Capacitance

1
Capacitance

• Physics 102
• Professor Lee Carkner
• Lecture 13

2
PAL 12 Electric Potential
 
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Yes
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No
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No
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Yes
       
3
Particle Motion
E
Decrease U (natural)
Increase U
High V
Increase U
Decrease U (natural)
Low V
4

• If a charge of value Q is at a point of potential
  V, we know,
• The velocity of the charge at that point
• The direction the charge will move in
• The amount of electrical potential energy the
  charge has
• The distance to the nearest other charge
• None of the above

5

• If a charged particle moves along an
  equipotential line (assuming no other forces),
• Its potential energy does not change
• No work is done
• Its kinetic energy does not change
• Its velocity does not change
• All of the above

6

• When a charge Q is placed at the corner of a
  square the potential at the center is 3 volts.
  What is the potential at the center if charges of
  Q are placed on all corners of the square?
• 0 V
• 3 V
• 9 V
• 12 V
• 24 V

7
Circuits

• What is the purpose of potential difference?
• It makes charges move
• e.g. light lightbulbs, induce movement in motors,
  move information etc.
• We will examine the key components of electric
  circuits
• Up first, the capacitor

8
Capacitance

• A capacitor is a device that can store charge and
  thus energy
• The amount of charge depends on the potential
  difference across the capacitor and the intrinsic
  properties of the device
• This intrinsic property is called capacitance and
  is represented by C

9
Capacitance Defined

• The amount of charge stored by a capacitor is
  just
• Or, defining the capacitance
• C Q/DV
• The units of capacitance are farads (F)
• 1 F 1 C/V
• Typical capacitances are much less than a farad
• e.g. microfarad mF 1 X 10-6 F

10
Capacitor Info

• Maintaining a potential difference across the
  plates causes the charge to separate
• Electrons are repelled from the negative terminal
  and end up on one plate
• Plates have a net charge
• Plates cant touch or charge would jump across

11
Capacitor Diagram
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DV
Q
DV


12
Capacitor Properties

• The capacitance depends on four things
• The distance between them (d)
• The dielectric constant of the material between
  the plates (k)
• The permittivity of free space (e0)
• A constant e0 8.85 X 10-12 C2/N m2
• The total capacitance can be written as
• C ke0(A/d)

13
Capacitance Dependences
14
Dielectric

• The molecules in the material will align with the
  electric field
• The polarized material partially cancels out the
  electric field between the plates reducing the
  voltage
• A dielectric allows a capacitor to store more
  charge with the same voltage

15
Dielectrics
16
Dielectric Constant

• The dielectric constant is a multiplicative
  factor for the capacitance
• C kC0
• e.g.
• The dielectric also allows you to move the plates
  closer together without touching

17
Breakdown

• The dielectric must be an insulator
• If the voltage is large enough, the charge will
  jump across anyway
• While Q CV, there is a limit to how much we can
  increase Q by increasing V
• Normally about 20 million volts

18
Energy in a Capacitor

• Every little batch of charge increases the
  potential difference between the plates and
  increases the work to move the next batch
• Charge stops moving when the DV across the plates
  is equal to the max DV possible for the circuit

19
Charging a Capacitor
20
Total Energy

• We find that the total energy stored in a
  capacitor is related to the charge and the final
  potential difference
• Energy 1/2 Q DV 1/2 C (DV)2 Q2/2C
• Large C and large DV produce large stored energy

21
Using Capacitors

• Generally only for short periods of time
• Charge can bleed-off if capacitor is not
  perfectly insulated and potential is not
  maintained
• Useful when you need a quick burst of energy
• For a flash, capacitor is discharged into a gas
  (like xenon) that will glow when ionized
• Since capacitance depends on d, can also use
  capacitance to measure separation

22
Next Time

• Read 18.1-18.5, 18.8-18.9
• Homework Ch 17, P 44, 49, Ch 18, P 4, 26