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Paschen's Law

Paschen's law is an equation that gives the breakdown voltage—that is, the voltage necessary to start a discharge or electric arc between two electrodes in a gas as a function of pressure and gap length.

The breakdown voltage equals the product of the constant a, the gap distance and the gas pressure divided by the natural logarithm of the product of the constant b, the gap distance and the gas pressure.

Formula

QuantityVariable["V", "ElectricPotential"] == (QuantityVariable["a", "Unitless"]*QuantityVariable["d", "Length"]*QuantityVariable["P", "Pressure"])/Log[QuantityVariable["b", "Unitless"]*QuantityVariable["d", "Length"]*QuantityVariable["P", "Pressure"]]

symbol description physical quantity
V breakdown voltage "ElectricPotential"
b constant b "Unitless"
d gap distance "Length"
P pressure "Pressure"
a constant a "Unitless"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Paschen's Law"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ResourceObject["Paschen's Law"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Paschen's Law"], {QuantityVariable["P","Pressure"] -> Quantity[1, "Atmospheres"]}]
Out[3]=

Source Metadata

  • Creator:
  • Date: 1889

Publisher Information