electrical potential and capacitors

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d B A q E ) b ( ) a ( g d B A m F IGURE 5 . 1 (a) When the electri c eld is directe d downward, point B is at a lower electric potential than point A. When a positive test charge moves from A to B, the charge–eld system loses electric potential energy. (b) A gravitational analogy: When an object with mass m moves downward in the direction of the gravita tional eld , the object eld system loses gravitational potential energy. g : E : E B C A r θ d F IGURE 5 . 2 A particle is moved in a uniform electric eld. Point B is at a lower potential than point A . Points B and C are at the same potential. Electric Potential and C apacitance Chapter 5

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A

Electric Potent

Chap

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+

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4.00 m

 C y 

2.00 C

3.00 m

µ 

µ 

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E

+

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a a 

 y 

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dq 

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(a) +

++ +

+ ++

+

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+Q 

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+Q 

(a)

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Capacitor

symbol

C1

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C 2

C 1

Q 2

C 2

Q 1

C 1

∆V  1 = ∆V  2 = ∆V  

C

C2C1

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(a)

+ –

C 2

∆V  

C 1∆V  1 ∆V  2

+Q –Q +Q –Q  

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F I GURE 5.25 (Example 5.8) To find the

equivalent combination of the capacitors in (a),

the various combinations are reduced in steps as

indicated in (b), (c), and (d), using the series and

parallel rules described in the text. Allcapacitance values are in microfarads.

C

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Q 1i +

b a 

C 1

S1 S2

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C 0 Q 0

+–

+

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)b(

–  + 

–  +

  –  +

–   

+     

     –    +

     –     +      –

       +

  –+

      –      +

     –     +

– +  –

      +

– + 

– +

 –+

–  +

–  + –+

 – + –  +

(a)

+

+

+

+

+

+

F IGURE 5.28 (a) Polar molecules are randomly orie

external electric field is applied, the molecules partially

modeled as an additional pair of parallel plates establish

Q

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+

Q 0C 0

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k m

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20.0 nC

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∆V  

Stud

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Capacitorplates

Stud finder

 Wallboard

Stud

(a)