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Solve diagonal resistance of resistor mesh.

SOLVED
ttokoro
17-Peridot

Solve diagonal resistance of resistor mesh.

 

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

1 ACCEPTED SOLUTION

Accepted Solutions

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

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View solution in original post

24 REPLIES 24

May be it will help you!May be it will help you!

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

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View solution in original post

ttokoro
17-Peridot
(To:ttokoro)

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

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ttokoro
17-Peridot
(To:ttokoro)

The answers from 16x16 mesh to 30x30 mesh.

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ttokoro
17-Peridot
(To:ttokoro)

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ttokoro
17-Peridot
(To:ttokoro)

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

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ttokoro
17-Peridot
(To:ttokoro)

ttokoro
17-Peridot
(To:ttokoro)

Resistor mesh of 50x50

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ttokoro
17-Peridot
(To:ttokoro)

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

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ttokoro
17-Peridot
(To:ttokoro)

250x250

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ttokoro
17-Peridot
(To:ttokoro)

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

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ttokoro
17-Peridot
(To:ttokoro)

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ttokoro
17-Peridot
(To:ttokoro)

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ttokoro
17-Peridot
(To:ttokoro)

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ttokoro
17-Peridot
(To:ttokoro)

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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
17-Peridot
(To:ttokoro)

R2D(10000*10000)=11.804

R2D(20000*20000)=12.687   ohm.

ttokoro
17-Peridot
(To:ttokoro)

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

ttokoro
17-Peridot
(To:ttokoro)

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

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ttokoro
17-Peridot
(To: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).

 

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ttokoro
17-Peridot
(To:ttokoro)

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ttokoro
17-Peridot
(To:ttokoro)

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

ttokoro
17-Peridot
(To:ttokoro)

The one of 10*10.image.pngimage.png

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

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ttokoro
17-Peridot
(To:ttokoro)

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ttokoro
17-Peridot
(To:ttokoro)

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