1. Capacitance
PHY 2049 Chapter 25

2. Chapter Capacitance
In this chapter we will cover the following topics:
-Capacitance C of a system of two isolated conductors Calculation of the capacitance for some simple geometries.
-Methods of connecting capacitors (in series , in parallel) Equivalent capacitance Energy stored in a capacitor Behavior of an insulator (a.k.a. dielectric) when placed in the electric field created in the space between the plates of a capacitor.
-Gauss’ law in the presence of dielectrics.
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3. Capacitors

4. Capacitor Composed of two metal plates. Each plate is charged
one positive
one negative
Stores energy
SYMBOL

5. A simple Capacitor
TWO PLATES
WIRES
Battery

6. INSIDE THE DEVICE

7. What is STORED in the capacitor?
An Electric Field
Energy
Charge
All three
None of these

8. Two Charged Plates (Neglect Fringing Fields)
Air or Vacuum
Area A
- Q Q E
V=Potential Difference
Symbol
ADDED CHARGE

9. Where is the charge? + + + + + - AREA=A s=Q/A + - Q +Q d Air or Vacuum
V=Potential Difference

10. The capacitor therefore stores energy!
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!

11. Capacitor
Demo

12. More on Capacitors - Q +Q d Air or Vacuum Area A E
V=Potential Difference
Gaussian
Surface
Same result from other plate!

13. DEFINITION - Capacity
The Potential Difference is APPLIED by a battery or a circuit.
The charge q on the capacitor is found to be proportional to the applied voltage.
The proportionality constant is C and is referred to as the CAPACITANCE of the device.

14. UNITS
A capacitor which acquires a charge of 1 coulomb on each plate with the application of one volt is defined to have a capacitance of 1 FARAD
One Farad is one Coulomb/Volt

15. Continuing…
The capacitance of a parallel plate capacitor depends only on the Area and separation between the plates.
C is dependent only on the geometry of the device!

16. After the switch is closed, how much charge passed through the capacitor?V
C/V
V/C CV
C+V

17. S P N
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18. Units of e0
pico

19. Simple Capacitor Circuits
Batteries
Apply potential differences
Capacitors
Wires
Wires are METALS.
Continuous strands of wire are all at the same potential.
Separate strands of wire connected to circuit elements may be at DIFFERENT potentials.

20. NOTE
Work to move a charge from one side of a capacitor to the other is = qEd.
Work to move a charge from one side of a capacitor to the other is qV
Thus qV = qEd
E=V/d As before

21. TWO Types of Connections
SERIES
PARALLEL

22. Parallel Connection V
CEquivalent=CE

23. Series Connection The charge on each capacitor is the same ! q -q q -qV
C C2
q q q q
The charge on each
capacitor is the same !

24. Series Connection ContinuedV
C C2
q q q q

25. More General

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

27. More on the Big C +q -q
E=e0A/d
+dq
We move a charge dq from the (-) plate to the (+) one.
The (-) plate becomes more (-)
The (+) plate becomes more (+).
dW=Fd=dq x E x d

28. So….

29. Not All Capacitors are Created Equal
Parallel Plate
Cylindrical
Spherical

30. Spherical Capacitor

31. Calculate Potential Difference V
(-) sign because E and ds are in OPPOSITE directions.

32. Continuing…
Lost (-) sign due to switch of limits.