Monday, 18 July 2016
Outline
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Capacitors
–
In parallel and series
–
Energy stored
–
Dielectrics
A. The potential difference
would increase.
B. The potential difference
would decrease.
C. The potential difference
would stay the same.
+
+
+
+
+
+
+
V
E
–
–
–
–
–
–
–
0
NEXUS/Physics Clicker
Questions
What would happen to the voltage
if you first disconnected the battery
and then pulled the plates
further apart?
A. The charge on each plate
would increase.
B. The charge on each plate
would decrease.
C. The charge on each plate
would stay the same.
+
+
+
+
+
+
V
–
–
–
–
–
–
–
0
NEXUS/Physics Clicker
Questions
What would happen to the charge on the plates
if you stayed connected to the battery
and then pulled the plates
E
further apart?
+
Capacitance and Capacitors
 The ratio of the charge Q to the potential difference VC is called the capacitance
C:
 Capacitance is a purely geometric property of two electrodes because it depends
only on their surface area and spacing.
 The SI unit of capacitance is the farad:
Slide 29-65
Three capacitors 1, 2, 3 are connected to identical batteries so they
each have the same ΔV.
Their plate areas and separations are as follows:
A2 = 2 A1 = 2 A3; d1 = d2 = 2d3.
A.
B.
C.
D.
E.
F.
G.
Q2 = Q 3 > Q 1
Q3 > Q 1 = Q 2
Q2 > Q 1 > Q 3
Q2 > Q 1 = Q 3
Q1 = Q 2 > Q 3
Q1 = Q 2 = Q 3
Other
NEXUS/Physics Clicker
Questions
How do the net charges on them rank?
Three capacitors 1, 2, 3 are connected to identical batteries so they
each have the same ΔV.
Their plate areas and separations are as follows:
A2 = 2 A1 = 2 A3; d1 = d2 = 2d3.
A.
B.
C.
D.
E.
F.
G.
Q2 = Q 3 > Q 1
Q3 > Q 1 = Q 2
Q2 > Q 1 > Q 3
Q2 > Q 1 = Q 3
Q1 = Q 2 > Q 3
Q1 = Q 2 = Q 3
Other
NEXUS/Physics Clicker
Questions
How do the positive charges on their top plate rank?
Capacitors in parallel.
At potential V:
+Q1
+V
+Q2
C1
0
C2
-Q1
-Q2
Capacitors Combined in Parallel
If capacitors C1, C2, C3, … are in parallel, their
equivalent capacitance is:
Slide 29-73
Capacitor in series.
Different potentials:
+V
C1
0
C2
Capacitor in series.
Different potentials:
+Q
-Q
+V
0
C2
C1
+Q
-Q
V1
V2
Capacitors in series.
From battery perspective:
+V
+Q
0
-Q
Ctotal
Q
Q
Q
 V  V1  V2 

Ctotal
C1
C2
Capacitors in series.
From battery perspective:
+V
+Q
0
-Q
Ctotal
Q
Q
Q
 V  V1  V2 

Ctotal
C1
C2
Capacitors Combined in Series
If capacitors C1, C2, C3, …
are in series, their
equivalent capacitance is:
Slide 29-77
Example: find the equivalent
capacitance
Example: What is the voltage
between a and b?
Three capacitors, each with capacitance C, are in
the following circuit:
The equivalent capacitance is…
C
A. 3C
B. C
C. 3C/2
D. 2C/3
C
C
Use potential, too.
C3
C1
C2
V
V1
V2
Rank in order, from largest to smallest, the equivalent capacitance
(Ceq)a to (Ceq)d of circuits a to d.
A. (Ceq)d > (Ceq)b > (Ceq)a > (Ceq)c
B. (Ceq)d > (Ceq)b = (Ceq)c > (Ceq)a
C. (Ceq)a > (Ceq)b = (Ceq)c > (Ceq)d
D. (Ceq)b > (Ceq)a = (Ceq)d > (Ceq)c
E. (Ceq)c > (Ceq)a = (Ceq)d > (Ceq)b
Capacitor at constant charge
We move two capacitor plates apart, while the
capacitor is disconnected from the battery. When
the plates are further apart, the energy of the
capacitor
A) Has increased
B) Stayed the same
C) Has decreased
Energy of a capacitor
Move small amount of charge
V
+q
0
-q
dq
Capacitance and Capacitors
Capacitor at constant voltage
We move two capacitor plates apart, while the
capacitor is connected to a 9V battery. When the
plates are further apart, the energy of the
capacitor
A) Has increased
B) Stayed the same
C) Has decreased
QuickCheck 29.13
A capacitor charged to 1.5 V stores 2.0 mJ of energy. If the capacitor
is charged to 3.0 V, it will store
A.
B.
C.
D.
E.
1.0 mJ.
2.0 mJ.
4.0 mJ.
6.0 mJ.
8.0 mJ.
Slide 29-83
The Energy Stored in a Capacitor
 A capacitor can be charged slowly but then
can release the energy very quickly.
 An important medical application of
capacitors is the defibrillator.


A heart attack or a serious injury can cause the heart to enter a state known as fibrillation in which the
heart muscles twitch randomly and cannot pump blood.
A strong electric shock through the chest completely stops the heart, giving the cells that control the
heart’s rhythm a chance to restore the proper heartbeat.
Slide 29-82
The energy stored in the electric field
The Energy in the Electric Field
The energy density of an electric field, such as the one inside a
capacitor, is:
The energy density has
units J/m3.
Slide 29-87
Dielectrics
Insulator in an E-field: Induced
polarization
Dielectrics
Dielectrics
Dielectrics
Increases capacitance:
V
0
+Q
- - - - - - - - + + + + + + +
(Q  Qind ) d
V 
0 A
-Q
Q
C
V
-Qind
+Qind
Dielectrics
Increases capacitance:
V
0
+Q
- - - - - - - - + + + + + + +
(Q  Qind ) d
V 
0 A
-Q
Q
C
V
-Qind
+Qind
Dielectrics
 We define the dielectric constant:
 The dielectric constant, like density or specific heat, is a
property of a material.
 Easily polarized materials have larger dielectric constants
than materials not easily polarized.
 Vacuum has  = 1 exactly.
 Filling a capacitor with a dielectric increases the
capacitance by a factor equal to the dielectric
constant:
Dielectrics
Slide 29-95
Dielectrics
 The production of a practical capacitor, as shown, almost
always involves the use of a solid or liquid dielectric.
 All materials have a maximum electric
field they can sustain without breakdown
—the production of a spark.
 The breakdown electric field
of air is about 3  106 V/m.
 A material’s maximum
sustainable electric field is
called its dielectric
strength.
Slide 29-94
Recall: St. Elmo’s light
http://www.youtube.com/
watch?v=1W9j6-jERpE&fea
ture=related
Other examples...
A.The stored electrical energy increases.
B.The stored electrical energy remains the same.
C.The stored electrical energy decreases.
NEXUS/Physics Clicker
Questions
Suppose the capacitor is connected to the
battery. The plates remain connected and an
insulating slab of dielectric constant � ( > 1) is
slid between the plates. What happens to the
electrical energy stored in the capacitor as a
result of inserting the insulating slab?