9/16/13 1 ANNOUNCEMENT Chapter 24 Capacitance

```9/16/13
ANNOUNCEMENT
Chapter 24 Capacitance
*Exam 1: Monday September 23, 2013, 8 PM - 10 PM
*Location: Elliot Hall of Music
*Covers all readings, lectures, homework from Chapters 21
through 23.
*The exam will be multiple choice (15questions).
•  Capacitor is a device that stores electrostatic
potential energy.
•  A capacitor consists of 2 spatially separated
conductors which can be charged to +Q and -Q.
•  The capacitance is defined as the ratio of the charge
on one conductor of the capacitor to the potential
difference between the conductors.
Be sure to bring your student ID card and
your own one-page (two-side) crib sheet.
NOTE THAT FEW EQUATIONS WILL BE GIVEN – YOU ARE REMINDED
THAT IT IS YOUR RESPONSIBILITY TO CREATE WHATEVER TWO-SIDED
CRIB SHEET YOU WANT TO BRING TO THIS EXAM.
The equation sheet that will be given with the exam is
posted on the course homepage. Click on the link on the
left labeled “EquationSheet”
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Capacitance
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Parallel Plates
C3
A
d
b
C1
C2
1.  Wires have no electrical resistance.
2.  Components are ideal
3.  PHYS241 only deals with:
Cylindrical Capacitor
(a) Resistors, R
(b) Capacitors, C
(c) Inductors, L
(d) Batteries, Generators, switches &amp;
wires
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3
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1
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Equivalent Capacitors
Capacitors in Parallel
Capacitors connected in parallel can be replaced with an
equivalent capacitor that has the same total charge, Q and the
same applied potential V.
a
Q3
Q1
Q2
V
C3
C1
C2
a
a
V
b
Q1
C1
Q2
Q3
C2
C3
V
a
+Q
-Q
+Q
-Q
+Q
-Q
b
C
b
a
V
Q
b
+Q
C
-Q
b
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Capacitors in Series
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Example
Capacitors are in series when a potential difference that is
applied across their combination is the sum of the resulting
potential differences across each capacitor.
a
C3
b
a
C1
C2
a
b
C
+Q
-Q
V
+Q
-Q
+Q
-Q
b
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2
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Question
Dielectrics
•  Empirical observation: Inserting a non-conducting
material between the plates of a capacitor changes
the VALUE of the capacitance.
•  What is the equivalent capacitance, Ceq, of the
combination?
o
Ceq
C
C
•  Definition:The dielectric constant of a material is
the ratio of the capacitance when filled with the
dielectric to that without it.
C
o
(a) Ceq = (3/2)C
(b) Ceq = (2/3)C
(c) Ceq = 3C
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Demo: Dielectrics &amp; Capacitance
–
–
–
–
–
–
++
+
++
++
++
+
E0
V→
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Dielectric Strength
*The maximum value of the electric field that a
dielectric material can tolerate before breaking
down.
–
–
–
–
–
* It limits the voltage that can be applied to a
capacitor. The maximum voltage is called the
breakdown potential.
k
V
κ
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E→
E
κ
11
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3
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Effect of Dielectrics on the Electric Field
Dielectric Properties
real charge
k
dielectric strength
(kV/mm)
1.00054
2.1–2.5
5.6
5.4
2.55
80
130
310
3
10
14
10–100
24
?
material
air (1 atm)
paraffin
glass (Pyrex)
mica
polystyrene
H2O (200 C)
titania ceramic
strontium
titanate
+
+
+
+
+
+
+
8
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Dielectric Combinations
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-+
-
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Summary
k1
=
=
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-+
-+
-+
-+
-+
-+
real charge
k2
A/2
k1
A
A
d
•  Capacitors in parallel and in series
d/2
d/2
•  Electric response of dielectric materials
–  atomistic view polarized atoms
–  dielectric constant
k2
A/2
d
15
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4
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