Capacitors

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Capacitors
Phy 1161 PreLecture 06

• Todays lecture will cover Textbook Sections 20-5
  20-6

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ComparisonElectric Potential Energy vs.
Electric Potential

• DVAB the difference in electric potential
  between points B and A
• DUAB the change in electric potential energy of
  a charge q when moved from A to B
• DUAB q DVAB

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Electric Potential Summary

• E field lines point from higher to lower
  potential
• For positive charges, going from higher to lower
  potential is downhill
• For a battery, the () terminal is at a higher
  potential than the () terminal
• Positive charges tend to go downhill, from to
  -
• Negative charges go in the opposite direction,
  from
• - to

DUAB q DVAB
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Important Special CaseUniform Electric Field
- - - - -

• Two large parallel conducting plates of area A
• Q on one plate
• -Q on other plate
• Then E is
• uniform between the two plates E4?kQ/A
• zero everywhere else
• This result is independent of plate separation
• This is call a parallel plate capacitor

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Parallel Plate CapacitorPotential Difference
Charge Q on plates
Charge 2Q on plates
V VA VB E0 d
V VA VB 2E0d
E
EE0
- - - - -

- - - - -


- - - - -
A
B
d
d
Potential difference is proportional to charge
Double Q ? Double V E0 4pkQ/A
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Capacitance

• The ability to store separated charge
• Definition
• Units Farad (F) named in honor of Michael
  Faraday
• 1 F 1C/V

From Faradays notebook
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Capacitor

• Any pair of conductors separated by a small
  distance. (e.g. two metal plates)
• Capacitor stores separated charge
• Positive Q on one conductor, negative Q on other
• Net charge is zero

Q CV

• Stores Energy

U (½) Q V
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Capacitance of Parallel Plate Capacitor

• V Ed AND E Q/(e0A)
• (Between two large plates)
• So V Qd/ /(e0A)
• Remember C?Q/V
• So
• Equation based on geometry of capacitor

V
E

-
A
A
d
If there is adielectric (?gt1) between plates C
? C0
e0 8.85x10-12 C2/Nm2
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Dielectric

• Placing a dielectric between the plates increases
  the capacitance.
• C k C0

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Dielectrics
Material Constant Material Constant
Vacuum 1 Germanium 16
Polyvinyl chloride 3.18 Strontium titanate 310
Mica 3 - 6 Water 80.4
Mylar 3.1 Glycerin 42.5
Neoprene 6.70 Benzene 2.284
Plexiglass 3.40 Glass 5 10
Polyethylene 2.25 Air (1 atm) 1
Liquid ammonia (-78oC) 25 Titanium dioxide (rutile) 173 perp 86 para
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Voltage in Circuits

• Elements are connected by wires.
• Any connected region of wire has the same
  potential.

• The potential difference across an element is the
  elements voltage.

C1
C2
C3
VC1 _____ V
VC3 _____ V
VC2 _____ V
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Voltage in Circuits

• Elements are connected by wires.
• Any connected region of wire has the same
  potential.

• The potential difference across an element is the
  elements voltage.

C1
C2
C3
VC1 5 V
VC3 3 V
VC2 7 V
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Capacitors in Parallel

• Both ends connected together by wire

• Share Charge Qeq Q1 Q2
• Total Cap Ceq (Q1 Q2)/V C1 C2

Veq

• Same voltage V1 V2

C1
C2
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Capacitors in Parallel

• Both ends connected together by wire

• Share Charge Qeq Q1 Q2
• Total Cap Ceq (Q1 Q2)/V C1 C2

Veq

• Same voltage V1 V2

15 V
15 V
C1
C2
10 V
10 V
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Capacitors in Series

• Connected end-to-end with NO other exits
• Same Charge Q1 Q2 Qeq

• Share Voltage V1V2Veq

Q


C1


-




C2
-Q
-

-



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Electromotive Force

• Battery
• Maintains potential difference V
• Not constant power
• Not constant current
• Does NOT produce or supply charges, just pushes
  them.

-