- Paschen's law
**Paschen's Law**, named afterFriedrich Paschen , was first stated in 1889. [*cite journal*] He studied the

title = Ueber die zum Funkenübergang in Luft, Wasserstoff und Kohlensäure bei verschiedenen Drucken erforderliche Potentialdifferenz

author = Friedrich Paschen

journal = Annalen der Physik

volume = 273

issue = 5

pages = 69–75

year = 1889

url =

doi = 10.1002/andp.18892730505breakdown voltage of parallel plates in agas as a function ofpressure and gapdistance . The voltage necessary to arc across the gap decreased up to a point as the pressure was reduced. It then increased, gradually exceeding its original value. He also found that decreasing the gap with normal pressure caused the same behavior in the voltage needed to cause an arc.**Paschen curve**Paschen found that breakdown voltage was described by the equation

: $V=frac\{a(pd)\}\{ln\; (pd)+b\}$.

Where "V" is the breakdown voltage in

Volts , "p" is the pressure, "d" is the gap distance. Theconstants "a" and "b" depend upon the composition of the gas. For air at standardatmospheric pressure of 760Torr , "a" = 43.6*10^{6}and "b" = 12.8 , where "p" is the pressure in atmospheres and "d" is the gap distance inmeter s. [*[*] The graph of this equation is the Paschen curve. By differentiating it with respect to (pd) and setting the derivative to zero, the minimum voltage can be found. This yields*http://www.ece.rochester.edu/courses/ECE234/MEMS_ESD.pdf Rochester University, Course Handout*]: $pd=e^\{1-b\}$

and predicts the occurrence of a minimum breakdown voltage for (pd)=7.5*10

^{-6}meter atmospheres. This is 327 Volts inair at standard atmospheric pressure at a distance of 7.5micrometers . The composition of the gas determines both the minimum arc voltage and the distance at which it occurs. Forargon , the minimum arc voltage is 137 Volts at a larger 12 micrometers. Withsulfur dioxide , the minimum arc voltage is 457 volts at only 4.4 micrometers.For air at STP, the intensity of the

electric field needed to arc the minimum voltage gap is much greater than that necessary to arc a gap of one meter. For 7.5 micrometers, the field is 43 Megavolts per meter and for one meter it is only 3.4 Megavolts per meter. This is about 13 times greater. The phenomenon is well verified experimentally and is referred to as the Paschen minimum. The equation fails for gaps under a few micrometers in air at one atmosphere and incorrectly predicts an infinite arc voltage at a gap of about 2.7 micrometers.Early vacuum experimenters found a rather surprising behavior. An arc would take place in a long irregular path rather than at the minimum distance between the electrodes. For example, at 1 Torr, the distance for minimum breakdown voltage is 5.7 millimeters or about 0.22 inch. The voltage required to arc that distance is 327 Volts and is greater for gaps above and below that point. For a 2.85 mm gap, the required voltage is 533 Volts, nearly twice as much. If 500 Volts were applied, it would not be sufficient to arc at the 2.85 mm distance, but would arc at a 5.7 mm distance.

**References****External links*** [

*http://home.earthlink.net/~jimlux/hv/paschen.htm High Voltage Experimenter's Handbook*]

* [*http://www.duniway.com/images/pdf/pg/Paschen-Curve.pdf Breakdown Voltage vs. Pressure*]

* [*http://www.stthomas.edu/physics/files/2005-Summer-Paschen-Mike_Cook.pdf Pachen Equation*]

* [*http://www.physics.csbsju.edu/370/jcalvert/dischg.htm.html Electrical Discharges*]

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