Enter the constants B and A, pressure of the gas, distance between the electrodes, and the secondary electron emission coefficient into the calculator to determine the breakdown voltage. This calculator can also evaluate any of the variables given the others are known.

## Paschen’s Law Formula

The following formula is used to calculate the breakdown voltage according to Paschen’s Law.

V = B * pd * ln(A * pd) + ln(1 + 1/γ)

Variables:

- V is the breakdown voltage (V)
- B is the constant that depends on the type of gas
- p is the pressure of the gas (Pa)
- d is the distance between the electrodes (m)
- A is another constant that depends on the type of gas
- γ is the secondary electron emission coefficient

To calculate the breakdown voltage, multiply the pressure of the gas by the distance between the electrodes. Multiply this result by the constant B and the natural logarithm of the product of the constant A and the pressure-distance product. Add the natural logarithm of 1 plus the reciprocal of the secondary electron emission coefficient. The result is the breakdown voltage according to Paschen’s Law.

## What is Paschen’s Law?

Paschen’s Law is a principle in physics that describes the electrical breakdown of gases. It states that the voltage necessary to initiate a discharge or spark in a gas is a function of the product of the pressure of the gas and the distance between the electrodes. This means that the breakdown voltage is determined by the type of gas, its pressure, and the gap between the electrodes. The law is named after Friedrich Paschen, a German physicist who first formulated it in 1889.

## How to Calculate Paschen’s Law?

The following steps outline how to calculate the breakdown voltage using Paschen’s Law.

- First, determine the constant B for the specific type of gas being used.
- Next, determine the pressure of the gas (p) in Pascal (Pa).
- Next, determine the distance between the electrodes (d) in meters (m).
- Next, determine the constant A for the specific type of gas being used.
- Next, determine the secondary electron emission coefficient (γ).
- Using the formula V = B * pd * ln(A * pd) + ln(1 + 1/γ), calculate the breakdown voltage (V).
- After inserting the variables and calculating the result, check your answer with the calculator above.

**Example Problem:**

Use the following variables as an example problem to test your knowledge.

Constant B = 0.8

Pressure of the gas (p) = 2.5 Pa

Distance between the electrodes (d) = 0.02 m

Constant A = 1.2

Secondary electron emission coefficient (γ) = 0.5