Constructing a 1nF Capacitor with >10kV Breakdown Potential

In summary, constructing a 1nF capacitor with a breakdown potential of >10kV requires careful design and selection of materials. The capacitor must have a small physical size and high dielectric strength to withstand the high voltage without breaking down. This can be achieved by using materials such as ceramic, mica, or polypropylene for the dielectric layer and metal foils for the electrodes. Additional measures, such as increasing the distance between electrodes and ensuring proper insulation, may also be necessary to improve the capacitor's breakdown potential.
  • #1
Bryon
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0

Homework Statement


You are asked to construct a capacitor having a capacitance of around 1 nF and a breakdown potential in excess of 10,000V. You're thinking of using the sides of a tall Pyrex laboratory cylindrical beaker. You can line the inside and outside of the sides of the beaker with aluminum foil to act as plates. The Pyrex of the beaker sides will keep the foil in place and with the added advantage of acting as a dielectric.
The height of your beaker is 17 cm. Its inside radius is 3.6 cm and its outer radius is 3.89 cm.

Homework Equations


Q = CV = ε0κA/d
A = 2πrh


The Attempt at a Solution


Ainner = 2*π*(0.036)*(0.17) = 0.03845309
Aouter = 2*π*(0.0389)*(0.17) = 0.04150744

C = ((5.6)*(8.85x10^-12)*(Ainner + Aouter))/(0.0389-0.036)
C = 1.367237x10^-9F

Was I correct in using only the difference between the inner and outer radius? I also thought that adding the total area of the inner and outer radius was the correct approach since the capacitance depends on the area as well. What did I do wrong?
 
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  • #2
The area in a parallel plate capacitor refers to the overlapping area of the plates, not the total of the two plate areas.

Cylindrical capacitors are a bit different because, a) the plates have different areas yet they completely overlap, so that b) the electric field will not be uniform from one plate to the other.

Presumably if the cylinder diameter is much greater than the thickness of the wall, then the plate sizes will be approximately equal and the field will be approximately uniform and you can use the average area of the plates to find the capacitance.

For more accuracy, you might want to check out the http://hyperphysics.phy-astr.gsu.edu/hbase/electric/capcyl.html" .

http://www.ajdesigner.com/phpcapacitor/cylindrical_capacitor_equation_l.php"
 
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  • #3
Great! Thanks that is what I needed. Plus it shows where it comes from.
 

FAQ: Constructing a 1nF Capacitor with >10kV Breakdown Potential

How do I construct a 1nF capacitor with >10kV breakdown potential?

To construct a 1nF capacitor with >10kV breakdown potential, you will need to use materials with high dielectric strength, such as ceramic or mica. The capacitor should also have a large surface area and small distance between the plates to increase its capacitance and breakdown potential. Additionally, you will need to use a high voltage power supply to charge the capacitor to >10kV.

Can I use any type of material to construct this capacitor?

No, not all materials can withstand high voltages and have a high dielectric strength. It is important to use materials specifically designed for high voltage applications, such as ceramic or mica, to ensure the capacitor does not break down.

Why do I need a >10kV breakdown potential for this capacitor?

If you are using this capacitor for high voltage applications, it is important to have a high breakdown potential to prevent the capacitor from breaking down and causing damage to your circuit. The >10kV breakdown potential ensures that the capacitor can handle high voltage without failing.

How can I test the breakdown potential of my capacitor?

You can use a high voltage, low current power supply to gradually increase the voltage across the capacitor while monitoring the current. When the current suddenly increases, it indicates that the capacitor has reached its breakdown potential. However, it is important to handle high voltage with caution and take necessary safety precautions.

Can I use multiple capacitors to achieve a 1nF capacitance with >10kV breakdown potential?

Yes, you can connect capacitors in parallel to increase the overall capacitance and in series to increase the breakdown potential. However, it is important to ensure that each individual capacitor has a high enough breakdown potential to handle the desired voltage.

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