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Registered Member #1438
Joined: Sat Apr 12 2008, 12:57AM
Location: Canada
Posts: 218
I was recently trying to figure out a more accurate breakdown voltage of air at my altitude however I obtained a very odd result.
Calculating according to the formula on the 4hv wiki which can be found here I calculated a breakdown voltage of 0.0979653682 volts at 2cm which does not seem correct at all.
When I cross checked the 'a' constant for standard atmospheric pressure towards wikipedia's 'a' constant which happened to be 4.36x10^7, I calculated my answer to be 97kv which again didn't seem correct.
Did I make a calculation mistake that I've failed to recognize or am I using an incorrect unit or constant?
Numbers used for calculation Pressure: 0.996792499 atm Distance: 0.02m 'a' constant: 43.66 and 4.36x10^7 'b' constant: 12.8
Registered Member #2939
Joined: Fri Jun 25 2010, 04:25AM
Location:
Posts: 615
After fiddling with a calculator for a while I conclude that the wikipedia value of 'a' is correct - it gives ~3.5MV for 1m at 1atm. Crude linear scaling to 2cm gives ~70kV, so your calculated 97kv seems reasonable.
Registered Member #2099
Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716
I agree with 2spoons, you're in the right ballpark. My rule of thumb is 3000 V/mm for breakdown electric field strength in air. That's not generally the same as voltage divided by gap length, because the field is intensified near conductor points and edges.
Here are some data from my 56th edition (1975-1976) CRC Handbook of Chemistry and Physics. It's more than 3 inches thick, in case that connotes authority.
Spark-Gap Voltages Based on results of the American Institute of Electric Engineers Air at 760 mm, 25 degrees C
For peak voltages of 20, 40, and 60 kV, the spark gap lengths for 2.5 cm diameter electrodes are 0.58, 1.41, and 2.82 cm. for 5 cm diameter electrodes are 0.60, 1.30, and 2.17 cm. for 10 cm diameter electrodes are 0.62, 1.29, and 2.02 cm. for needle points are 1.75, 3.81, 6.81 cm.
Needle points give voltage/gaplength values around 1000 V/mm, but they are the least repeatable electrode size in spark-gap voltmeters,
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Paschen's Law (problem)
