Electrical Engineering: Equivalent Resistance Problem

[student4321]

Homework Statement

** note that the circuit resembles a 3-d square (the wires aren't "crossing over" each other

In the problem, all circuits have resistance R

If it helps, assume current i flows into a, and leaves through b and c

We are asked to find the equivalent resistance between
a) points a and b
b) points a and c

Homework Equations

series resistance: R(eq) = R1 + R2 + ...
parallel: R(eq) = 1 / ( (1/R1) + (1/R2) + ... )

The Attempt at a Solution

I'm really not sure what to do. How do I go about combining them in the right order, and determining which are in series and which are in parallel?

Thanks

 

[Marioqwe]

If you look at the front side of the cube, you can combine the parallel resistors, top with bottom, and left with right. Now assume that the resulting resistor for the left-right combination is in the right front edge; you can combine it with the resistor parallel to it. And now assume that this new resistor is in the back right edge. Combine that one with the one parallel to it. Just keep doing this with the other resistors and you are going to end up with two resistors in series.

 

[vk6kro]

Sometimes you can make it a bit easier to solve this sort of puzzle if you look for points of symmetry.

For example, in this diagram:
[PLAIN]http://dl.dropbox.com/u/4222062/cube.PNG

You could say that the red points would have the same voltage on them and so would the blue points if you are passing a current from A to C.

So, if they have the same voltage on them, there will not be a current flowing between them if you joined them together with wires.

You can decide if this makes the problem easier. I think it does.

 

[Theaumasch]

Since I'm a Physics major, I don't really know if this is much help, but you could use Kirchoff's laws: http://en.wikipedia.org/wiki/Kirchhoff's_circuit_laws.