Transcript 8capacitors1s

Capacitors
PH 203
Professor Lee Carkner
Lecture 8
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
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
+
-
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
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
Simple Circuit
C
-
+
Battery (DV) connected to
capacitor (C)

Q
+
DV
The capacitor experiences
potential difference of DV
and has stored charge of Q
= C DV
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
1
2
3
DV
V1 + V2 + V3 = DV
1
2

3
 each element has the same potential
DV
V1 = V2 = V3 = DV
Junctions
How can you tell if capacitors
are in series or parallel?

C1
C2
+
DV
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
Capacitors in Parallel
Potential difference across
each is the same (DV)
Total stored charge is the
sum (Q = Q1 + Q2)
But:
C1
C2


Q = CeqDV
+
DV

Ceq = C1 + C2
Capacitors in Series
C1
+
- +
C2
-
Charge stored by each is the
same (Q)
Equivalent capacitor also has
a charge of Q

Since DV = Q/C:
+
DV

The equivalent capacitance is:
1/Ceq = 1/C1 + 1/C2
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
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
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
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
Capacitor Properties
What kinds of capacitors can hold a lot of
charge?

Very close together (small d)

e0 = Cd/A

So we can write:
e0 = 8.85 X 10-12 F/m
and think of e0 as being the “capacitor constant”
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

Next Time
Read 25.5-25.8
Problems: Ch 25, P: 6, 9, 14, 26, 36
If the potential at the center of the square from
charge A is 1, what is the net potential from
all the charges at the center of the square?
A)
B)
C)
D)
E)
0
1
√2
4
You cannot tell
without knowing the
value of “a”
A
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
B) The work would equal
zero
C) You would do “negative
work”, the charge would
move in on its own
D) The work would first be
positive, then negative
E) You cannot tell without
knowing the value of “a”
A