Capacitor of different plate dimensions

In summary: The Attempt at a SolutionThere is no mathematical computation guideline for this capacitor system since there is no standard or mathematical model for it. However, if you assume that the field due to the capacitor plates are like those due to an infinite plane, then the capacitance can be calculated using the following equation:
  • #1
arka210
3
0
1. Is it possible to calculate the capacitance of a system where the top plate has the dimension d1 and the bottom plate has a dimension d2 and d1<<d2. Now, the difference between the plates are t. Is it possible to calculate the capacitance of this system where the dielectric is oil?

2. In one of the thread here namely "Capacitance of two different circular plates" (last post June, 08), I got some basic idea from this thread but they consider air as dielectric, while in my case dielectric is oil. Also I need a mathematical computation guideline for this capacitor system








The Attempt at a Solution


 
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  • #2
You can assume that not all of the bigger plate contributes. The part of the bottom (bigger) plate directly below the top plate would only contribute. So, it is just like a capacitor of plates with dimensions as that of the smaller plate.

This comes from the assumption that that field due to the capacitor plates are like those due to an infinite plane. If not, then it'd be messy.

What happens to the field in a dielectric?
 
  • #3
Thanks graphene for your reply.

From one of the thread here I got an idea, quite similar to what you said >> "one can start with the smaller area to get an initial number, and then add in some more to account for the field lines that go from the outer part of the larger plate to the fringe / edge / backside of the smaller plate. It might be easiest to do it numerically". Question is whether this idea is applicable or not if the dielectric is oil and not air?
 
  • #4
Only difference it would make is that dielectric constant K would change from 1 to a greater number.
 
  • #5
As I mentioned before "one can start with the smaller area to get an initial number, and then add in some more to account for the field lines that go from the outer part of the larger plate to the fringe / edge / backside of the smaller plate. It might be easiest to do it numerically".
Now adding some more field lines is possible.
The question is how can I justify it? Is there any papers/publications or theory from which I can justify this computation?
 

1. What is a capacitor and how does it work?

A capacitor is an electronic component that stores electrical energy in the form of an electric field. It consists of two conductive plates separated by an insulating material, known as a dielectric. When a voltage is applied to the capacitor, one plate becomes positively charged and the other becomes negatively charged, creating an electric field between them. This electric field stores energy, which can be released when the capacitor is connected to a circuit.

2. How do the dimensions of the plates affect the capacitance of a capacitor?

The capacitance of a capacitor is directly proportional to the surface area of the plates and inversely proportional to the distance between them. This means that increasing the surface area of the plates will increase the capacitance, while increasing the distance between the plates will decrease the capacitance. Therefore, changing the dimensions of the plates can significantly affect the capacitance of a capacitor.

3. What is the role of the dielectric material in a capacitor?

The dielectric material in a capacitor serves as an insulating layer between the two plates. It prevents the plates from coming into direct contact with each other and controls the distance between them. Different dielectric materials have different properties, which can affect the capacitance, voltage rating, and other characteristics of a capacitor.

4. How do different plate dimensions impact the performance of a capacitor?

The dimensions of the plates can greatly affect the performance of a capacitor. Larger surface area plates can store more charge, resulting in a higher capacitance. However, they can also increase the size and cost of the capacitor. On the other hand, smaller surface area plates may have lower capacitance but can offer higher voltage ratings and faster response times. The distance between the plates also affects the capacitance and can impact the stability and reliability of the capacitor.

5. How do I choose the right capacitor based on plate dimensions for my application?

Choosing the right capacitor based on plate dimensions depends on the requirements of your specific application. Larger surface area plates are suitable for applications that require high capacitance, while smaller surface area plates may be better for applications that require high voltage ratings or fast response times. It is important to consider the overall design, cost, and performance requirements when selecting a capacitor with the appropriate plate dimensions.

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