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Mike Raiford wrote:
> The resistor blob reminds me of this:
>
> http://www.falstad.com/circuit/e-thevenin.html :D
Impressive...
--
http://blog.orphi.me.uk/
http://www.zazzle.com/MathematicalOrchid*
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> Possibly the most alarming part of this whole thing is the number of forum
> users who have managed to compute the actual resistance of the tangle of
> resistors near the middle.
V = I * R for each resistor
and
Sum(current into a node) = 0
Solve.
There's probably a matrix method for doing it, where you get to invert a big
matrix, rather than solving all the simultaneous equations by hand.
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scott wrote:
>> Possibly the most alarming part of this whole thing is the number of
>> forum users who have managed to compute the actual resistance of the
>> tangle of resistors near the middle.
>
> V = I * R for each resistor
> and
> Sum(current into a node) = 0
>
> Solve.
>
> There's probably a matrix method for doing it, where you get to invert a
> big matrix, rather than solving all the simultaneous equations by hand.
Sure. But the drawing isn't exactly ledgible, and there's a hell of a
lot of resistors in there...
(This probably explains why every single poster got a different answer.)
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> Sure. But the drawing isn't exactly ledgible, and there's a hell of a lot
> of resistors in there...
I took a screen shot and zoomed it up 400%, the connections are quite clear.
> (This probably explains why every single poster got a different answer.)
I got 0.625 ohm by building a Ybus matrix (basically tells you the
conductance between each pair of nodes) and inverting it.
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>> (This probably explains why every single poster got a different answer.)
>
> I got 0.625 ohm by building a Ybus matrix (basically tells you the
> conductance between each pair of nodes) and inverting it.
Right.
Scott: 0.625 Ohms
pyroman: 1.3141 Ohms
hthall: 167294/195327 Ohms ( ~0.856 Ohms)
phlip: 25265/33783 Ohms ( ~0.747861 Ohms)
mu-zak: 0.77 Ohms
EngPhys: 0.758 Ohms
Kirby: 0.7479 Ohms
So most people agree it's roughly 1 Ohm, but there's still a fair bit of
variation there...
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>> I got 0.625 ohm by building a Ybus matrix (basically tells you the
>> conductance between each pair of nodes) and inverting it.
>
> Right.
>
> Scott: 0.625 Ohms
> pyroman: 1.3141 Ohms
> hthall: 167294/195327 Ohms ( ~0.856 Ohms)
> phlip: 25265/33783 Ohms ( ~0.747861 Ohms)
> mu-zak: 0.77 Ohms
> EngPhys: 0.758 Ohms
> Kirby: 0.7479 Ohms
>
> So most people agree it's roughly 1 Ohm, but there's still a fair bit of
> variation there...
:-) I never said I got the right answer, I just told you the simple way to
calculate it (rather than trying to solve 100 simultaneous equations)
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Invisible wrote:
> Scott: 0.625 Ohms
> pyroman: 1.3141 Ohms
> hthall: 167294/195327 Ohms ( ~0.856 Ohms)
> phlip: 25265/33783 Ohms ( ~0.747861 Ohms)
> mu-zak: 0.77 Ohms
> EngPhys: 0.758 Ohms
> Kirby: 0.7479 Ohms
Oh, we've got more:
fewfriesshort: 265 mOhm, revised to 1.97 Ohms.
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Invisible wrote:
> http://www.xkcd.com/730/
>
> Possibly the most alarming part of this whole thing is the number of
> forum users who have managed to compute the actual resistance of the
> tangle of resistors near the middle.
The computations are not that difficult. For any triangular
configuration of resistors there is a Y-shaped configuration that has
the same resistance, between any two of the three corners, as the
triangular configuration. Repeated substitution, and combination of
resistors in series and parallel, allows the circuit to be simplified.
Regards,
John
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> The computations are not that difficult. For any triangular
> configuration of resistors there is a Y-shaped configuration that has
> the same resistance, between any two of the three corners, as the
> triangular configuration. Repeated substitution, and combination of
> resistors in series and parallel, allows the circuit to be simplified.
That's a lot of scope for errors, if you're doing it by hand...
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>> I got 0.625 ohm by building a Ybus matrix (basically tells you the
>> conductance between each pair of nodes) and inverting it.
>
> Right.
>
> Scott: 0.625 Ohms
> pyroman: 1.3141 Ohms
> hthall: 167294/195327 Ohms ( ~0.856 Ohms)
> phlip: 25265/33783 Ohms ( ~0.747861 Ohms)
> mu-zak: 0.77 Ohms
> EngPhys: 0.758 Ohms
> Kirby: 0.7479 Ohms
>
> So most people agree it's roughly 1 Ohm, but there's still a fair bit of
> variation there...
OK so I should have checked my 14x14 matrix before asking Excel to invert
it, apparently the numerical error is quite high in Excel's matrix inverse
function (and this matrix is quite badly formulated). Solving it with a
Gauss solver I wrote before (probably for some random Project Euler problem)
I get 0.7479 ohms, which is the same as Kirby.
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