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Capacitors Physics 102:   Lecture 04
Recall from last lecture….. Electric Fields, Electric Potential
Comparison: Electric  Potential Energy  vs. Electric  Potential   ,[object Object],[object Object],[object Object],q A B
 
Electric Potential:  Summary ,[object Object],[object Object],[object Object],[object Object],[object Object], U AB  = q   V AB
Important Special Case Uniform Electric Field + + + + + - - - - - ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Parallel Plate Capacitor: Potential Difference  E=E 0 d V =V A  – V B  = +E 0  d + + + + + - - - - - A B d + + + + + - - - - - + + + + + - - - - - E=2 E 0 V =V A  – V B  = +2E 0  d Potential difference is proportional to charge:  Double Q    Double V Charge Q on plates Charge 2Q on plates  ,[object Object],A B
 
Capacitance: The ability to store separated charge  C  Q/V ,[object Object],[object Object],[object Object],[object Object],Q=CV U =(½) Q V   ,[object Object],Units:  1 Coulomb/Volt = 1 Farad (F) E d + + + + + - - - - -
Why Separate Charge? ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Capacitance Practice   ,[object Object],How much energy is stored in this capacitor? Example
 
Capacitance of  Parallel Plate Capacitor ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],A d A E + - V C =  0 A/d  Parallel plate capacitor
Parallel Plate Capacitor C =   0 A/d ,[object Object],A d A Example
Dielectric ,[object Object],[object Object],Capacitance  with  dielectric Dielectric constant (   > 1) Capacitance  without  dielectric
 
A parallel plate capacitor given a charge q.  The plates are then pulled a  small  distance further apart. What happens to the charge q on each plate of the capacitor? ACT: Parallel Plates 1)  Increases 2) Constant 3) Decreases Remember charge is real/physical. There is no place for the charges to go.  +q -q + + + + - - - - d pull pull
A parallel plate capacitor given a charge q.  The plates are then pulled a  small   distance further apart. Which of the following apply to the situation after the plates have been moved? 1)The capacitance increases    True  False 2)The electric field increases      True  False 3)The voltage between the plates increases  True  False Preflight 4.1 +q -q + + + + - - - - d pull pull
A parallel plate capacitor given a charge q.  The plates are then pulled a  small  distance further apart. Which of the following apply to the situation after the plates have been moved? ACT/Preflight 4.1 The energy stored in the capacitor A)  increases B) constant C) decreases +q -q + + + + - - - - d pull pull
 
Two identical parallel plate capacitors are shown in end-view in A) of the figure.  Each has a capacitance of C. A ) B ) If the two are joined as in (B) of the figure, forming a single capacitor, what is the final capacitance? 1)  2C  2)  C  3)  C/2  ACT/Preflight 4.2
Voltage in Circuits ,[object Object],[object Object],V C 1 = 5-0 V= 5 V V C 3 = 15-12 V= 3 V V C 2 = 12-5 V= 7 V C 1 C 2 C 3 Example ,[object Object],V wire 1 = 0 V V wire 2 = 5 V V wire 3 = 12 V V wire 4 = 15 V
Capacitors in Parallel ,[object Object],C 1 C 2 15 V 10 V 15 V 10 V ,[object Object],[object Object],= V eq  ,[object Object],C eq 15 V 10 V
 
Parallel Practice ,[object Object],C 4 C 6 C eq 5 V 0 V 5 V 0 V 5 V 0 V C eq  = C 4 +C 6 Q 4  = C 4  V 4 Q 6  = C 6  V 6 Q eq  = C eq  V eq = 4   F+6   F = 10   F = (4   F)(5 V) = 20   C = (6   F)(5 V) = 30   C = (10   F)(5 V) = 50   C = Q4+Q6 V =  5 V Example
Capacitors in Series ,[object Object],[object Object],[object Object],C 1 C 2 + + + + + + + + + + + + + - + - + - +Q  -Q  ,[object Object],C eq - + - + +Q  -Q  +Q  -Q
Series Practice ,[object Object],C eq C 4 C 6 + - + - 5 V 0 V Q = CV Example + - +Q  -Q  +Q  -Q  +Q  -Q  5 V 0 V
 
Comparison: Series  vs.  Parallel ,[object Object],[object Object],[object Object],[object Object],C 1 C 2 C 2 C 1
Electromotive Force ,[object Object],[object Object],[object Object],+ -
Preflight 4.4 A circuit consists of three initially uncharged capacitors C 1 , C 2 , and C 3 , which are then connected to a battery of emf   .  The  capacitors obtain charges q 1 , q 2 ,q 3 , and have voltages across their plates V 1 , V 2 , and V 3 .   Which of these are true?   ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],C 2 C 3 C 1 E + - -q 2 +q 1 -q 1 +q 3   -q 3 +q 2 V 1 V 2 V 3
 
