. Variable Capacitor and 1940’s Radio

7. One Way to Charge: • Start with two isolated uncharged plates. • Take electrons and move them from the + to the – plate through the region between. • As the charge builds up, an electric field forms between the plates. • You therefore have to do work against the field as you continue to move charge from one plate to another. The capacitor therefore stores energy!

8. The two metal objects in the figure have net charges of +79 pC and -79 pC, which result in a 10 V potential difference between them. (a) What is the capacitance of the system? [7.9] pF(b) If the charges are changed to +222 pC and -222 pC, what does the capacitance become? [7.9] pF(c) What does the potential difference become?[28.1] V

9. TWO Types of Connections SERIES PARALLEL

10. V CEquivalent=CE Parallel Connection

11. q -q q -q V C1 C2 Series Connection The charge on each capacitor is the same !

12. q -q q -q V C1 C2 Series Connection Continued

13. More General

14. Example C1=12.0 uf C2= 5.3 uf C3= 4.5 ud C1 C2 series (12+5.3)pf (12+5.3)pf V C3

15. A Thunker Find the equivalent capacitance between points a and b in the combination of capacitors shown in the figure. V(ab) same across each

17. A capacitor is charged by being connected to a battery and is then disconnected from the battery. The plates are then pulled apart a little. How does each of the following quantities change as all this goes on? (a) the electric field between the plates, (b) the charge on the plates, (c) the potential difference across the plates, (d) the total energy stored in the capacitor.

18. Stored Energy • Charge the Capacitor by moving Dq charge from + to – side. • Work = Dq Ed= Dq(V/d)d=DqV

19. DW=DqV=Sum of strips DV

20. Energy Density

21. What's Happening? DIELECTRIC

22. Stick a new material between the plates.

24. We can measure the C of a capacitor (later) C0 = Vacuum or air Value C = With dielectric in place C=kC0

26. Dielectric Breakdown!

28. Messing with Capacitors The battery means that the potential difference across the capacitor remains constant. For this case, we insert the dielectric but hold the voltage constant, q=CV since C  kC0 qk kC0V THE EXTRA CHARGE COMES FROM THE BATTERY! + V - + - + - + V - Remember – We hold V constant with the battery.

29. Another Case • We charge the capacitor to a voltage V0. • We disconnect the battery. • We slip a dielectric in between the two plates. • We look at the voltage across the capacitor to see what happens.

30. No Battery q0 =C0Vo When the dielectric is inserted, no charge is added so the charge must be the same. q0 + - + - V0 V qk

31. Another Way to Think About This • There is an original charge q on the capacitor. • If you slide the dielectric into the capacitor, you are adding no additional STORED charge. Just moving some charge around in the dielectric material. • If you short the capacitors with your fingers, only the original charge on the capacitor can burn your fingers to a crisp! • The charge in q=CV must therefore be the free charge on the metal plates of the capacitor.

32. A little sheet from the past.. -q’ +q’ - - - +++ -q q 0 2xEsheet 0

33. Some more sheet…