Resistance calculation in a cube

In summary, the conversation discusses finding the equivalent resistance across any two adjacent vertices of a cube, where each edge and body diagonal is built with a one ohm resistor. The person attempting the question is considering using star and delta transformations and is hoping for a reply with some help. They also provide a figure with parallel and series connections of resistors. Eventually, they are able to solve the question and thank the person for their effort.
  • #1
cooltwins
3
0

Homework Statement



each edge of a cube is built with a one ohm resistor, body diagonals are also built with one ohm resistors each. find out equivalent resistance across any two adjacent vertices.

Homework Equations



i guess it deals with star and delta transformations

The Attempt at a Solution



i'm attempting the question at the present and will post my solution once I'm done with the question.

hoping for a reply from you,

cheers
cooltwins
 
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  • #2
come on guys,

any help...

i've been trying frantically with no results. i could do with some help
 
  • #3
hay..

just look at the network. here resistor a,b, and c(color green) are parallel and d,e,f,g,h,i(blue) are in parallel and j,k,l(red) are parallel in figure 1. While all these(green-blue-red) are connected in series. Look figure 2.
 

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  • #4
thanks for taking the effort mate :) got the solution :D
thanks again
 
  • #5


Hello cooltwins,

Thank you for reaching out and sharing your question. The calculation of resistance in a cube can be approached in a few different ways, one of which is using the star-delta transformation method as you mentioned. This method involves transforming the resistors in the cube into a star or delta configuration, which can then be simplified to find the equivalent resistance.

Another method is to use the concept of parallel and series resistors. In this case, the resistors along the edges of the cube are in series with each other, while the resistors along the body diagonals are in parallel with each other. By simplifying these combinations, you can find the equivalent resistance across any two adjacent vertices.

I look forward to seeing your solution and discussing it further. Keep up the good work in your studies as a scientist!

Best regards,
 

1. How do you calculate the resistance of a cube?

To calculate the resistance of a cube, you will need to know the resistivity of the material the cube is made of and the dimensions of the cube. The formula for resistance is R = (ρ x L)/A, where ρ is the resistivity, L is the length of the cube, and A is the cross-sectional area.

2. What is the unit of measurement for resistance?

The unit of measurement for resistance is ohms (Ω). This unit is named after the German physicist Georg Ohm, who discovered the relationship between voltage, current, and resistance.

3. Can the resistance of a cube change?

Yes, the resistance of a cube can change depending on the material, temperature, and other factors. Some materials have a constant resistivity, while others have a variable resistivity that changes with temperature. Additionally, the resistance of a cube can also change if there are any imperfections or damage to the material.

4. How does the shape of a cube affect its resistance?

The shape of a cube can affect its resistance if the material has a variable resistivity. For example, if a cube has a length of 1 meter on each side, it will have a different resistance than a cube with a length of 2 meters on each side, even if they are made of the same material. This is because the longer cube has a larger cross-sectional area, resulting in a lower resistance.

5. What are some practical applications of calculating resistance in a cube?

Calculating resistance in a cube is important in many areas of science and technology. It is used in designing and building electronic circuits, as well as in materials engineering to understand the conductivity of different materials. It is also crucial in fields like electrical and mechanical engineering, where the resistance of various components needs to be calculated for proper functioning of machines and devices.

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