Capacitance and Dielectrics

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Capacitance and Dielectrics
Any two conductors separated by an insulator
forms a Capacitor. Definition 1F 1 farad 1
C/V 1 coulomb /volt
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Capacitors and Capacitance (Chapter 24, Sec 1)
Coul/m2
Figure 24-2
Farads
1 ?F 1 x 10-6 Farads
1 pF 1 x 10-12 Farads
1 nF 1 x 10-9 Farads
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Useful Definitions and Relationships
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Practical Capacitors
Practical Values 100µF 1µF 0.01µF 100pF 1pF
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Some examples of flat, cylindrical, and spherical
capacitors

• See just how large a 1 F capacitor would be.
  Refer to Example 24.1.
• Refer to Example 24.2 to calculate properties of
  a parallel-plate capacitor.
• Follow Example 24.3 and Figure 24.5 to consider a
  spherical capacitor.
• Follow Example 24.3 and Figure 24.5 to consider a
  cylindrical capacitor.

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Capacitors in Series
All capacitors in series have the same charge Q
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Capacitors in Parallel
All Capacitors in Parallel have the same voltage V
Figure 24-7
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Capacitors in Series and Parallel - Example 24.6
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Energy Storage in Capacitors
Let q equal the changing charge increasing from 0
to Q as the changing voltage v is increasing from
0 to Vab. We will determine the energy stored in
the capacitor when the charge reaches Q and the
voltage reaches Vab. (q and v are the
intermediate charge and charging voltage
joules
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Example 24-7, Page 827 Text Transferring charge
and energy between capacitors
Calculate the initial charge Calculate the
initial stored energy Connect the
capacitors Calculate the resulting
voltage Calculate the charge distribution Calculat
e the energy change
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Capacitor Dielectrics Solve Three Problems

• Provides mechanical spacing between two large
  plates
• Increases the maximum possible potential between
  plates.
• For a given plate area the dielectric increases
  the capacitance.

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Dielectrics change the potential difference

• The potential between to parallel plates of a
  capacitor changes when the material between the
  plates changes. It does not matter if the plates
  are rolled into a tube as they are in Figure
  24.13 or if they are flat as shown in Figure
  24.14.

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What Happens with a Dielectric
A
A
C
V ? V0 (Q unchanged)
C0
Therefore C ? C0
Figure 24-12
(Definition of Dielectric Constant)
(24-12)
(24-13)
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Dielectric Constants
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Field lines as dielectrics change

• Moving from part (a) to part (b) of Figure 24.15
  shows the change induced by the dielectric.

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Induced Charge and Polarization
Inserting the dielectric increases permittivity
by K, decreases E by 1/K and decreases energy
density by 1/K The E field does work on the
dielectric as it is inserted. Removing the
dielectric the energy is returned to the field.
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Dielectrics (Chapter 24, Sec 4)
Induced Charge and Polarization
0
(24-15)
(24-18)
Therefore E ? E0
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Dielectric Breakdown
V Ed
Vmax Emax d
where Emax is the dielectric strength of the
dielectric in volts/meter.
For dry air Emax 3 x 106 V/m For Mylar,
K3.1, Emax 9.3 x 106 V/m
d
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Dielectric breakdown

• A very strong electrical field can exceed the
  strength of the dielectric to contain it. Table
  24.2 at the bottom of the page lists some limits.

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Electric Field Effect on Molecules
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Polarization and electric field lines
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