From: Jim Thompson
Subject: Re: Resistance of a Sphere Revisited
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Date: Sat, 30 Nov 2002 23:36:43 GMT
NNTP-Posting-Date: Sat, 30 Nov 2002 18:36:43 EST
Organization: Cox Communications
On Sat, 30 Nov 2002 23:10:07 GMT,
"Ed Price" ,
In Newsgroup: sci.electronics.design,
Entitled: "Re: Resistance of a Sphere Revisited",
Wrote the following:
|"John Larkin" wrote in
|> On 30 Nov 2002 12:43:30 -0800, firstname.lastname@example.org (bill) wrote:
|> >If a solid sphere of diameter D has a resistance of 1 ohm (as measured
|> >across the diameter), what will be the resistance of a sphere with
|> >diameter 2D? We use the same meter and probes for both measurements,
|> >so the contact area should be the same, yes?
|> >I've seen other posts on this subject where all sorts of nuances
|> >affecting the measurement are postulated, but how 'bout skipping all
|> >that, make reasonable assumption about the contact area, the meter and
|> >its leads, and give an answer within 10%.
|> >I'm in an arguement with my brother about this and we do not agree.
|> >Seems like there should be a simple way to compute an approximation
|> >for this.
|> >Thanks, Bill
|> As I recall, the resistance is hugely dependent on the contact area,
|> so the 'reasonable assumption' you suggest is impossible. The contact
|> area is not a 'nuance'; for a solid copper sphere, you can get
|> micro-ohms to megohms depending on the contact area.
|> The constriction resistance of a small round contact on a flat surface
|> is Rc = r/d
|> where r = resistivity of material
|> d = diameter of contact.
|> which goes infinite as d approaches zero.
|> This will get weird on a sphere as the contact gets big and approaches
|> covering a hemisphere.
|> And it's not nice to argue with your brother on Thanksgiving.
|Unless your large contact is appreciably crushing the sphere, you would have
|to assume a very small point-contact to any sphere. Imagine the contact to
|be an infinitely large, perfectly flat plane. An undistorted sphere can
|touch the plane at only one, infinitely small point.
|For the purpose of the original poster's question, lets assume the first
|sphere has a diameter of one meter, and is compared to a sphere of two
|meters diameter. Let's assume the probes each have a tiny contact area (if
|you must, make it 0.0005 square cm) in relation to the surface of either a
|one- or two-meter diameter sphere.
|Now, let's get to the geometry of the problem.
Wasn't this problem beaten to death a few months ago? Do a Google
| James E.Thompson, P.E. | mens |
| Analog Innovations, Inc. | et |
| Analog/Mixed-Signal ASIC's and Discrete Systems | manus |
| Phoenix, Arizona Voice:(480)460-2350 | |
| Jim-T@analog_innovations.com Fax:(480)460-2142 | Brass Rat |
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