1. What is Paschen's Equation?

Paschen's equation describes the breakdown voltage necessary to initiate an electric discharge in a gas between two electrodes as a function of pressure and gap length. It's fundamental in electrical engineering and plasma physics.

2. How Does the Calculator Work?

The calculator uses Paschen's equation:

Where:

• \( V_{min} \) — Minimum breakdown voltage (V)
• \( B \) — Material-specific coefficient (V/(Torr·cm))
• \( \gamma \) — Secondary electron emission coefficient (unitless)
• \( A \) — Material-specific coefficient (1/(Torr·cm))

Explanation: The equation calculates the minimum voltage required to initiate electrical breakdown in a gas, considering the gas properties and electrode material.

3. Importance of Minimum Voltage Calculation

Details: Knowing the breakdown voltage is crucial for designing electrical insulation systems, high-voltage equipment, and understanding gas discharge phenomena.

4. Using the Calculator

Tips: Enter the B coefficient in V/(Torr·cm), γ (unitless), and A coefficient in 1/(Torr·cm). All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for B and A?
A: For air, A ≈ 15 (1/(Torr·cm)) and B ≈ 365 V/(Torr·cm). Values vary for different gases and electrode materials.

Q2: What is the secondary emission coefficient γ?
A: γ represents the number of secondary electrons emitted per incident positive ion, typically between 0.01 and 0.1 for most materials.

Q3: Does this equation work for all pressure ranges?
A: The equation is valid for the range where the product of pressure and gap distance (pd) falls within the Paschen curve minimum region.

Q4: What factors affect the breakdown voltage?
A: Gas composition, electrode material, surface conditions, temperature, and the product of pressure and gap distance (pd).

Q5: How accurate is this calculation?
A: It provides a theoretical minimum. Actual breakdown voltages may vary due to surface irregularities, impurities, and other practical factors.