A circuit consists of three initially uncharged capacitors C 1 , C 2 , and C 3 , which are then connected to a battery of emf   .  The  capacitors obtain charges q 1 , q 2 ,q 3 , and have voltages across their plates V 1 , V 2 , and V 3 .  1) q 1  = q 2 Not necessarily  C 1  and C 2  are NOT in series. 2) q 2  = q 3 Yes!  C 2  and C 3  are in series. ACT/Preflight 4.4:  Which is true? C 2 C 3 C 1 E + - -q 2 +q 1 -q 1 +q 3   -q 3 +q 2 V 1 V 2 V 3
1) V 2  = V 3 Not necessarily, only if C 1  = C 2 2) E = V 1 Yes! Both ends are connected by wires A circuit consists of three initially uncharged capacitors C 1 , C 2 , and C 3 , which are then connected to a battery of emf   .  The  capacitors obtain charges q 1 , q 2 ,q 3 , and have voltages across their plates V 1 , V 2 , and V 3 .  ACT/Preflight 4.4:  Which is true? C 2 C 3 C 1 E + - -q 2 +q 1 -q 1 +q 3   -q 3 +q 2 V 1 V 2 V 3 10V 0V 7V??
1) V 1  < V 2 Nope, V 1  > V 2 . (E.g. V 1  = 10-0, V 2  =10-7)  2) C eq  > C 1 Yes! C 1  is in parallel with C 23 A circuit consists of three initially uncharged capacitors C 1 , C 2 , and C 3 , which are then connected to a battery of emf   .  The  capacitors obtain charges q 1 , q 2 ,q 3 , and have voltages across their plates V 1 , V 2 , and V 3 .  ACT/Preflight 4.4:  Which is true? C 2 C 3 C 1 E + - -q 2 +q 1 -q 1 +q 3   -q 3 +q 2 V 1 V 2 V 3 10V 0V 7V??
[object Object],[object Object],[object Object],[object Object],[object Object],Recap of Today’s Lecture

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Lect04 handout

  • 2. Recall from last lecture….. Electric Fields, Electric Potential
  • 3.
  • 4.  
  • 5.
  • 6.
  • 7.
  • 8.  
  • 9.
  • 10.
  • 11.
  • 12.  
  • 13.
  • 14.
  • 15.
  • 16.  
  • 17. A parallel plate capacitor given a charge q. The plates are then pulled a small distance further apart. What happens to the charge q on each plate of the capacitor? ACT: Parallel Plates 1) Increases 2) Constant 3) Decreases Remember charge is real/physical. There is no place for the charges to go. +q -q + + + + - - - - d pull pull
  • 18. A parallel plate capacitor given a charge q. The plates are then pulled a small distance further apart. Which of the following apply to the situation after the plates have been moved? 1)The capacitance increases True False 2)The electric field increases True False 3)The voltage between the plates increases True False Preflight 4.1 +q -q + + + + - - - - d pull pull
  • 19. A parallel plate capacitor given a charge q. The plates are then pulled a small distance further apart. Which of the following apply to the situation after the plates have been moved? ACT/Preflight 4.1 The energy stored in the capacitor A) increases B) constant C) decreases +q -q + + + + - - - - d pull pull
  • 20.  
  • 21. Two identical parallel plate capacitors are shown in end-view in A) of the figure. Each has a capacitance of C. A ) B ) If the two are joined as in (B) of the figure, forming a single capacitor, what is the final capacitance? 1) 2C 2) C 3) C/2 ACT/Preflight 4.2
  • 22.
  • 23.
  • 24.  
  • 25.
  • 26.
  • 27.
  • 28.  
  • 29.
  • 30.
  • 31.
  • 32.  
  • 33. A circuit consists of three initially uncharged capacitors C 1 , C 2 , and C 3 , which are then connected to a battery of emf  . The capacitors obtain charges q 1 , q 2 ,q 3 , and have voltages across their plates V 1 , V 2 , and V 3 . 1) q 1 = q 2 Not necessarily C 1 and C 2 are NOT in series. 2) q 2 = q 3 Yes! C 2 and C 3 are in series. ACT/Preflight 4.4: Which is true? C 2 C 3 C 1 E + - -q 2 +q 1 -q 1 +q 3 -q 3 +q 2 V 1 V 2 V 3
  • 34. 1) V 2 = V 3 Not necessarily, only if C 1 = C 2 2) E = V 1 Yes! Both ends are connected by wires A circuit consists of three initially uncharged capacitors C 1 , C 2 , and C 3 , which are then connected to a battery of emf  . The capacitors obtain charges q 1 , q 2 ,q 3 , and have voltages across their plates V 1 , V 2 , and V 3 . ACT/Preflight 4.4: Which is true? C 2 C 3 C 1 E + - -q 2 +q 1 -q 1 +q 3 -q 3 +q 2 V 1 V 2 V 3 10V 0V 7V??
  • 35. 1) V 1 < V 2 Nope, V 1 > V 2 . (E.g. V 1 = 10-0, V 2 =10-7) 2) C eq > C 1 Yes! C 1 is in parallel with C 23 A circuit consists of three initially uncharged capacitors C 1 , C 2 , and C 3 , which are then connected to a battery of emf  . The capacitors obtain charges q 1 , q 2 ,q 3 , and have voltages across their plates V 1 , V 2 , and V 3 . ACT/Preflight 4.4: Which is true? C 2 C 3 C 1 E + - -q 2 +q 1 -q 1 +q 3 -q 3 +q 2 V 1 V 2 V 3 10V 0V 7V??
  • 36.

Notas del editor

  1. Electric potential energy Potential difference PED = qV V = Ed
  2. Use fire extinguisher analogy?
  3. Stores energy….electrical potential energy. If the plates were free to move, they would collapse on each other. Just like releasing a brick from height h above the floor. Or, if charges were free to move, the capacitor would “discharge”. Demo. Can I make U more plausible?
  4. Here note that this is small number for such a big device. How do they make “real” capacitors?
  5. Same Q, smaller E, therefore smaller V, larger Q