How Is Capacitance Calculated for Different Capacitor Areas?

In summary, the conversation revolves around calculating the capacitance of a parallel plate capacitor with a composite dielectric medium. The participants discuss the transformed circuit diagram and the total area of the capacitor, which is divided into three capacitors with an area of A each. The conversation also includes clarification on the arrangement of the capacitors and their respective areas.
  • #1
gracy
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83

Homework Statement


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


Homework Equations


##C##=##\frac{Kε0A}{d}##

The Attempt at a Solution


Which capacitor has an area "A"?
I will have to transform this into circuit diagram.
CIRCUIT.png
 
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  • #2
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
NascentOxygen said:
I would not assume the dimension A to be of an area unless that were clearly stated somewhere.
Yes it is mentioned that A=area
 
  • #4
Please show the original figure and text, not the one, modified by you.
 
  • #5
ehild said:
Please show the original figure and text, not the one, modified by you.
Calculate the capacitance of the parallel plate capacitor shown in the following figure,between points X and Y.

MODIFIED.png
 
  • #6
Show the real figure in the book, without modifying it.
 
  • #7
ehild said:
Show the real figure in the book, without modifying it.
That's what it is.
 
  • #8
upload_2015-12-13_12-13-48.png


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

Attachments

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  • #10
Don't see attached file.
 
  • #11
gracy said:
Sorry
Now this one should be perfect.This is what I have in my textbook.
View attachment 93303
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
cnh1995 said:
Both the capacitors are having area A.
But there are 3 capacitors ,right?
 
  • #13
gracy said:
But there are 3 capacitors ,right?
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:
  • #14
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.
 
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  • #15
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
But what about area?The question does not clearly mention which capacitor has an area A?
 
  • #17
modified-png.93298.png

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
cnh1995 said:
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.
How in case of three capacitors the area of each capacitor will be A?
 
  • #19
gracy said:
How in case of three capacitors the area of each capacitor will be A?
I believe it means that the area of each side of every metal plate of the equivalent three capacitors here is A.
 
  • #20
gracy said:
But what about area?The question does not clearly mention which capacitor has an area A?
In the case of your equivalent set of three capacitors, each capacitor, C1, C2, and C3 has area A.
upload_2015-12-14_9-45-34.png
 

What is a capacitor with dielectric?

A capacitor with dielectric is an electronic component that stores electrical energy by accumulating opposite charges on two conductive plates separated by an insulating material called a dielectric.

What is the role of the dielectric in a capacitor?

The dielectric in a capacitor plays a crucial role in increasing the capacitance and reducing the electric field between the plates. It acts as an insulator, preventing the charges on the plates from coming into direct contact and losing their stored energy.

What is the difference between a capacitor with dielectric and without dielectric?

A capacitor with dielectric has a higher capacitance compared to a capacitor without dielectric. The dielectric material increases the distance between the plates, allowing more charge to be stored. It also lowers the electric field between the plates, which makes the capacitor more stable and less prone to breakdown.

What are some examples of dielectric materials used in capacitors?

Some common dielectric materials used in capacitors include air, paper, ceramic, plastic, and electrolytic materials. The choice of dielectric material depends on the desired capacitance, voltage rating, and other factors such as cost and size constraints.

What is the effect of temperature on a capacitor with dielectric?

The dielectric constant of a material can change with temperature, which can affect the capacitance of a capacitor with dielectric. In some cases, the dielectric material can also degrade at high temperatures, reducing the overall performance and lifespan of the capacitor.

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