# Capacitor question - Estimate the required radius of each plate

1. Dec 12, 2013

### brenfox

1. The problem statement, all variables and given/known data
Estimate the required radius of each plate. The plates are separated in air by 0.01mm and has a capacitance of 400pF. There are 4 pairs of plates.

2. Relevant equations
c= εrε0*A(n-1)/ d

3. The attempt at a solution Find area. Transposing for A

A = dc/εrεo
A= 1*10^-5*400*10^-12/1*8.85*10^-12*7

I am getting 6.457^-27mm.
I am going wrong somewhere, pretty sure the equation is correct though.

2. Dec 12, 2013

### Staff: Mentor

If yoiu have 4 pairs of plates, how many parallel capacitors does that form?

3. Dec 13, 2013

### brenfox

This produces 4 parallel capacitors.

4. Dec 13, 2013

### Staff: Mentor

Nope.

Hold your two hands out in front of you, with the fingers of each hand interlacing (no thumbs). That puts two sets of 4 fingers interlacing. Count how many gaps there are between opposing hand/fingers. The answer is not n.

5. Dec 13, 2013

### brenfox

So this produces 7 parallel capacitors. Makes sense using that analogy. Thats why the equation is n-1. eg 8-1 equals 7. My answer still doesn`t add up though!

6. Dec 13, 2013

### Staff: Mentor

can you show your new calculations?

7. Dec 13, 2013

### brenfox

A= dc/εrεo*7. This is the equation i get to find area.
So.. A= 1*10^-5*400*10^-12 / 1*8.85*10^-12*7

which equates to 6.456^-27!...somethings wrong with that answer.

8. Dec 13, 2013

### Staff: Mentor

It's just an error with how you are entering it into your calculator. You have the equation correct.

If you write the equation out like this, you can see that the 10^-12 terms will cancel...

$$A = \frac{10^{-5} * 400 * 10^{-12}}{7 * 8.85 * 10^{-12}}$$

Last edited: Dec 13, 2013
9. Dec 13, 2013

### brenfox

This is where i struggle.My defence is the fact that im an electrician trying to achieve an HND!. So... the 10^-12 cancels each other out leaving 10-5*400/7*8.85. Which equates to. 0.0006? Which feels too small a number.

10. Dec 13, 2013

### Staff: Mentor

It's an area. What are the units?

11. Dec 14, 2013

### brenfox

So A= 6.46*10^-5

A = 6.45*10^-5*10^6= 64.5mm2?

Last edited: Dec 14, 2013
12. Dec 14, 2013

### brenfox

To find radius. A = 0.5*3.14*r^2
Transpose to r = √ a/∏*0.5

r= √64.5/*0.5

r = 3.2mm?

13. Dec 14, 2013

### Staff: Mentor

Lose the 0.5; The area of a circle is $A = \pi r^2$.

14. Dec 14, 2013

### brenfox

ah right. so..

r=√a/∏ so my answer is √64.5/∏ = 4.53mm. thanks for your help.

15. Apr 24, 2014

### biggdogg9

Should this not be μm ?

16. Apr 24, 2014

### brenfox

My tutor marked my answer as correct.

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