Capacitance

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Chapter 25

• Capacitance

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Real Parallel Plates
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Chapter 25 CAPACITANCE

• Depends on geometry and materials
• Units are Farad Coulomb/Volt (F C/V)
• microfarad (mF 10-6 F) and
• picofarad (pF 10-12 F)
• Examples
• Parallel Plates
• Coaxial Conductors (cylindrical symmetry)
• Capacitance the ratio of the charge to
• the electric potential difference

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Circuits and Capacitors
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Parallel Plate Capacitor
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Coaxial Capacitor cylindrical symmetry !!!
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Calculating Capacitance

• Use Gauss LAW
• Use relationship btwn and

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Parallel Plates
Assume A1/2 gtgtd, then E is constant
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Coaxial Conductors
Determine the potential difference
Solve for the ratio of Q to V
Consider a Gaussian Surface between the inner
and outer conductorthen
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Wiring Schemes

• Series
• the elements are connected end to end
• all elements are encountered as one follows the
  wires
• Parallel
• the elements are connected with left ends
  together and right ends together
• the elements may be encountered as one follows
  alternate paths

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Equivalent Capacitance

• Series

The charge on each capacitor is the same as the
charge on the equivalent capacitance
Potential differences must add to the total of
the battery
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Equivalent Capacitance

• Parallel

The charge on each capacitor mustadd up to the
total charge on theequivalent capacitance
The potential differenceeach capacitor must
matchthe battery potential difference
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Equivalent Capacitance
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Equivalent Capacitance

• Example

What is the equivalent capacitance between a and
b?
C1 and 6 mF in parallel
C2 and 20 mF in series
15 mF and 3 mf in series
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Example 25-2
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Energy Stored by a Capacitor
The work done by an outsideagent to move a small
amountof charge from one plate of a capacitor
to the other plate is
To charge the entire capacitor
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Energy Stored by a Parallel Plate Capacitor
Ad is the volume of the capacitor
u energy/volume or energy density
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Problems

• What is the energy stored in a 1.0 mF capacitor
  charged to 500 V?
• What is the energy density if the area of the
  capacitor is 0.1 m2 and the plates are separated
  by 0.02 mm?
• What is the electric field strength between the
  plates of the capacitor?

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Dielectrics (Atomic View)
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Dielectrics (Macroscopic View)
The dielectric (k gt 1)increases the capacitance
to a larger value than the original value since
C gt Co
Eo
Start with a charge Q which wont change
e keo
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Example 25-7
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Work done while inserting the dielectric
There is a net force to the right, the field does
the work
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Schematics of Capacitor Design
c is a electrolytic capacitor which must be wired
accordingto its marked polarity
What is the dielectric strength?