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Solve diagonal resistance of resistor 3D mesh.

ttokoro
20-Turquoise

Solve diagonal resistance of resistor 3D mesh.

image.pngimage.png

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
ttokoro
20-Turquoise
(To:-MFra-)

53 REPLIES 53

Cube.png

-MFra-
21-Topaz II
(To:ttokoro)

Hi,

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

rete composta 2.jpg

ttokoro
20-Turquoise
(To:-MFra-)

image.pngimage.png

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

LucMeekes
23-Emerald III
(To:-MFra-)

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

-MFra-
21-Topaz II
(To:LucMeekes)

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

3D Network.jpg

ttokoro
20-Turquoise
(To:ttokoro)

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

How about 1*2 3D Mesh?

image.png

Each branch resister is 1 ohm. 

ttokoro
20-Turquoise
(To:ttokoro)

image.png

image.png

ttokoro
20-Turquoise
(To:ttokoro)

image.pngimage.png

i=2:    1*1*1

i=3:    1*1*2

i=4:    1*1*3....

ttokoro
20-Turquoise
(To:ttokoro)

image.pngimage.png

i=2:    2*2*1

i=3:    2*2*2

i=4:    2*2*3....

ttokoro
20-Turquoise
(To:ttokoro)

image.pngimage.png

i=2:    3*3*1

i=3:    3*3*2

i=4:    3*3*3....

ttokoro
20-Turquoise
(To:ttokoro)

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

 

image.png

image.png

ttokoro
20-Turquoise
(To:ttokoro)

image.pngimage.png

ttokoro
20-Turquoise
(To:ttokoro)

image.pngimage.png

ttokoro
20-Turquoise
(To:ttokoro)

image.png

image.png

image.png

image.png

ttokoro
20-Turquoise
(To:ttokoro)

image.pngimage.pngimage.png

ttokoro
20-Turquoise
(To:ttokoro)

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

ttokoro
20-Turquoise
(To:ttokoro)

ttokoro_0-1602565747622.png

 

ttokoro
20-Turquoise
(To:ttokoro)

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

ttokoro
20-Turquoise
(To:ttokoro)

image.pngimage.png

ttokoro
20-Turquoise
(To:ttokoro)

image.pngimage.png

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.  

 

ttokoro
20-Turquoise
(To:ttokoro)

image.pngimage.pngimage.pngimage.pngimage.png

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

ttokoro
20-Turquoise
(To:ttokoro)

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

image.png

image.pngimage.pngimage.png

ttokoro
20-Turquoise
(To:ttokoro)

Diagonal resistance of resistor 3D mesh.

n=1 The resistance of resistor 3D mesh of (0,0,0) to (1,0,0) is 7/12 ohm.

n=2 Do you know the resistance of resistor 3D mesh of (0,0,0) to (2,0,0) ?

 

image.pngimage.pngimage.png

ttokoro
20-Turquoise
(To:ttokoro)

 

The answer of 2*2*2 (0,0,0)-(2,0,0) is 179/210. What is 3*3*3 (0,0,0)-(3,0,0)?

image.pngimage.png

ttokoro
20-Turquoise
(To:ttokoro)

The answer is

image.png.

ttokoro
20-Turquoise
(To:ttokoro)

image.pngimage.pngimage.pngimage.png

ttokoro
20-Turquoise
(To:ttokoro)

Face center to center resistance of 11*11*11 mesh. 

image.pngimage.pngThe answer.

 image.png The node potentials 3D view.image.png The 3D field view.  

ttokoro
20-Turquoise
(To:ttokoro)

 

Mathcad is more powerful and faster than Maple. However, Maple with using compiler, it can calculate the 3D resistance mesh problem as follows.

image.png

 

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