# Capacitance of a variable capacitor

astenroo

## 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=$$\frac{\alpha}{360\circ}\pi r^{2}$$
The capacitance C=$$\frac{\epsilon_{0}A}{d}$$
$$\alpha = angle$$
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?

cupid.callin
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

astenroo
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?

cupid.callin
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?

Yes ... why not ... and will the fact that they are in parallal affect them?

check this: http://en.wikipedia.org/wiki/Variable_capacitor#Mechanically_controlled"

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Mentor
Find the total area of overlap for + and - faces. Then do the obvious. astenroo
Find the total area of overlap for + and - faces. Then do the obvious. 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.

Mentor
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.

cupid.callin
Yes they do have fields till they have some effective area acting as capacitor

astenroo
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.