1. What is Paschen's Law?

Paschen's Law describes the breakdown voltage necessary to initiate an electric discharge between two electrodes in a gas as a function of pressure and gap distance. It's fundamental in designing high-voltage equipment and understanding electrical breakdown in gases.

2. How Does the Calculator Work?

The calculator uses the Paschen's Law equation:

Where:

• \( V \) — Breakdown voltage (V)
• \( a \) — Constant dependent on gas composition (V/(Torr·cm))
• \( p \) — Pressure (Torr)
• \( d \) — Distance between electrodes (cm)
• \( b \) — Secondary coefficient (unitless)

Explanation: The equation shows that breakdown voltage depends on the product of pressure and distance (pd), not on them separately.

3. Importance of Breakdown Voltage Calculation

Details: Accurate breakdown voltage estimation is crucial for designing electrical insulation systems, vacuum equipment, and high-voltage devices to prevent unwanted arcing.

4. Using the Calculator

Tips: Enter the gas-specific constants (a and b), pressure in Torr, and electrode distance in cm. All values must be valid (pressure > 0, distance > 0).

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for constants a and b?
A: For air: a ≈ 43.6×10⁶ V/(Torr·cm), b ≈ 12.8. Values vary for different gases.

Q2: What is the Paschen minimum?
A: The minimum voltage where breakdown occurs at optimal pd product (typically around 1 Torr·cm for air).

Q3: When does Paschen's Law not apply?
A: At very small gaps (< few μm) or very high pressures where field emission dominates.

Q4: How does temperature affect the calculation?
A: Temperature affects gas density, so pressure should be corrected to standard temperature.

Q5: What about AC voltages?
A: Paschen's Law applies to DC. For AC, use peak voltage and consider frequency effects.