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Capacitance of a variable capacitor

  • Thread starter astenroo
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  • #1
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Homework Statement


Hi again!

I've been handed an assignment in which we are to find the capacitance of a variable capacitor consisting of seven semicircular plates with a radius of 2 cm spaced 1 mm from each other. Every other plate is connected to a common +terminal, and every other to a common -terminal. We are to find the capacitance at different angles.


Homework Equations



Area of a circle sector is A=[tex]\frac{\alpha}{360\circ}\pi r^{2}[/tex]
The capacitance C=[tex]\frac{\epsilon_{0}A}{d}[/tex]
[tex]\alpha = angle[/tex]
and d=distance between plates
C for parallell coupling is C=C1+C2+C3+C4+C5+C6

The Attempt at a Solution


Now, my intuition tells me that this variable capacitor could be treated as six capacitors in parallell. Is my intuition right or did I make serious blunder? Calculating the areas is straight forward, and iff it can be treated as a parallell coupling of capacitors, then that part is also straight forward. My actual problem statement is, can a variabel capacitor be treated as parallell coupled capacitor?
 

Answers and Replies

  • #2
1,137
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well i couldnt properly understand what is your question but i guess as the plates are semicircular .. rotating them along the center will change effective area, so A dec and therefore C also dec.

So you can alter the capacitance
 
  • #3
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well i couldnt properly understand what is your question but i guess as the plates are semicircular .. rotating them along the center will change effective area, so A dec and therefore C also dec.

So you can alter the capacitance
Yes I understand how the area affects capacitance. But, in a variable capacitor, can each pair of "+- plates" be considered as a separate capacitor? If so, then they are in parallell, aren't they?
 
  • #4
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  • #5
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  • #6
gneill
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Find the total area of overlap for + and - faces. Then do the obvious.:wink:
 
  • #7
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Find the total area of overlap for + and - faces. Then do the obvious.:wink:
Ok, and then I suddenly began thinking:

Let's say that plates 1, 3, 5 and 7 are + and 2, 4 and 6 are -. Do I have a field between plates 1&2 and 2&3 etc? I believe I have a field, but I am not completely sure.
 
  • #8
gneill
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Ok, and then I suddenly began thinking:

Let's say that plates 1, 3, 5 and 7 are + and 2, 4 and 6 are -. Do I have a field between plates 1&2 and 2&3 etc? I believe I have a field, but I am not completely sure.
All facing surfaces with opposite charges count. That includes both sides of a single plate if they're both facing oppositely charged other plates.
 
  • #9
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Yes they do have fields till they have some effective area acting as capacitor
 
  • #10
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All facing surfaces with opposite charges count. That includes both sides of a single plate if they're both facing oppositely charged other plates.
Thank you very much for your help. Goes for you as well cupid.
 

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