1. Capacitance
October 6, 2012

2. Maximum Charge on a Conductor
A battery establishes a difference of potential that can pump electrons e- from a ground (earth) to a conductor
Earth
Battery
Conductor - e-
There is a limit to the amount of charge that a conductor can hold without leaking to the air. There is a certain capacity for holding charge.

3. Capacitance
The capacitance C of a conductor is defined as the ratio of the charge Q on the conductor to the potential V produced.
Earth
Battery
Conductor - e-
Q, V
Capacitance:

4. Capacitance in Farads
One farad (F) is the capacitance C of a conductor that holds one coulomb of charge for each volt of potential.
Example: When 40 μC of charge are placed on a conductor, the potential is 8 V. What is the capacitance?

5. Capacitance of Spherical Conductor
At surface of sphere: +Q r
E and V at surface.
Capacitance, C

6. Example 1: What is the capacitance of a metal sphere of radius 8 cm?
r = 0.08 m
Capacitance, C +Q r
Note: The capacitance depends only on physical para- meters (the radius r) and is not determined by either charge or potential. This is true for all capacitors.

7. Example 1 (Cont.): What charge Q is needed to give a potential of 400 V?
r = 0.08 m
Capacitance, C +Q r
Note: The farad (F) and the coulomb (C) are extremely large units for static electricity. The SI prefixes micro μ, nano n, and pico p are often used.

8. Parallel Plate Capacitanced
Area A +Q -Q

9. Example 3. The plates of a parallel plate capacitor have an area of 0
Example 3. The plates of a parallel plate capacitor have an area of 0.4 m2 and are 3 mm apart in air. What is the capacitance?
3 mm d A
0.4 m2

10. Dielectric Materials
Most capacitors have a dielectric material between their plates to provide greater dielectric strength and less probability for electrical discharge. + -
Air Co Eo + -
Dielectric
reduced E + -
C > Co
E < Eo
The separation of dielectric charge allows more charge to be placed on the plates—greater capacitance C > Co.

11. Dielectric constant: K = 1 for Air
The dielectric constant K for a material is the ratio of the capacitance C with this material as compared with the capacitance Co in a vacuum.
Dielectric constant: K = 1 for Air

12. Energy of Charged Capacitor
The potential energy U of a charged capacitor is equal to the work (qV) required to charge the capacitor.
If we consider the average potential difference from 0 to Vf to be V/2:
Work = Q(V/2) = ½QV

13. Only, great theory but how does one use it?

14. Capacitors in Circuits
Let’s start with the most basic circuit.
Typically, we are solving for the charge on the capacitor and potential difference across the plates
At times, we will also be asked about the stored energy.

15. Series Circuits The key here is - no choice
Let’s find Q and ∆V for each capacitor.

16. Series Circuits The key here is - no choice
Let’s find Q and ∆V for each capacitor.

17. Parallel Circuits The key here is - choice
Let’s find Q and ∆V for each capacitor.

18. Complex Circuits
The key here is - make it look either like series or parallel
Let’s find Q and ∆V for each capacitor.

19. Complex Circuits
The key here is - make it look either like series or parallel
Let’s find Q and ∆V for each capacitor.