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Re: [Phys-l] Infinite net resistors expression deduction

Hi all-
This mostly works, but there are conditions. Se Hardy"s book on Divergent Series. There has been some discussion of this in AJP.
Regards,
Jack

"Trust me. I have a lot of experience at this."
General Custer's unremembered message to his men,
just before leading them into the Little Big Horn Valley




On Tue, 19 Apr 2011, Herbert Schulz wrote:


On Apr 19, 2011, at 8:29 AM, CARABAJAL PEREZ, MARCIAL ROBERTO wrote:

Hello:

Please, I am looking to develop an infinite network of resistances in this way

--R1 ----|----R1----|----
R3 R3 ...................>>>>
--R1 ----|----R1----|----

I know that the solution is Req = R1 + sqr(R1*R1 + 2 R1*R3)

The idea is to resolve it as a limit of a serie, but I can´t find the way. Does this class of solution exists? I could not find it anywhere.

I would appreciate any help with this problem.

My best regards.
Roberto


Howdy,

Call the total resistance of the system R. Imagine making a vertical cut to the right of the first R3. Notice that since it's infinite what is left to the right is the same circuit so it must have resistance R. Then what you have is just


--R1 ----|----|
R3 R
--R1 ----|----|

so that

R = 2(R1) + 1/(1/(R3) + 1/R)

and solve for R.

Good Luck,

Herb Schulz
(herbs at wideopenwest dot com)



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