Voltage distance at elevation

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dhalligan
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Voltage distance at elevation

Post by dhalligan »

My son is conducting the static charge experiment and is trying to determine voltage. The formula says that it takes 30,000 V to travel 1 cm at 1 atm. Using an air pressure calculator, we have determined that our atm at 7400ft is .76 atm. Would it take 30,000v / .76 = ~40,000V to travel 1cm at elevation of 7400ft? Or should our calculation be 30,000V * .76 = ~22,500v to travel 1cm at elevation of 7400 ft?
bfinio
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Re: Voltage distance at elevation

Post by bfinio »

Hi dhalligan,

This is an interesting physics question - and frankly one that I had to Google because I'd never considered this before. It looks like the relationship between breakdown voltage, gas pressure, and gap length is determined by something called Paschen's Law:

https://en.wikipedia.org/wiki/Paschen%27s_law

Which as you can see from the description and the graph over on the right, is not a simple linear relationship. Depending on where you are on the graph, if you decrease pressure the breakdown voltage could go up or down.

Just to be clear, when you say "the formula says" - were you already referring to Paschen's Law, or did you find a different formula?

Thanks,

Ben
dhalligan
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Re: Voltage distance at elevation

Post by dhalligan »

Ben, it was a simple experiment posted on this site...
https://www.sciencebuddies.org/science- ... rks?id=944

At the bottom it said "Determining Voltage". So, when it said atmosphere I thought, well we have a little thinner air up here, I wonder if that affects it. Looking at your link is a little beyond the scope of the 4th grade project. But thank you! Very interesting
bfinio
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Re: Voltage distance at elevation

Post by bfinio »

Ah - OK, from your initial description I thought this was a higher grade level project. I did look into it a bit more out of curiosity though. The graph on the Wikipedia page doesn't show air, but if you Google it you can find graphs that do (this one isn't great resolution, just choosing it as an example):

http://www.highvoltageconnection.com/im ... age002.jpg

Notice how the x-axis of the graph is a logarthmic scale, so it shows a huge range. It's also it's measured in torr. 1 atmosphere = 760 torr. So in your case you're at 0.76 * 760 = 577.6 torr...and if you move from 760 to 577 torr on the x-axis of that graph, the breakdown voltage doesn't change THAT much. To see a big change you need to change the pressure by a factor of 10 or so.

Point being - yes, technically the pressure matters, but for a 4th grade project and the amount of pressure change you're dealing with, I think you can safely ignore it. I'm sure it would impress the judges if he mentioned it though!
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