Fun with Capacitors

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Fun with Capacitors
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Capacitor

• Composed of two metal plates.
• Each plate is charged
• one positive
• one negative
• Stores Charge

SYMBOL
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A simple Capacitor
TWO PLATES
WIRES
Battery
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INSIDE THE DEVICE
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Two Charged Plates(Neglect Fringing Fields)
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More on Capacitors
Same result from other plate!
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Device

• The Potential Difference is APPLIED by a battery
  or a circuit.
• The charge q on the capacitor is found to be
  proportional to the applied voltage.
• The proportionality constant is C and is referred
  to as the CAPACITANCE of the device.

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NOTE

• Work to move a charge from one side of a
  capacitor to the other is qEd.
• Work to move a charge from one side of a
  capacitor to the other is qV
• Thus qVqEd
• EV/d (Hold this thought.)

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UNITS

• A capacitor which acquires a charge of 1 coulomb
  on each plate with the application of one volt is
  defined to have a capacitance of 1 FARAD
• One Farad is one Coulomb/Volt

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Continuing

• The capacitance of a parallel plate capacitor
  depends only on the Area and separation between
  the plates.
• C is dependent only on the geometry of the device!

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Units of e0
pico
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Simple Capacitor Circuits

• Batteries
• Apply potential differences
• Capacitors
• Wires
• Wires are METALS.
• Continuous strands of wire are all at the same
  potential.
• Separate strands of wire connected to circuit
  elements may be at DIFFERENT potentials.

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Size Matters!

• A Random Access Memory stores information on
  small capacitors which are either charged (bit1)
  or uncharged (bit0).
• Voltage across one of these capacitors ie either
  zero or the power source voltage (5.3 volts in
  this example).
• Typical capacitance is 55 fF (femto10-15)
• Question How many electrons are stored on one of
  these capacitors in the 1 state?

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Small is better in the IC world!
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TWO Types of Connections
SERIES PARALLEL
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Parallel Connection
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Series Connection
The charge on each capacitor is the same !
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Series Connection Continued
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More General
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Example
C112.0 uf C2 5.3 uf C3 4.5 ud
C1 C2
series
(125.3)pf
(125.3)pf
V
C3
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More on the Big C

• We move a charge dq from the (-) plate to the ()
  one.
• The (-) plate becomes more (-)
• The () plate becomes more ().
• dWFddq x E x d

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So.
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Not All Capacitors are Created Equal

• Parallel Plate
• Cylindrical
• Spherical

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Spherical Capacitor
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Calculate Potential Difference V
(-) sign because E and ds are in OPPOSITE
directions.
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Continuing
Lost (-) sign due to switch of limits.