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Solve diagonal resistance of resistor 3D mesh.

SOLVED
ttokoro
Peridot

Solve diagonal resistance of resistor 3D mesh.

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Diagonal resistance of regular polyhedron. R(4)=1/2, R(6)=5/6. How about R(8), R(12) and R(20)?

1 ACCEPTED SOLUTION

Accepted Solutions

Re: Solve diagonal resistance of resistor 3D mesh.

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23 REPLIES 23

Re: Solve diagonal resistance of resistor 3D mesh.

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Re: Solve diagonal resistance of resistor 3D mesh.

Hi,

A simplification of the network topology allows you to easily apply Thevenin's theorem:

rete composta 2.jpg

Re: Solve diagonal resistance of resistor 3D mesh.

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Re: Solve diagonal resistance of resistor 3D mesh.

the solution you have provided is more accurate, thanks for sharing this with use... this will really help to other also tellpopeyes!

Re: Solve diagonal resistance of resistor 3D mesh.

Note that this is a different network than the original network of Ttokoro.

If the entrance is at the top (as shown) then the exit should be at the crossing of Z7, Z11 and Z12, not on the crossing of Z2, Z3 and Z7!

 

Success!
Luc

Re: Solve diagonal resistance of resistor 3D mesh.

In fact, I referred to the network (1) in the photo, instead I should have analyze the (2):

3D Network.jpg

Re: Solve diagonal resistance of resistor 3D mesh.

image.pngThe diagonal resistance of resistor 3D mesh is 5/6 ohm.

How about 1*2 3D Mesh?

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Each branch resister is 1 ohm. 

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Re: Solve diagonal resistance of resistor 3D mesh.

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Re: Solve diagonal resistance of resistor 3D mesh.

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i=2:    1*1*1

i=3:    1*1*2

i=4:    1*1*3....

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Re: Solve diagonal resistance of resistor 3D mesh.

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i=2:    2*2*1

i=3:    2*2*2

i=4:    2*2*3....

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Re: Solve diagonal resistance of resistor 3D mesh.

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i=2:    3*3*1

i=3:    3*3*2

i=4:    3*3*3....

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Re: Solve diagonal resistance of resistor 3D mesh.

Diagonal resistance of resistor 3D mesh.4*4*4=

 

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Re: Solve diagonal resistance of resistor 3D mesh.

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Re: Solve diagonal resistance of resistor 3D mesh.

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Re: Solve diagonal resistance of resistor 3D mesh.

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Re: Solve diagonal resistance of resistor 3D mesh.

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Re: Solve diagonal resistance of resistor 3D mesh.

image.pngimage.png Diagonal resistance of resistor 3D mesh 20x20x20.

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Re: Solve diagonal resistance of resistor 3D mesh.

ttokoro_0-1602565747622.png

 

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Re: Solve diagonal resistance of resistor 3D mesh.

R3D(1000*1000*1000)=1.43886 ohm.

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Re: Solve diagonal resistance of resistor 3D mesh.

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Re: Solve diagonal resistance of resistor 3D mesh.

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Infinity 2D mesh. RCD=4/π-1/2. This is Google puzzle.

How about Infinity 3D mesh. R(0,0,0)-(1,1,2)

image.pngin the infinity 3D mesh. The answer is 

image.pngimage.pngThis is well known 1/3.  

 

Re: Solve diagonal resistance of resistor 3D mesh.

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Diagonal resistance of resistor 3D mesh 1000x1000x1000. 1 h to solve the 1000^3 3D mesh.

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Re: Solve diagonal resistance of resistor 3D mesh.

Now Prime 6 can solve all 3D resistor mesh problems for both finite and infinity connections. 

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