1. Chapter 24 Capacitance, dielectrics and electric energy storage
Basic circuit devices
Resistors
Capacitors
Inductors
Power supply (Battery, Generator)
Use our knowledge of electric fields, potentials, and energy to describe how capacitors work.

2. Parallel Plate Capacitor

3. Active Figure 26.4 (b) When the switch is closed, the battery establishes an electric field in the wire that causes electrons to move from the left plate into the wire and into the right plate from the wire. As a result, a separation of charge exists on the plates, which represents an increase in electric potential energy of the system of the circuit. This energy in the system has been transformed from chemical energy in the battery.
Fig 26-4b, p.800

4. Active Figure 26.4
(SLIDESHOW MODE ONLY)

5. Potential difference and electric fields in a uniform electric field+Q -Q b d a

6. Potential difference and electric fields in a uniform electric field+Q -Q b d a
The constant of proportionality is called “capacitance.”
For a parallel plate capacitor, the capacitance is:

7. Factors affecting capacitance
Size of the capacitor (A, d)
Geometric arrangement
Plates
Cylinders
Material between conductors
Air
Paper
Wax

8. Units of capacitance
A Farad is a lot of capacitance. Typical capacitors are
“micro, nano, pico-Farad

9. Capacitance – Isolated Sphere
Assume a spherical charged conductor
Assume V = 0 at infinity
Note, this is independent of the charge and the potential difference

10. Cylindrical capacitorb
+Q on center conducting cylinder
-Q on outer conducting cylinder

11. Capacitance of a cylindrical capacitorb

12. Example
How strong is the electric field between the plates of a 0.80 mF air gap capacitor if they are 2.0 mm apart and each has a charge of 72 mC?

13. Capacitors in Parallelb

14. Capacitors in Series a b

15. Capacitor circuit example
3 V
What single capacitor can replace the four shown here?
How much charge can the system hold?
How much charge is on one of the 2 mF capacitors?

16. Energy Storage in Capacitors
(Like problem 23-50)
Change in potential energy
while charging capacitor
Parallel Plates
Concentric Cylinders
In General

17. Alternate Energy Expressions

18. Energy Density Energy per unit volume:
Consider a Parallel Plate Capacitor:

19. Dielectrics k is the Dielectric Constant - - + + - + + + - - + -
A dielectric is a nonconducting material that, when placed between the plates of a capacitor, increases the capacitance
Materials with Dipoles that can align with an external electric Field. Dielectrics include rubber, plastic, and waxed paper - -
+ + -
+ + + - - + -
k is the Dielectric Constant
Measure of the degree of dipole alignment in the material

20. Dielectrics

21. Example values of dielectric constant
“Dielectric strength” is the
maximum field in the
dielectric before breakdown.
(a spark or flow of charge)

22. Effect of a dielectric on capacitance
Potential difference with a dielectric
is less than the potential difference
across free space
Results in a higher capacitance.
Allows more charge to be stored before breakdown voltage.

23. Effect of the dielectric constant
Parallel Plate Capacitor
Material permittivity measures
degree to which the material
permits induced dipoles
to align with an external field
Example modifications
using permittivity

24. Example – Parallel Plate Capacitor+Q
What is new capacitance? d A -Q

25. Dipoles
The combination of two equal charges of opposite sign, +Q and –Q, separated by a distance l -Q +Q

26. Dipoles in a Uniform Electric Field+Q -Q

27. Work Rotating a Dipole in an Uniform Electric Field+Q -Q

28. Example P26.9
When a potential difference of 150 V is applied to the plates of a parallel-plate capacitor, the plates carry a surface charge density of 30.0 nC/cm2. What is the spacing between the plates?

29. Example P26.21
Four capacitors are connected as shown in Figure P26.21.
Find the equivalent capacitance between points a and b.
Calculate the charge on each capacitor if ΔVab = 15.0 V.

30. Example P26.27
Find the equivalent capacitance between points a and b for the group of capacitors connected as shown in Figure P Take C1 = 5.00 μF, C2 = 10.0 μF, and C3 = 2.00 μF.

31. Example P26.35
A parallel-plate capacitor is charged and then disconnected from a battery. By what fraction does the stored energy change (increase or decrease) when the plate separation is doubled?
. Therefore, the ,

32. Example P26.43
Determine (a) the capacitance and (b) the maximum potential difference that can be applied to a Teflon-filled parallel-plate capacitor having a plate area of 1.75 cm2 and plate separation of mm.

33. Example P26.59
A parallel-plate capacitor is constructed using a dielectric material whose dielectric constant is 3.00 and whose dielectric strength is 2.00 × 108 V/m. The desired capacitance is μF, and the capacitor must withstand a maximum potential difference of V. Find the minimum area of the capacitor plates.