# Capacitor with dielectric

1. Dec 13, 2015

### gracy

1. The problem statement, all variables and given/known data
Calculate the capacitance of the parallel plate capacitor shown in the following figure,between points X and Y.

2. Relevant equations
$C$=$\frac{Kε0A}{d}$

3. The attempt at a solution
Which capacitor has an area "A"?
I will have to transform this into circuit diagram.

2. Dec 13, 2015

### Staff: Mentor

Yes, calculate using your 'transformed' equivalent. I would not assume the dimension A to be of an area unless that were clearly stated somewhere.

3. Dec 13, 2015

### gracy

Yes it is mentioned that A=area

4. Dec 13, 2015

### ehild

Please show the original figure and text, not the one, modified by you.

5. Dec 13, 2015

### gracy

Calculate the capacitance of the parallel plate capacitor shown in the following figure,between points X and Y.

6. Dec 13, 2015

### ehild

Show the real figure in the book, without modifying it.

7. Dec 13, 2015

### gracy

That's what it is.

8. Dec 13, 2015

### ehild

You show what areas are A, then ask "Which capacitor has an area "A"?" in the OP. Where is A in the original picture? Where are X and Y in the original picture?

9. Dec 13, 2015

### gracy

Sorry
Now this one should be perfect.This is what I have in my textbook.

#### Attached Files:

• ###### perfect.png
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10. Dec 13, 2015

### gracy

Don't see attached file.

11. Dec 13, 2015

### cnh1995

I think the transformed circuit diagram by you is correct. Both the capacitors are having area A. You'll have to calculate the equivalent capacitance of the composite capacitor (the one with dielectric constants k2 and k3).

12. Dec 13, 2015

### gracy

But there are 3 capacitors ,right?

13. Dec 13, 2015

### cnh1995

I'll prefer to call the capacitor on the right as a single capacitor with veriable dielectric constant. There is no metal connection between the dielectrics k2 and k3. So, I don't think they can be a series combination.

Last edited: Dec 13, 2015
14. Dec 13, 2015

### Staff: Mentor

Although there is no metal plate shown separating the different dielectrics, nothing would effectively change were you to include a third parallel metal plate as a separator because it would all be along a line of equipotential. So you can indeed analyse it as a series pair of capacitors.

15. Dec 13, 2015

### cnh1995

You're right. Seeing the answer I've got using the composite dielectric method, it turns out that it is effectively a series combination of the two.

16. Dec 14, 2015

### gracy

But what about area?The question does not clearly mention which capacitor has an area A?

17. Dec 14, 2015

### cnh1995

From the diagram,the total area is 2A. So, when you split this capacitor into two( or three) capacitors, the area of each capacitor will be A.

18. Dec 14, 2015

### gracy

How in case of three capacitors the area of each capacitor will be A?

19. Dec 14, 2015

### Staff: Mentor

I believe it means that the area of each side of every metal plate of the equivalent three capacitors here is A.

20. Dec 14, 2015

### SammyS

Staff Emeritus
In the case of your equivalent set of three capacitors, each capacitor, C1, C2, and C3 has area A.