January 17, 2006
Consider a spherical cow, covered in resistors
(Anybody who didn't take an A-level in Physics may as well switch off now. Any readers who sat next to me throughout A-level Physics lessons may wish to consider that it might be their fault I wasn't paying enough attention to be able to work this out. ;-) )
This question's been bugging me for days. I did have an answer, but after a spot of googling showed me I was wrong, I realised I was talking rubbish.
Imagine, if you will, a flat square grid of points, such that every point is connected to the 4 adjacent points by a 1Ω resistor. The grid extends infinitely in all directions. What is the resistance between 2 points on the grid a knight's move apart? (e.g. 2 squares up and 1 across, WLOG) Or, for a simpler starter question, what about between 2 points diagonally adjacent? Or even just 2 adjacent points? (Is that as simple as just 1Ω? My hunch is no.)
Maybe I've missed something while googling for answers to this, but if anyone has a good solution I'd be very interested to hear it! Just to clarify, I have some numerical answers from googling, but I'm far more interested in how they're arrived at than what the actual numbers are.
[Update: Chris has considerably better google-fu than me, and found a solution for the diagonal case. It contains hard maths that I can't really justify spending the time to get my head around in the middle of exam season, alas. There's a paper with even more on this too. Eek!]
Posted by James at 22:59
Tags for this entry: questions
lazyweb
maths
electronics
TrackBack URL for this entry:
http://blog.jimbo.org.uk/mt3/mt-tb.cgi/118
You can now subscribe to RSS of comments on this entry or RSS of all comments on this site.
Comments
Post a comment
If you have an OpenID, you can use it to sign in here. Note that Livejournal users can enter the URL of their journal here, and things should work. Let me know of any bugs, this is new!