1. PH 203 Professor Lee Carkner Lecture 8
Capacitors
PH 203
Professor Lee Carkner
Lecture 8

2. Circuits A potential difference produces work
Moving charges can do things
e.g. light lightbulbs, induce movement in motors, move information etc.
We will examine the key components of electric circuits
Up first, the capacitor

3. Battery
The source of potential difference in a direct current (DC) circuit is a battery
If we connect one end of a wire to the positive terminal and the other end to the negative terminal, the electrons in the wire will move
often called a voltage
it just provides the potential to move the electrons that are already in the wire + -

4. Capacitance
Not to be confused with a battery which doesn’t store charge but rather makes charge move
This intrinsic property is called capacitance and is represented by C

5. Capacitance Defined
The amount of charge stored by a capacitor is just:
Q = C DV
C = Q/DV
The units of capacitance are farads (F)
1 F = 1 C/V
Typical capacitances are much less than a farad:
e.g. microfarad = mF = 1 X 10-6 F

6. Simple Circuit Battery (DV) connected to capacitor (C)
The capacitor experiences potential difference of DV and has stored charge of Q = C DV - + Q + - DV

7. Connections
When connecting things to a battery the arrangement can be in series or parallel
Series
with potential source connected to each end of line
Parallel
each element has the same potential 1 2 3 DV
V1 + V2 + V3 = DV 1 2 3 DV
V1 = V2 = V3 = DV

8. Junctions How can you tell if capacitors are in series or parallel?
A place where the current has to split
If you can’t draw a path from one capacitor to the other without hitting a junction, they are in parallel C1 C2 + - DV

9. Capacitors in Parallel
Potential difference across each is the same (DV)
Total stored charge is the sum (Q = Q1 + Q2)
But:
Q = CeqDV
Ceq = C1 + C2 C1 C2 + - DV

10. Capacitors in Series Charge stored by each is the same (Q)
Equivalent capacitor also has a charge of Q
Since DV = Q/C:
The equivalent capacitance is:
1/Ceq = 1/C1 + 1/C2 C1 C2 - - + + + - DV

11. Capacitors in Circuits
Remember series and parallel rules extend to any number of capacitors
Keep simplifying until you find the equivalent capacitance for the whole circuit

12. Capacitor Info A capacitor generally consists of two metal surfaces
Maintaining a potential difference across the plates causes the charge to separate
Electrons are repelled from the negative terminal and end up on one plate
Electrons are attracted to the positive terminal and are lost by the second plate
Plates can’t touch or charge would jump across

13. Finding Capacitance We will enclose one plate with a Gaussian surface
But for the special case of our capacitors:
The plate has a charge q
Thus
EA = q/e0
q = e0EA
q = CV = e0EA
C = e0EA/V

14. Parallel Plate
What is the relation between E and V for two parallel plates?
But E is constant between the plates and ∫ ds = d, the distance between the plates
C = e0A/d

15. Permittivity e0 = Cd/A So we can write: e0 = 8.85 X 10-12 F/m
and think of e0 as being the “capacitor constant”

16. Using Capacitors Capacitors store energy
Generally only for short periods of time
Useful when you need a quick burst of energy
Defibrillator, flash
Since capacitance depends on d, can also use capacitance to measure separation

17. Next Time
Read
Problems: Ch 25, P: 6, 9, 14, 26, 36

18. The potential energy of two like charges a distance a apart is x
The potential energy of two like charges a distance a apart is x. The potential energy of two like charges a distance 2a apart is y. What is the total potential energy of the system? A x y
4x-4y
4x-2y

19. If the other three charges were already fixed in place, how much work would you have to do to bring charge A into place from infinity? A
You would have to do positive work
The work would equal zero
You would do “negative work”, the charge would move in on its own
The work would first be positive, then negative
You cannot tell without knowing the value of “a”