Equivalent Resistance of Cube of Resistors: A to B

In summary, the problem involves finding the equivalent resistance between points A and B in a cube of resistors with each resistance having a value of "R". The suggested solution in the book includes using parallel combinations, which the speaker agrees with but also expresses doubt due to symmetry. The speaker also mentions that the potentials of points D and E, as well as C and F, are equal due to a symmetry plane, making it possible to connect them with a wire.
  • #1
nil1996
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7

Homework Statement


Here is a cube of resistors with each resistance of value "R".Find the equivalent resistance between A and B.

attachment.php?attachmentid=66606&stc=1&d=1392346578.jpg


Homework Equations


The Attempt at a Solution



My book says the equivalent circuit of the cube is :

attachment.php?attachmentid=66607&stc=1&d=1392346578.jpg


But i don't think it is correct.They have made parallel combinations which don't seem right.Is the book correct??
 

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  • #2
you need to make your figures smaller. They are HUGE.

I agree w/ you that it doesn't seem correct but I'm guessing they are using some trick of symmetry in the redrawing.
 
  • #3
The plane through the points ABGH is a symmetry plane, so the potentials of the points D and E must be equal, so you can connect them with a wire. Same for the points C and F.
 
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  • #4
willem2 said:
The plane through the points ABGH is a symmetry plane, so the potentials of the points D and E must be equal, so you can connect them with a wire. Same for the points C and F.

O,thanks a lot :smile:
 
  • #5


I cannot definitively say whether the book is correct or incorrect without further information. However, based on the provided diagram, it appears that the book has correctly applied the principles of parallel and series resistors to determine the equivalent resistance between points A and B. It is possible that the book has simplified the circuit in a way that may not be immediately apparent, but it is also possible that there is an error in the diagram or solution. If you have doubts about the solution provided, it would be best to consult with your instructor or a more experienced scientist for clarification.
 
  • #6
nil1996 said:

Homework Statement


Here is a cube of resistors with each resistance of value "R".Find the equivalent resistance between A and B.

View attachment 167327

Homework Equations


The Attempt at a Solution



My book says the equivalent circuit of the cube is :

View attachment 167328

But i don't think it is correct.They have made parallel combinations which don't seem right.Is the book correct??
I realize this is a decade old thread but I checked it and it is correct.
 
Last edited:
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  • #7
bob012345 said:
I realize this is a decade old thread but I checked it and it is correct.
I thought of your simulations when I saw this thread pop up! :smile:
 
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FAQ: Equivalent Resistance of Cube of Resistors: A to B

1. What is the definition of equivalent resistance?

Equivalent resistance refers to the combined resistance of multiple resistors that are connected in a circuit. It represents the total resistance that the current experiences as it flows through the circuit.

2. How is the equivalent resistance of a cube of resistors calculated?

The equivalent resistance of a cube of resistors can be calculated by taking the sum of the individual resistances in the cube and then dividing it by the number of resistors. For example, if a cube has 8 resistors with a resistance of 10 ohms each, the equivalent resistance would be 10 ohms (8 resistors x 10 ohms each = 80 ohms; 80 ohms / 8 resistors = 10 ohms).

3. What is the purpose of calculating the equivalent resistance of a cube of resistors?

Calculating the equivalent resistance of a cube of resistors allows scientists and engineers to understand how the resistors in a circuit will affect the flow of current. It also helps in designing circuits by determining the appropriate resistor values to achieve the desired resistance.

4. What factors can affect the equivalent resistance of a cube of resistors?

The equivalent resistance of a cube of resistors can be affected by factors such as the number of resistors, their individual resistance values, and how they are connected in the circuit. For example, resistors connected in parallel will result in a lower equivalent resistance compared to resistors connected in series.

5. How can the equivalent resistance of a cube of resistors be used in real-world applications?

The concept of equivalent resistance is important in various real-world applications, such as in electrical circuits, electronic devices, and power systems. It helps in determining the overall resistance of a circuit and ensuring that the correct amount of current is supplied to the components. It is also used in designing and troubleshooting circuits to ensure proper functioning and safety.

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