Breakdown voltages for insulators can be obtained from tables. In some cases, they also can be calculated with formulae. A simple system consists of two parallel conducting plates, with air in between, and an applied voltage V across them. The result is an electric field E = V/d going from one plate to the other, where d is the distance between the plates. If the applied voltage becomes large enough, ionization of the air occurs. Atoms normally have equal amounts of negative and positive electrical charge, which means they are not able to conduct electric current under the force of an electric field. When ionization occurs, atoms lose some of the negative charge, resulting in a gas of electrically charged particles that moves under the influence of the electric field.

Write out the formula for the breakdown voltage. The formula for the breakdown voltage is: Vbreakdown = B * p * d / (C + ln( p * d)), where p is the pressure of the gas, d is the distance between the two conducting plates and B and C are constants that are determined by experiments. For example, the gas could be air.

Get the constants B and C. The constants can be obtained from published articles that give experimental results, such as "Nuclear Instruments and Methods in Physics Research”; Standardization of gas amplification description in proportional counters, by A Zastawny in 1997. This article is available online. For air, the constants have the values B = 365 V/(cm Torr) and C = 1.18.

Calculate the pressure. For example, if the pressure of the gas is the same as your surroundings, then it is at atmospheric pressure. In SI units, the pressure is given in pascals. However, most data on this subject is given using the unit torr instead. To convert from pascals to torr, multiply the pressure in pascals by 0.0075. For atmospheric pressure, the value is p=760 torr.

Calculate the distance d between the plates. The units should be consistent with the length of units of the constant B. In this case, centimeters are used as the length unit.

Calculate the breakdown voltage. For example, for air at atmospheric pressure with a 1 cm gap between the plates, Vbreakdown = 365 * 760 * 1 / (1.18 + ln( 760 * 1)) = 35,503 Volts.

#### References

- “Introduction to Plasma Physics and Controlled Fusion”; Francis F. Chen; 1984
- dielectrics
- breakdown voltage

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