Calculation of capacitance of conductors

In summary, the capacitance between two conductors in a 2D space can be calculated using the dimensions of the conductors and the properties of the dielectrics between them. This can be approximated using the equation C = εrε0A/d, where C is the capacitance in farads, A is the area of overlap in square meters, εr is the relative static permittivity, ε0 is the permittivity of free space, and d is the separation between the plates. However, this equation is only accurate if d is small compared to the other dimensions of the plates and the fringing field around the periphery is minimal. An alternative method for calculating capacitance is to analyze radio antennas by taking
  • #1
Ravaner
134
3
Hello,

I would like to get a method for calculation of capacitance of conductors. Let say, I have several conductors in space (2D). I know voltage everywhere between and on conductors, and I need to know the value of capacitance between 2 conductors among several. I'm looking for a general method in order to program an algorithm.
 
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  • #2


The capacitance is determined by the dimensions of the conductors and the properties of the dielectrics between and around them.

Here is Wikipedias description:

The capacitance can be calculated if the geometry of the conductors and the dielectric properties of the insulator between the conductors are known. For example, the capacitance of a parallel-plate capacitor constructed of two parallel plates both of area A separated by a distance d is approximately equal to the following:

C = \epsilon_{r}\epsilon_{0} \frac{A}{d} (in SI units)

where

C is the capacitance in farads, F
A is the area of overlap of the two plates measured in square metres
εr is the relative static permittivity (sometimes called the dielectric constant) of the material between the plates, (vacuum =1)
ε0 is the permittivity of free space where ε0 = 8.854x10-12 F/m
d is the separation between the plates, measured in metres

The equation is a good approximation if d is small compared to the other dimensions of the plates so the field in the capacitor over most of its area is uniform, and the so-called fringing field around the periphery provides a small contribution


End quote.
A technique that is used to analyse radio antennas is to take small segments of each part of the antenna and calculate the effect of all other parts on that part, and vice versa.

So, if you knew the diameter of a wire, you could take a small section of it and work out the area facing each other section of other conductors and estimate the capacitance.
Wire segments along the same wire could have their capacitances added in parallel.
 
  • #3


Thanks for reply. I've programmed this formula, resultats lack of accuracy bur anyway it's better that nothing. I've also tried using Gass theorem with calculation of flux for electrical field, results are not better !
 
  • #4


Yes, even the Wikipedia article I quoted said this:

The equation is a good approximation if d is small compared to the other dimensions of the plates so the field in the capacitor over most of its area is uniform, and the so-called fringing field around the periphery provides a small contribution.

Meaning that it wasn't a good approximation if d, the separation between the plates, measured in metres, was large. And not if the so-called fringing field around the periphery provides a large contribution.

So, these problems might be contributing to the inaccuracy.
 

What is capacitance and why is it important in the calculation of conductors?

Capacitance is the measure of a conductor's ability to store electric charge. It is an important factor in the calculation of conductors because it determines the amount of charge a conductor can hold and how it will behave in an electrical circuit.

How is the capacitance of a conductor calculated?

The capacitance of a conductor can be calculated by dividing the charge on the conductor by the potential difference across it. It is also affected by the geometry and material of the conductor.

What is the unit of capacitance and how is it represented in equations?

The unit of capacitance is the farad (F), named after the scientist Michael Faraday. In equations, capacitance is represented by the symbol C.

How does the distance between conductors affect capacitance?

The distance between conductors has an inverse relationship with capacitance. As the distance increases, the capacitance decreases. This is because a larger distance between conductors means there is less interaction and thus less charge can be stored.

How does the material of a conductor affect its capacitance?

The capacitance of a conductor is directly proportional to the permittivity of the material it is made of. Materials with high permittivity, such as dielectrics, have a higher capacitance compared to materials with lower permittivity, such as air.

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