Find the resistance between A and B

davieddy · 2009-03-29, 13:21

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.

Orgasmic Troll · 2009-03-29, 22:01

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?

akruppa · 2009-03-29, 22:19

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

davieddy · 2009-03-30, 01:11

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.

frmky · 2009-03-30, 01:57

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.

wblipp · 2009-03-30, 02:55

0.535ar

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

William

Visu · 2009-03-30, 06:16

ar, the length from A to B (a) multiplied by the resistance per unit length r.

Batalov · 2009-03-30, 07:03

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...

davieddy · 2009-03-30, 09:41

Quote:

Originally Posted by wblipp

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.

davieddy · 2009-03-30, 09:51

Quote:

Originally Posted by Visu

ar, the length from A to B (a) multiplied by the resistance per unit length r.

In parallel with something a bit trickier.

davieddy · 2009-03-30, 10:59

Quote:

Originally Posted by davieddy

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

2009-03-29, 13:21	#1
davieddy "Lucan" Dec 2006 England 1100101001010₂ Posts	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. Attached Thumbnails

2009-03-29, 22:01	#2
Orgasmic Troll Cranksta Rap Ayatollah Jul 2003 641 Posts	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? Attached Thumbnails

2009-03-30, 07:03	#8
Batalov "Serge" Mar 2008 Phi(4,2^7658614+1)/2 2438₁₆ Posts	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... Last fiddled with by Batalov on 2009-03-30 at 07:55

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2009-03-29, 22:19	#3
akruppa "Nancy" Aug 2002 Alexandria 2,467 Posts	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

2009-03-30, 01:11	#4
davieddy "Lucan" Dec 2006 England 2×3×13×83 Posts	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.

2009-03-30, 01:57	#5
frmky Jul 2003 So Cal 11²·17 Posts	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.

2009-03-30, 02:55	#6
wblipp "William" May 2003 New Haven 2³×5×59 Posts	0.535ar Details available upon request if it turns out to be correct. William

2009-03-30, 06:16	#7
Visu Nov 2006 Singapore 113₈ Posts	ar, the length from A to B (a) multiplied by the resistance per unit length r.