1. Physics 1161: Pre-Lecture 05
Capacitors
Sections 20-5 – 20-6

2. Comparison: Electric Potential Energy vs. Electric Potentialq A B
DVAB : the difference in electric potential between points B and A
DUAB : the change in electric potential energy of a charge q when moved from A to B
DUAB = q DVAB

3. Electric Potential: Summary
E field lines point from higher to lower potential
For positive charges, going from higher to lower potential is “downhill”
For a battery, the (+) terminal is at a higher potential than the (–) terminal
Positive charges tend to go “downhill”, from + to -
Negative charges go in the opposite direction, from
- to +
DUAB = q DVAB

4. Important Special Case Uniform Electric Field+ -
Two large parallel conducting plates of area A
+Q on one plate
-Q on other plate
Then E is
uniform between the two plates: E=4kQ/A
zero everywhere else
This result is independent of plate separation
i.e. it doesn’t matter how far away the plates are from each other
This is called a parallel plate capacitor

5. Parallel Plate Capacitor Potential Difference
Charge Q on plates
Charge 2Q on plates
V = VA – VB = +E0 d
V = VA – VB = +2E0d
E=2E0
E=E0 + - + - + - A B A B d d
Potential difference is proportional to charge: Double Q  Double V
E0 = 4πkQ/A

6. Capacitance The ability to store separated charge Definition:
Units: Farad (F) – named in honor of Michael Faraday
1 F = 1C/V
From Faraday’s notebook

7. Capacitor
Any pair of conductors separated by a small distance. (e.g. two metal plates)
Capacitor stores separated charge
Positive Q on one conductor, negative Q on other
Net charge is zero
Q = CV E d + -
Stores Energy
U = (½) Q V

8. Capacitance of Parallel Plate Capacitor
V = Ed AND E = Q/(e0A)
(Between two large plates)
So: V = Qd/ /(e0A)
Remember: CQ/V
So:
Equation based on geometry of capacitor V + E - A A d
If there is adielectric (κ>1) between plates C = κ C0
e0= 8.85x10-12 C2/Nm2

9. Dielectric
Placing a dielectric between the plates increases the capacitance.
C = k C0
Dielectric constant (k > 1)
Capacitance without dielectric
Capacitance with dielectric

10. Dielectrics Material Constant Vacuum 1 Germanium 16 Polyvinyl chloride
3.18
Strontium titanate
310
Mica
3 - 6
Water
80.4
Mylar
3.1
Glycerin
42.5
Neoprene
6.70
Benzene
2.284
Plexiglass
3.40
Glass
5 – 10
Polyethylene
2.25
Air (1 atm)
Liquid ammonia
(-78oC) 25
Titanium dioxide (rutile)
173 perp
86 para

11. Voltage in Circuits Elements are connected by wires.
Any connected region of wire has the same potential.
The potential difference across an element is the element’s “voltage.”
Vwire 1= 0 V
Vwire 2= 5 V
Vwire 3= 12 V
Vwire 4= 15 V C1 C2 C3
VC1= _____ V
VC2= _____ V
VC3= _____ V

12. Voltage in Circuits Elements are connected by wires.
Any connected region of wire has the same potential.
The potential difference across an element is the element’s “voltage.”
Vwire 1= 0 V
Vwire 2= 5 V
Vwire 3= 12 V
Vwire 4= 15 V C1 C2 C3
VC1= 5 V
VC2= 7 V
VC3= 3 V

13. Capacitors in Parallel
Both ends connected together by wire
Share Charge: Qeq = Q1 + Q2
Total Cap: Ceq = (Q1 + Q2)/V = C1 + C2
Same voltage: V1 = V2
= Veq
Ceq C1 C2

14. Capacitors in Parallel
Both ends connected together by wire
Share Charge: Qeq = Q1+ Q2
Total Cap: Ceq = (Q1+ Q2)/V = C1+ C2
Same voltage: V1 = V2
= Veq
15 V
15 V
15 V
Ceq C1 C2
10 V
10 V
10 V

15. Capacitors in Series Connected end-to-end with NO other exits
Same Charge: Q1 = Q2 = Qeq
Share Voltage: V1+V2=Veq + + +Q -Q + +Q + +
Ceq C1 + - + - + + +Q -Q + + + C2 -Q - - - + + + + +

16. Electromotive Force + Battery - Maintains potential difference V
Not constant power
Not constant current
Does NOT produce or supply charges, just “pushes” them. -