1. Capacitance Van de Graaff Generator Static Charge Generator

2. Capacitance Van de Graaff Generator Let’s say it generates negative charges… Capacitance is a measure of how much charge can be stored on a device.

3. Capacitance Van de Graaff Generator Mathematically, Capacitance is this way:

4. Capacitance Van de Graaff Generator Mathematically, Capacitance is this way:

5. Capacitance Van de Graaff Generator The greater the capacitance, the greater the amount of charge that can be stored.

6. Capacitance Van de Graaff Generator Let’s see how much charge is on the Van de Graaff generator. The voltage is rated as 400,000 V:

7. Capacitance Van de Graaff Generator What is the Capacitance of the Van de Graaff generator?

8. Capacitance Van de Graaff Generator What limits how many charges the dome can hold?

9. Capacitance Van de Graaff Generator What limits how many charges the dome can hold? Repulsion

10. Capacitance Van de Graaff Generator What limits how many charges the dome can hold? We can’t force any more electrons on the dome

11. Capacitance Van de Graaff Generator What limits how many charges the dome can hold? We can’t force any more electrons on the dome Solutions?

12. Capacitance A bigger dome is one solution. We can fit more electrons.

13. Capacitance But there’s another solution…

14. Capacitance Introduce another generator with the opposite charge What will that make the electrons do?

15. Capacitance As they move closer…

16. Capacitance The charges attract…

17. Capacitance And the charges become more concentrated…leaving room for?

18. Capacitance And the charges become more concentrated…leaving room for? MORE CHARGES!

19. Capacitance Capacitance is a measure of how much charge can be stored on a device. Our two van de Graaff generators constitute a what is called a “capacitor”: two oppositely charged conductors in close proximity.

20. Capacitance More typically, a capacitor is a “parallel plate” capacitor:

21. Capacitance More typically, a capacitor is a “parallel plate” capacitor: Let’s place insulating material between the plates

22. Capacitance More typically, a capacitor is a “parallel plate” capacitor: Press the plates closer together…

23. Capacitance More typically, a capacitor is a “parallel plate” capacitor: Press the plates closer together…

24. Capacitance More typically, a capacitor is a “parallel plate” capacitor: Then roll them up…

25. Capacitance How much energy is stored in a capacitor? We answer this by determining the WORK done in forcing charges on to the plate (against the repulsion of the voltage – increasing ‘q’) The incremental increase in Work is:

26. Capacitance Recall our definition of work (area under the curve) Charge, Q Voltage Charge, Q Voltage area

27. Capacitance Charge, Q Voltage area Area = ?

28. Capacitance Charge, Q Voltage area Area = ½ bh

29. Capacitance Charge, Q Voltage area Area = ½ bh = ½ VQ = ½ (Q/C)Q =

30. Capacitance Variations: Prove that 2 and 3 follow from 1

31. Capacitance Show that each of these formulas ends up in Joules

32. Capacitance 3. Find the energy stored in a capacitor were C = 12 x 10 -6 F and Q = 2.3 x 10 -3 C. 1. Find the energy stored in a capacitor where C = 50 F and V = 2.7 volts. 2. Find the energy stored in a capacitor where V = 5.00 volts and Q = 75.0 C.

33. Capacitance Answers: 1.182 J 2.188 J 3.0.22 J