# Breakdown Potential of a Cylindrical Capacitor

• breez
In summary: The website I'm working on doesn't seem to have the breakdown potential inputted correctly. In summary, the capacitance is around 1 nF and the breakdown potential is around 25.2 kV.
breez

## Homework Statement

You are asked to construct a capacitor having a capacitance near 1 nF and a breakdown potential in excess of 13000 V. You think of using the sides of a tall plastic drinking glass as a dielectric (with a dielectric constant 5.2 and dielectric strength 12 kV/mm), lining the inside and outside curved surfaces with aluminum foil to act as the plates. The glass is 14 cm tall with an inner radius of 3.17 cm and an outer radius of 3.38 cm. (a) What are the capacitance and (b) breakdown potential in kilovolts of this capacitor?

## Homework Equations

$$C = \frac{2\pi \epsilon_0 \kappa L}{\ln \frac{b}{a}}$$

## The Attempt at a Solution

I used the above formula to compute the capacitance, which is pretty much plug and chug.

I don't know how to compute breakdown potential though. I multiplied the dielectric strength by the thickness of the capacitor (difference in radii in mm) but that was marked wrong.

Anyone know how to properly compute the breakdown potential? This problem has me stumped.

You are given a dielectric strength of 12kV/mm. Don't you just multiply that by the thickness of the glass in mm?

I did (3.38 - 3.17) x 10 mm x 12 kV/mm, but this was marked incorrect on the website that my online course runs on.

Gotta confess, I don't see why it was marked wrong. It looks fine to me. Let me know if you find out. 2.1*12kV=25.2kV total, right?

yeah it's strange, that's exactly what I got, but it's marked incorrect.

I've been presented with an extremely similar problem. I'm given a wire with a coaxial shell of equal length with a dielectric between them of strength 1x106V/m, and I subtracted the inner radius of the shell (1.5cm) from the radius of the wire (.1mm) to get .0149m of separation but when I multiply it by 1 million volts/m to get 14.9kV breakdown voltage, it's marked incorrect. Furthermore I'm supposed to calculate the maximum charge per unit length of the wire, which is obviously dependent on the capacitance (which I can calculate) and the maximum voltage (which I apparently have gotten the wrong answer for).

I also attempted to calculate the maximum charge per unit length just see if it was an error in the answer for the first portion of the question, but no dice.

## What is a cylindrical capacitor?

A cylindrical capacitor is a type of capacitor that consists of two conductive plates separated by a dielectric material in the shape of a cylinder. It is used to store electrical energy and can be found in many electronic devices.

## What is breakdown potential?

Breakdown potential, also known as breakdown voltage, is the maximum voltage that a capacitor can withstand before it becomes damaged or malfunctions. It is an important factor to consider when designing and using capacitors.

## How is the breakdown potential of a cylindrical capacitor determined?

The breakdown potential of a cylindrical capacitor is determined by the properties of the dielectric material used, the distance between the two conductive plates, and the shape and size of the plates. It can also be affected by external factors such as temperature and humidity.

## What factors can cause breakdown in a cylindrical capacitor?

There are several factors that can cause breakdown in a cylindrical capacitor, including high voltage, excessive heat, mechanical stress, and contamination. These factors can weaken the dielectric material and lead to a breakdown in the capacitor.

## How can the breakdown potential of a cylindrical capacitor be increased?

The breakdown potential of a cylindrical capacitor can be increased by using a higher quality dielectric material, increasing the distance between the plates, and reducing external factors such as temperature and humidity. The shape and size of the plates can also be optimized to improve the breakdown potential.

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