# Electrical Engineering: Equivalent Resistance Problem

• student4321
In summary, the problem involves finding the equivalent resistance between points a and b, and between points a and c in a 3-D square circuit with all resistors having resistance R. To solve this, you can combine parallel resistors on the front, left, and back edges and continue combining resistors in series until you end up with only two resistors left. Alternatively, you can use Kirchoff's laws and take advantage of points of symmetry in the circuit to simplify the 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

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.

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.

Last edited by a moderator:
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!

## What is electrical engineering?

Electrical engineering is a field of engineering that deals with the study and application of electricity, electronics, and electromagnetism. It involves the design, development, and maintenance of electrical systems, devices, and components.

## What is equivalent resistance?

Equivalent resistance is a term used in electrical engineering to describe the total resistance of a circuit when resistors are connected in a series or parallel configuration. It represents the combined effect of all the resistors in the circuit.

## How do you calculate equivalent resistance?

The calculation of equivalent resistance depends on the configuration of the resistors in the circuit. For resistors in series, you simply add their resistances together. For resistors in parallel, you can use the formula 1/Req = 1/R1 + 1/R2 + ... + 1/Rn, where Req is the equivalent resistance and R1, R2, etc. are the individual resistances.

## Why is equivalent resistance important?

Equivalent resistance is important because it helps simplify complex circuits into a single resistor, making it easier to calculate the total current and voltage in the circuit. It also allows for the replacement of multiple resistors with a single resistor, reducing the complexity and cost of a circuit.

## What are some practical applications of equivalent resistance?

Equivalent resistance is used in various electrical engineering applications, including circuit analysis, design, and troubleshooting. It is also important in designing electrical systems for buildings, vehicles, and electronic devices, as well as in the development of renewable energy technologies such as solar panels and wind turbines.

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