http://xkcd.com/356/
Solve THAT!
Heck, sneak that into the teachers pile to be graded and watch'em implode!
Solve THAT!
Heck, sneak that into the teachers pile to be graded and watch'em implode!
then again, infinite resistance in parallel should tend to zero resistance.Just a stab-in-the-dark.
Hmmm, the delights of infinities. In fact if I = 0 then this would violate KCL so that can't be right.then again, infinite resistance in parallel should tend to zero resistance.
If we only accounted with those 7 resistors in the middle, we should have actually less than 3Ohm. There is a potential difference across that resistor in the middle, and that is a problem.Well, couldn't you just do R=1/(1OHM*n) as n approaches infinity Anyways, what we do know about the problem is that the maximum resistance is 3 Ohms, and the theoretical minimum is 0.
Yes. But my above question still stands about current distributed through an infinite number of branches.Should have near zero resistance. It is an infinite resistor grid, right?
I guess the current will not be equal in all branches if we apply voltage to those nodes. My guess is that the current will be greater between those two points.Yes. But my above question still stands about current distributed through an infinite number of branches.
Dave
Sure, each branch will have a different resistance depending on your routing. It's unimaginable becuase the grid is infinite.I guess the current will not be equal in all branches if we apply voltage to those nodes. My guess is that the current will be greater between those two points.
But then again, it depends on where you apply the voltage.
I though I could use the formula of the distance for that, but diagonally across each square you have 1Ohm (not accounting with the other resistors). Was a wild guess. The solution was in Fourier analysis indeed, as I first guessed.Sure, each branch will have a different resistance depending on your routing. It's unimaginable becuase the grid is infinite.
In fact I've just done a Google search and come up something that will help (I say help tongue in cheek!) with the answer. If we assume each resistor is 1\(\Omega\) (keep it simple) then the resistance diagonally across a box is:
R = \(\frac{2}{\pi}\)
See: http://www.geocities.com/frooha/grid/node2.html (get your calculus books out! )
Dave
When dealing with solutions tending into infinity it is often the soundest (and many cases, along side Laplacian, the only) approach. The treatise of the solution in the above link is an impressive effort, and I cannot (at the moment) see a flaw in the logic.The solution was in Fourier analysis indeed, as I first guessed.
Would it be necessary to resort to Fourier analysis if we were to calculate the resistance of a finite grid with 7 resistors arranged the same way between those two points? I can't see how to calculate using other method.When dealing with solutions tending into infinity it is often the soundest (and many cases, along side Laplacian, the only) approach. The treatise of the solution in the above link is an impressive effort, and I cannot (at the moment) see a flaw in the logic.
Dave
0---0---B
| | | Determine resistance between points A and B, assuming that the resistors are 1Ohm ideal resistors.
A---0---0
You need to use the DsFT to allow you to calculate the current and voltages at nodes A and B since m and n (the grid dimensions) are infinite; ref. equations (28) and (30). In your example above the current and voltage calculations at A and B would be different and hence the resistance will be different.Would it be necessary to resort to Fourier analysis if we were to calculate the resistance of a finite grid with 7 resistors arranged the same way between those two points? I can't see how to calculate using other method.
Rich (BB code):0---0---B | | | Determine resistance between points A and B, assuming that the resistors are 1Ohm ideal resistors. A---0---0
Spoilsport!One: there is no such thing as an "ideal" resistor.
Two: there are a finite number of resistors in the real universe.
Lol! Is that secret answer number 4?!Three: Having adroitly invoked the logical fallacy of hypothesis contrary to fact I can quite deftly sidestep the oncoming bus, beat up the guy with the sign, steal the sign, and study the problem at my leisure.
by Duane Benson
by Aaron Carman
by Jake Hertz
by Jake Hertz