Re: What's the total resistance of this network?



Dave Farrance wrote:

I'm designing a circuit and found myself unable to figure out the
resistor values. How embarrassing. After trying to break down the
problem using equivalent circuits, I found that the problem in its most
basic form is that I can't figure out the total resistance of this:

(fixed pitch needed to display this, of course)


---------------/\/\/\/-----------
| d |
a | b c |
o----+----/\/\/\/----+----/\/\/\/----+----/\/\/\/----+----o
| |
| e |
----------/\/\/\/----------------


Anybody know? Or maybe somebody could point me to a web resource with
tips on how to get to grips with a tangled network like this?

Here is a rare case when delta-to-wye conversion is useful; take the 3 points described by b, c, and d (note the delta configuration, and convert it to a wye resistor configuration B, C, and D (same points; now have an extra point in "middle".
The derivation of that conversion is fairly simple but i have never seen it mentioned in any university of note (over the past 50 years).
Once you have the wye values, the reduction is simple.
BTW, this is the classical bridge, so if there is any symmetry, even on a ratio basis, take advantage.

There are at least 4 different ways to solve the "resistor cube" problem (what is the resistance across the farmost corners, given all sides are of one ohm resistors); many "cheat" based on the symmetry.

.



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