From: John Larkin
Subject: Re: Resistance of a Sphere Revisited
Date: Sat, 30 Nov 2002 14:10:53 -0800
Organization: Posted via Supernews, http://www.supernews.com
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On 30 Nov 2002 12:43:30 -0800, email@example.com (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
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.