Paschen Law Calculator California

Paschen's Law Equation:

\[ V_{bd} = \frac{B \cdot p \cdot d}{\ln(A \cdot p \cdot d) - \ln\left(\ln\left(1 + \frac{1}{\gamma}\right)\right)} \]

Constant B:

V/(Torr·cm)

Pressure (p):

Torr

Distance (d):

Constant A:

1/(Torr·cm)

Secondary Emission Coefficient (γ):

unitless

Breakdown Voltage (V_bd):

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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 gas discharge phenomena.

2. How Does the Calculator Work?

The calculator uses Paschen's Law equation:

\[ V_{bd} = \frac{B \cdot p \cdot d}{\ln(A \cdot p \cdot d) - \ln\left(\ln\left(1 + \frac{1}{\gamma}\right)\right)} \]

Where:

\( V_{bd} \) — Breakdown voltage (V)
\( B \) — Constant (V/(Torr·cm))
\( p \) — Pressure (Torr)
\( d \) — Distance between electrodes (cm)
\( A \) — Constant (1/(Torr·cm))
\( \gamma \) — Secondary emission coefficient (unitless)

Explanation: The equation shows that breakdown voltage depends on the product of pressure and gap distance (p·d), with constants that vary with gas composition.

3. Importance of Breakdown Voltage Calculation

Details: Accurate breakdown voltage calculation is crucial for designing electrical insulation systems, high-voltage equipment, and understanding discharge phenomena in various gases.

4. Using the Calculator

Tips: Enter all parameters in the specified units. Typical values for dry air: A = 14.6, B = 365, γ = 0.01. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What gases does Paschen's Law apply to?
A: Paschen's Law applies to all gases, but the constants A and B vary with gas composition and electrode material.

Q2: What is the Paschen minimum?
A: The minimum breakdown voltage occurs at a specific p·d product, typically around 0.5-1 Torr·cm for air.

Q3: How does temperature affect the calculation?
A: Temperature affects gas density and thus the effective pressure. Use corrected pressure values for accurate results at different temperatures.

Q4: What are typical γ values?
A: γ typically ranges from 0.001 to 0.1, depending on electrode material and gas composition.

Q5: How accurate is this calculation?
A: The calculation provides theoretical values. Actual breakdown voltages may vary due to surface conditions, electrode geometry, and gas impurities.