Designing a Parallel Capacitor: Help Needed!

In summary: Well not if you want to build a simple air capacitor for an experiment or demonstration, as opposed to practical use.
  • #1
skyT
2
0
do u all mind sharing with me what are the steps needed/ the procedures to design a capacitor? Its like I've been given only its electric field intensity. And is required to find out the capacitance... mind chip in some ideas for me? btw, I am designing a parallel capacitor.

relevant equations :
electric flux density, D = epsilon * electric field intensity + polarisation vector
polarisation vector = epsilon*electric susceptibility*electric field intensity

the attempt at a solution :
I've manage to solve the above and I am now stuck at the Gauss' law equation...
where
E=Q/(4*pi*r^2*epsilon)
can i know what does the radius stands for? is it the radius of a charge? or the radius of the capacitor? is it fixed or we can determine it ourselves? please help...
 
Last edited:
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  • #2
skyT said:
do u all mind sharing with me what are the steps needed/ the procedures to design a capacitor? Its like I've been given only its electric field intensity. And is required to find out the capacitance... mind chip in some ideas for me? btw, I am designing a parallel capacitor.

relevant equations :
electric flux density, D = epsilon * electric field intensity + polarisation vector
polarisation vector = epsilon*electric susceptibility*electric field intensity

the attempt at a solution :
I've manage to solve the above and I am now stuck at the Gauss' law equation...
where
E=Q/(4*pi*r^2*epsilon)
can i know what does the radius stands for? is it the radius of a charge? or the radius of the capacitor? is it fixed or we can determine it ourselves? please help...

You essentially need two pieces of information to get started:

1. [itex]C = \varepsilon_{r} \frac{A}{4\pi d},[/itex] where:
A is the area of conductors
d is the distance between them
[itex]\varepsilon_{r}[/itex] is the dialetric constant of the materials separating the plates. The dialetric constant for air is about one, for a common commericial capacitor material such as Barium Titanate the value can reach 10,000.

2. The breakdown voltage of the particular material you use to separate the conductors. The breakdown voltage of air for instance is about 3 million volts per meter of separation (3000 volts per mm and so on).

The above concerns the primary physics.

Then there are the practicallities: How long will your dialetric material last? Will it chemically react with the conductors over time? If and when an overvoltage breakdown occurs, will the device fail explosively? What kind of container will you use? Will the container prevent other materials from entering the capacitor over time and changing its performance?
 
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  • #3
wow. That sounds like a lot of work. Is it possible to prove that both Laplace Equation and Gauss' Law can be used to get the same value of capacitance for a spherical capacitor?
 
  • #4
skyT said:
wow. That sounds like a lot of work.
Well not if you want to build a simple air capacitor for an experiment or demonstration, as opposed to practical use.

Is it possible to prove that both Laplace Equation and Gauss' Law can be used to get the same value of capacitance for a spherical capacitor?
The equation above for capacitance is independent of the geometry you chose. If you want to look into the derivation of capacitance from fundamental electromagnetic principals, perhaps the physics sub forum is a better place to ask, though I expect the wikipedia pages on capacitance already answer your questions.
 
  • #5


Hello,

Designing a parallel capacitor involves several steps and considerations. First, you need to determine the desired capacitance value for your capacitor. This can be done by considering the specific application and the required energy storage capacity. Once you have the desired capacitance, you can move on to designing the physical dimensions and materials of the capacitor.

To design a parallel capacitor, you need to consider the electric field intensity and the electric flux density. The electric field intensity is the measure of the electric force exerted on a unit charge, while the electric flux density is the amount of electric flux passing through a unit area. These two parameters are related through the permittivity of the material, which is a measure of how well a material can store electric charges.

To determine the capacitance of a parallel capacitor, you can use the equation C = εA/d, where C is the capacitance, ε is the permittivity of the material, A is the area of the capacitor plates, and d is the distance between the plates. This equation shows that the capacitance is directly proportional to the area of the plates and inversely proportional to the distance between them.

To design the physical dimensions of the capacitor, you need to consider the electric field intensity and the voltage rating. The electric field intensity should be kept below the breakdown strength of the material to avoid damaging the capacitor. The voltage rating should also be considered to ensure that the capacitor can handle the desired voltage without breaking down.

In terms of the Gauss' law equation, the radius (r) represents the distance from the center of the capacitor to a point where you want to calculate the electric field. This is usually the distance between the plates of the capacitor. The value of r is fixed and determined by the physical dimensions of the capacitor.

In summary, the steps for designing a parallel capacitor include determining the desired capacitance, selecting the appropriate material, designing the physical dimensions, and considering the electric field intensity and voltage rating. I hope this helps and feel free to ask for any clarification or further assistance. Good luck with your design!
 

1. How do I determine the capacitance of a parallel capacitor?

In order to determine the capacitance of a parallel capacitor, you will need to know the formula C=Q/V, where C is the capacitance, Q is the charge on one of the capacitor plates, and V is the voltage applied to the capacitor. You can also use a capacitance meter to measure the capacitance directly.

2. What materials are commonly used for parallel capacitors?

The most commonly used materials for parallel capacitors are ceramic, film, and electrolytic capacitors. Ceramic capacitors are typically used in high frequency applications, while film capacitors are used in high voltage and high temperature environments. Electrolytic capacitors are often used in power supply circuits.

3. How do I connect multiple parallel capacitors?

To connect multiple parallel capacitors, you simply need to connect the positive terminals of all the capacitors together and the negative terminals together. This will create a larger overall capacitance, as the capacitors will work together to store more charge.

4. What is the purpose of a parallel capacitor?

The purpose of a parallel capacitor is to store electrical energy. They are commonly used in electronic circuits to filter out unwanted noise and provide stable power to sensitive components.

5. How do I calculate the overall capacitance of multiple parallel capacitors?

To calculate the overall capacitance of multiple parallel capacitors, you can simply add the individual capacitance values together. For example, if you have three 10μF capacitors connected in parallel, the overall capacitance would be 30μF.

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