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Old 2009-03-29, 13:21   #1
davieddy
 
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"Lucan"
Dec 2006
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Default Find the resistance between A and B

Equilateral triangles are inscribed ad infinitum by joining
the midpoints of the sides of the previous one.
They are made of wire with resistance r per unit length.
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Old 2009-03-29, 22:01   #2
Orgasmic Troll
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just to see if I have the right idea of calculating resistance, if the following diagram has 1 ohm of resistance on each segment, is the total resistance from A to C 5/6?
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Old 2009-03-29, 22:19   #3
akruppa
 
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B and D are on the same potential, so there's never any current between them. The resistance is still 1 Ohm from A to C.

Alex
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Old 2009-03-30, 01:11   #4
davieddy
 
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This wasn't supposed to turn into an elementary physics
lesson, but in the vein of the last posts, it is worth noting
that for the purposes of the question, the midpoint of AB could
be isolated from the inner triangles.
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Old 2009-03-30, 01:57   #5
frmky
 
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Hmmm. I did a few cases, using symmetry to simplify the calculations, and ended up with resistances (in units of ar) of 2, 5/4, 28/23, and 79/65 in parallel with the straight section from A to B. These lead to total resistances of 2/3, 5/9, 28/51, and 79/144 between A and B. Definitely converging, but to what I'm not sure.
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Old 2009-03-30, 02:55   #6
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0.535ar

Details available upon request if it turns out to be correct.

William
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Old 2009-03-30, 06:16   #7
Visu
 
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ar, the length from A to B (a) multiplied by the resistance per unit length r.
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Old 2009-03-30, 07:03   #8
Batalov
 
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Too easy. Go on to the infamous google labs problem depicted in [URL]http://xkcd.com/356/[/URL] "It's fun! Physicists are two points, mathematicians three."

(sqrt7-1)/3 ~= 0.54858...

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Old 2009-03-30, 09:41   #9
davieddy
 
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Quote:
Originally Posted by wblipp View Post
0.535ar

Details available upon request if it turns out to be correct.

William
You expect me to work it out?

I know how to do it in principle.
Meanwhile Batalov doesn't quite agree.

I have every confidence in you William, and am definitely
sure about the ar bit of it.

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Old 2009-03-30, 09:51   #10
davieddy
 
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Quote:
Originally Posted by Visu View Post
ar, the length from A to B (a) multiplied by the resistance per unit length r.
In parallel with something a bit trickier.
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Old 2009-03-30, 10:59   #11
davieddy
 
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Quote:
Originally Posted by davieddy View Post
and am definitely
sure about the ar bit of it.
Nudge nudge, wink wink, this was a hint folks.
No I don't come from Purley, although like that Jacqui minister
woman, I do share some partiality with "Photography" (geddit?)

David
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