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Posted on 2006-06-05

Consider a cube in which each side has a resistance "R"

What is the resistance between opposite corners?

What is the resistance between opposite corners?

21 Comments

The combined Resistance between two corners is the value of a voltage measured across the two corners divided by the electric current flowing through all paths that connect these two corners.

http://mathforum.org/libra

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Harish

"There are 12 resistors each of resistance R along the sides of a cube and connected at the vertices. What is the effective resistance between opposite corners."

Here is another problem, Consider two vertical walls and a and a flat horizontal plane betwwn them

A 30 foot ladder rests from one corner and rests against the opposite wall

Another 20 foot ladder rest from the oppsite corner to its opssite wall

The ladders cross 10 feet above the flat plane

How far apart are the walls?

http://mathforum.org/library/drmath/view/55279.html

AB = 12.3118572378

AB = 12.3118572378

or, going with the doraiswamy description the answer shall be (3*R)

http://www.experts-exchang

Now it is turn to concentrate on the cube resistance.. :)

Without a picture it is hard to tell if "side" means a face or an edge of the cube.

A cube has six faces, eight vetices, and twelve edges.

Vertices that share an edge are connected by a resistance R. There are twelve resistors.

What is resistance between diagonal vertices?

Put 1 Amp into a top vetex and take 1 Amp out the opposite bottom vetex. Look at the symmetry.

The input and output vertices are connected to three resistor.

Symmetry requires that the current split evenly ==> I_Rin = I_Rout = 1/3 A

The other six resistor are connected between and input and an output resistor.

The current also splits evenly here ==> I_Rmid = 1/6 A.

The voltage drop between the opposite vertices is R*[I_Rin + I_Rmid + I_Rout] = R*[1/3 + 1/6 + 1/3] = R*5/6

Since the current is 1 A, the net resistance is also R*5/6

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