Solve diagonal resistance of resistor mesh.

[ttokoro]

R(1*1)=1, R(2*2)=3/2. How about R(3*3),R(4*4) and R(5*5)?

[ValeryOchkov]

May be it will help you!

[ttokoro · Accepted solution]

Approximate expression of diagonal resistance of x*x resistor mesh by Mathcad Prime 6.0.

[ttokoro]

Approximate expression of diagonal resistance of (0,0)-(x,x) of infinity resistor mesh by Mathcad.

[ttokoro]

The answers from 16x16 mesh to 30x30 mesh.

[ttokoro]

[ttokoro]

4*4,5*5,6*6,7*7,8*8=

[ttokoro]

Resistor mesh - Rosetta Code

[ttokoro]

Resistor mesh of 50x50

[ttokoro]

Resistor mesh of 200x200. This is my limit of evaluation of Mathcad Prime 6. 

[ttokoro]

250x250

[ttokoro]

Solve diagonal resistance of resistor 2*3 mesh. This is good question for university students.

[ttokoro]

[ttokoro]

[ttokoro]

[ttokoro]

A. J. W. Duijvestijn, "SIMPLE PERFECT SQUARED SQUARES AND 2 x 1 SQUARED RECTANGLES OF ORDER 25" Math. Comp. 62 , pp. 325–332, 1994.

[ttokoro]

R2D(10000*10000)=11.804

R2D(20000*20000)=12.687   ohm.

[ttokoro]

Diagonal resistance of resistor mesh 50000x50000 is 13.854 ohm. 20 min. to solve the mesh.

[ttokoro]

Now all 2D resistor mesh electric circuits are solved. Not only diagonal resistance but also any two point of nodes of the circuit.

[ttokoro]

Diagonal resistance of Triangle resistor mesh of 1 ohm.

n=1 blue is 1*2/(1+2)=2/3 ohm.

n=2 green is 10/9 ohm.

n=3 red is 10/7 ohm.

Do you know the answer of n=4 ?  The resistance of node (0,0) to (4,0).

[ttokoro]

[ttokoro]

Maple with compiler to solve 2D resistor mesh problem.

[ttokoro]

Resistor mesh of 60 nodes is made by Maple 2021. Resistance of node 1 to 31 is 17/11 ohm. The one of node 1 to 2 is 0.649 ohm. Not sure this is true or not but Mathcad can solve them.

[ttokoro]

104/165 ohm, 764/1171 ohm, 58/95 ohm, 47/110 ohm.
Now can solve any node to node resistance for many Graph Theory functions. Pictures made by Maple 2021.

[ttokoro]

Can you solve the (0,0)-(3,0) resistance?

[ttokoro]

The one of 10*10.

The potential views of the one of 40*40 register mesh. 

[ttokoro]

[ttokoro]

[ttokoro]