Cubic resistor
A wire-frame cube is made of 12 resistors of resistance R. What is the resistance between diagonally opposite corners of the cube?
Labels: funphysics
posted by Chris at
1:16 PM
Friday, February 26, 2010
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10 Comments:
3R?
5/6 R. Dig out your Kirchoff's laws.
A better explanation than I have time for can be found by Googling "cube of resistors".
Oh well! To save you Googling - let a current I enter one of the corners. By symmetry, the current splits down each resistor equally. So I/3 goes down each own. Following the path to the next corner, it can be seen, again by symmetry, that the current is split in half, so each resistor carries I/6. It follows by symmetry (yawn) that the last resistor will be carrying a current I/3. The potential difference, V, across the cube will therefore be RI/3 + RI/6 + RI/3 = 5IR/6. The effective resistance = V/I = 5R/6 Ω.
Sorry Chris. I had a rough day and was feeling somewhat bad-tempered when I posted that ... I remember fighting the resistor cube problem all night back in undergrad school only to have it revealed in minutes during the next class ...
Ross. Don't worry about it. I was the smart Alec who ended up showing everyone how to do it in my class ;)
I know nothing about electricktrickery, other than my brother bought me a really nice chair, powered by the stuff.
Still, as it is effectively a cage, does the Farraday Effect mean there will be no resistance. This probably shows my O-level physics ignorance....
Karl, you're thinking of the situation where there cannot be an electric field inside a good conductor. That is intimately related to the Faraday cage.
Karl. Did this chair have a hemispherical metal cap fixture?
Yes it did, I think it was the built in popcorn maker...
I thought so.
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