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.

 

[DeeNos]

for providing the problem statement. As an electrical engineer, I can see that this problem is asking for the equivalent resistance in a 3-dimensional square circuit. To solve this, we can break down the circuit into smaller parts and use the series and parallel resistance equations to find the equivalent resistance. We can start by identifying which resistors are in series and which are in parallel.

From the problem statement, it is mentioned that current flows into point a and leaves through points b and c. This means that resistors connected to points b and c are in parallel with each other. We can use the parallel resistance equation to find the equivalent resistance between points b and c.

Next, we can see that resistors connected to point a are in series with each other. We can use the series resistance equation to find the equivalent resistance between points a and b or points a and c.

Once we have found the equivalent resistances for each part, we can combine them using the series or parallel resistance equations to find the overall equivalent resistance between points a and b or points a and c.

It is important to carefully analyze the circuit and identify which resistors are in series and which are in parallel. This will help us determine the correct order for combining them and finding the equivalent resistance.

I hope this helps to guide you in solving the problem. Good luck!