Paschen's Law Calculator Manual

Paschen's Law Equation:

\[ V = \frac{B p d}{\ln(A p d) + 1} \]

Breakdown Voltage (V):

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1. What is Paschen's Law?

Paschen's Law describes the breakdown voltage necessary to initiate an electrical discharge in a gas between two electrodes. It shows the relationship between breakdown voltage and the product of gas pressure and electrode distance.

2. How Does the Calculator Work?

The calculator uses Paschen's Law equation:

\[ V = \frac{B p d}{\ln(A p d) + 1} \]

Where:

\( V \) — Breakdown voltage (V)
\( p \) — Gas pressure (torr)
\( d \) — Distance between electrodes (cm)
\( A \) — Constant related to gas properties
\( B \) — Constant related to gas properties

Explanation: The equation shows that breakdown voltage depends on the product of pressure and distance, with constants A and B specific to the gas type.

3. Importance of Breakdown Voltage Calculation

Details: Accurate breakdown voltage calculation is crucial for designing electrical insulation systems, gas-filled devices, and preventing unwanted electrical discharges in various applications.

4. Using the Calculator

Tips: Enter pressure in torr, distance in cm, and appropriate A and B constants for your specific gas. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for constants A and B?
A: Constants vary by gas type. For air: A ≈ 15 cm⁻¹·torr⁻¹, B ≈ 365 V·cm⁻¹·torr⁻¹. Consult gas-specific references for accurate values.

Q2: What is the Paschen minimum?
A: The minimum breakdown voltage occurs at a specific p·d product value. Below and above this minimum, higher voltages are required for breakdown.

Q3: How does temperature affect the calculation?
A: Temperature affects gas density, which influences breakdown characteristics. The equation assumes constant temperature conditions.

Q4: Are there limitations to Paschen's Law?
A: The law works well for uniform electric fields and moderate pressure/distance ranges. It may be less accurate for very high pressures, very small gaps, or non-uniform fields.

Q5: Can this be used for all gases?
A: Yes, but with appropriate A and B constants specific to each gas type and electrode material combination.