A question on finding the resistance from a 3D cube

[Kudo Shinichi]

Homework Statement

Find the resistance between the points a and b for the resistor network shown.
http://s5.tinypic.com/1073kvd.jpg

The Attempt at a Solution

I changed to 3D cube into a 1D square and each side of the square contains 3r because each side of the cube contains an r(for each line it has up side, middle side and the down side)
http://s5.tinypic.com/2chu7hk.jpg
opposite line: 1/3r+1/3r=(3r+3r)/(9r^2)
and there are two sets of opposite line and we add them together
the final answer I got is (12r)/(18r^2)
I am wondering is it the right way to solve this problem?
any comment or help would be great. thank you very much

 

[alphysicist]

Hi Kudo Shinichi,

Homework Statement

Find the resistance between the points a and b for the resistor network shown.
http://s5.tinypic.com/1073kvd.jpg

The Attempt at a Solution

I changed to 3D cube into a 1D square and each side of the square contains 3r because each side of the cube contains an r(for each line it has up side, middle side and the down side)
http://s5.tinypic.com/2chu7hk.jpg

I don't think that will give the correct answer here. The usual way to solve these types of problems are to look for points that have the same potential (using a symmetry reasoning) and think about connecting those points with a bare wire. If the points are at the same potential then adding a wire will have no effect on the circuit, but it will allow you to see how you can combine resistors in parallel, etc. So what points can you connect with a bare wire in this cube?

Also, if a resistor is connected between two points that are at the same potential, then no current goes through the resistor and you can disregard it.

 

[Kudo Shinichi]

Hi Kudo Shinichi,



I don't think that will give the correct answer here. The usual way to solve these types of problems are to look for points that have the same potential (using a symmetry reasoning) and think about connecting those points with a bare wire. If the points are at the same potential then adding a wire will have no effect on the circuit, but it will allow you to see how you can combine resistors in parallel, etc. So what points can you connect with a bare wire in this cube?

Also, if a resistor is connected between two points that are at the same potential, then no current goes through the resistor and you can disregard it.

Sorry, I don't really get what you were saying... I think that all the eight points have the same potential and should since there are no extra battery in the circuit. should I connect all the point diagonally with wires? but the question says each side of the cube has the resistance of r and i don't really know how will this help me to get the total resistance in this circuit.

 

[alphysicist]

Sorry, I don't really get what you were saying... I think that all the eight points have the same potential and should since there are no extra battery in the circuit. should I connect all the point diagonally with wires? but the question says each side of the cube has the resistance of r and i don't really know how will this help me to get the total resistance in this circuit.

There's no battery shown, but the equivalent resistance between points A and B is the same as if there were a battery between A and B. So the idea is that if there were a potential difference between A and B, then which points would have the same potential?

For example, let's pretend that instead of a cube you just have the square that is the bottom of the cube, and you still want to find the resistance between the bottom left corner and the top right corner. That would actually be a straightforward calculation, because you could first combine the left and top side in series, then the bottom and right side in series, and then combine the two in parallel. (Shown in the top two diagrams of the image below.)

However, an alternate method (and that would also help in your more complicated problem) would be to say that if a battery were connected between A and B, then the symmetry shows that the potential of the top left and bottom right corners are the same (because all the resistors are the same). So you could connect the top left and bottom right corners with a bare wire (no resistance). Once that is done, the bottom and left resistors are in parallel, and the top and right resistors are in parallel. So you could first combine those in parallel and then add them in series.



http://img4.imageshack.us/img4/8080/circuitconnections.jpg



The point of this simpler case is just that you can connect the top left and bottom right corners with a wire, if that would help combine the resistors.

So for your cube, what points would be at the same potential, if points A and B were connected to a battery? If you combine those points with a bare wire, you can start combining resistors.