Equivalent Resistance of Cube of Resistors: A to B

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SUMMARY

The equivalent resistance between points A and B in a cube of resistors, each with resistance value "R", can be determined using symmetry principles. The discussion confirms that the book's approach, which involves connecting points D and E, as well as C and F, due to equal potentials, is indeed correct. This method simplifies the circuit by recognizing the symmetry plane through points ABGH, allowing for accurate calculations of equivalent resistance.

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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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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.
 
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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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:
 
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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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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