Paschen’s Law Calculator
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Paschen’s Law describes the breakdown voltage between two electrodes in a gas, as a function of pressure and the distance between the electrodes. It's a fundamental principle in the field of electrical engineering, especially in the design of insulators and in the study of electrical discharges in gases.
Historical Background
The law is named after Friedrich Paschen who, in 1889, first described the relationship between the breakdown voltage and the product of pressure and distance in a gas. His work laid the groundwork for understanding how electrical discharges occur through gases.
Calculation Formula
Paschen’s Law is given by:
\[ V = B \cdot pd \cdot \ln\left(\frac{pd}{C}\right) \]
Where:
 \(V\) is the breakdown voltage,
 \(p\) is the pressure of the gas (in Pascals),
 \(d\) is the distance between the electrodes (in meters),
 \(B\) and \(C\) are constants that depend on the gas composition and electrode material.
Example Calculation
For air, assuming \(B = 2.5 \times 10^7 \, \text{Pa} \cdot \text{m}\) and \(C = 1\) (simplified), if the pressure is \(101,325 \, \text{Pa}\) (1 atm) and the distance between electrodes is \(0.01 \, \text{m}\), then:
\[ pd = 101,325 \cdot 0.01 = 1,013.25 \, \text{Pa} \cdot \text{m} \]
\[ V = 2.5 \times 10^7 \cdot 1,013.25 \cdot \ln\left(\frac{1,013.25}{1}\right) \approx \text{V} \]
Importance and Usage Scenarios
Understanding Paschen’s Law is crucial for designing electrical equipment that operates under different pressures and distances, such as insulators, gas discharge tubes, and highvoltage equipment. It helps in preventing unintended electrical discharges that could lead to equipment failure or accidents.
Common FAQs

Why does the breakdown voltage change with pressure and distance?
 The ionization mechanism in gases depends on the collision frequency of gas molecules, which is affected by pressure and the distance between electrodes.

Can Paschen’s Law be applied to any gas?
 Yes, but the constants \(B\) and \(C\) vary with the type of gas and the material of the electrodes.

Is there a minimum breakdown voltage according to Paschen’s Law?
 Yes, there's a minimum value of the breakdown voltage at a certain \(pd\) value, indicating an optimal condition for the onset of a discharge.
Paschen’s Law plays a pivotal role in the fields of electrical engineering and physics, guiding the design and analysis of various electrical systems and contributing to our understanding of gas discharge phenomena.