Chapter 24 Capacitance, dielectrics and electric energy storage

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Chapter 24Capacitance, dielectrics and electric
energy storage

• Basic circuit devices
• Resistors
• Capacitors
• Inductors
• Power supply (Battery, Generator)
• Use our knowledge of electric fields, potentials,
  and energy to describe how capacitors work.

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Parallel Plate Capacitor
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Fig 26-4b, p.800
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Active Figure 26.4
(SLIDESHOW MODE ONLY)
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Potential difference and electric fields in a
uniform electric field
b
d
a
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Potential difference and electric fields in a
uniform electric field
b
d
a
The constant of proportionality is called
capacitance. For a parallel plate capacitor,
the capacitance is
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Factors affecting capacitance

• Size of the capacitor (A, d)
• Geometric arrangement
• Plates
• Cylinders
• Material between conductors
• Air
• Paper
• Wax

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Units of capacitance
A Farad is a lot of capacitance. Typical
capacitors are micro, nano, pico-Farad
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Capacitance Isolated Sphere

• Assume a spherical charged conductor
• Assume V 0 at infinity
• Note, this is independent of the charge and the
  potential difference

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Cylindrical capacitor
L
a
b
Q on center conducting cylinder
-Q on outer conducting cylinder
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Capacitance of a cylindrical capacitor
L
a
L
b
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Example

• How strong is the electric field between the
  plates of a 0.80 mF air gap capacitor if they are
  2.0 mm apart and each has a charge of 72 mC?

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Capacitors in Parallel
a
b
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Capacitors in Series
a
b
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Capacitor circuit example
3 V
What single capacitor can replace the four shown
here? How much charge can the system hold? How
much charge is on one of the 2 mF capacitors?
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Energy Storage in Capacitors
(Like problem 23-50)
Change in potential energy while charging
capacitor
Parallel Plates
Concentric Cylinders
In General
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Alternate Energy Expressions
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Energy Density
Energy per unit volume
Consider a Parallel Plate Capacitor
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Dielectrics

• A dielectric is a nonconducting material that,
  when placed between the plates of a capacitor,
  increases the capacitance
• Materials with Dipoles that can align with an
  external electric Field. Dielectrics include
  rubber, plastic, and waxed paper

-
-

-


-

-
-
k is the Dielectric Constant
Measure of the degree of dipole alignment in the
material
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Dielectrics
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Example values of dielectric constant
Dielectric strength is the maximum field in the
dielectric before breakdown. (a spark or flow of
charge)
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Effect of a dielectric on capacitance
Potential difference with a dielectric is less
than the potential difference across free space
Results in a higher capacitance.
Allows more charge to be stored before breakdown
voltage.
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Effect of the dielectric constant
Parallel Plate Capacitor
Material permittivity measures degree to which
the material permits induced dipoles to align
with an external field
Example modifications using permittivity
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Example Parallel Plate Capacitor
Q
d
A
-Q
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Dipoles
The combination of two equal charges of opposite
sign, Q and Q, separated by a distance l
-Q
Q
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Dipoles in a Uniform Electric Field
Q
-Q
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Work Rotating a Dipole in an Uniform Electric
Field
Q
-Q
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Example P26.9
When a potential difference of 150 V is applied
to the plates of a parallel-plate capacitor, the
plates carry a surface charge density of 30.0
nC/cm2. What is the spacing between the plates?
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Example P26.21

• Four capacitors are connected as shown in Figure
  P26.21.
• Find the equivalent capacitance between points a
  and b.
• Calculate the charge on each capacitor if ?Vab
  15.0 V.

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Example P26.27
Find the equivalent capacitance between points a
and b for the group of capacitors connected as
shown in Figure P26.27. Take C1 5.00 µF, C2
10.0 µF, and C3 2.00 µF.
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Example P26.35
A parallel-plate capacitor is charged and then
disconnected from a battery. By what fraction
does the stored energy change (increase or
decrease) when the plate separation is doubled?
. Therefore, the
,
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Example P26.43
Determine (a) the capacitance and (b) the maximum
potential difference that can be applied to a
Teflon-filled parallel-plate capacitor having a
plate area of 1.75 cm2 and plate separation of
0.040 0 mm.
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Example P26.59
A parallel-plate capacitor is constructed using a
dielectric material whose dielectric constant is
3.00 and whose dielectric strength is 2.00 108
V/m. The desired capacitance is 0.250 µF, and the
capacitor must withstand a maximum potential
difference of 4 000 V. Find the minimum area of
the capacitor plates.