Question

Show that the resistance across any opposite sides of a conductor in the shape of cube is inversely proportional to the length of its side.​

Answer 1

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Answer 2

How do you show that the resistance across any opposite sides of a conductor in the shapes of a cube is inversely proportional to the length of its side?

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Keith Morgan

Answered 2 years ago

This is a very simplistic explanation but does show what is mentioned in your question.

Let an initial cube = resistor of 1 ohm in value

If you double the size of the cube it will consist of 8 of these cubes, 2 x layers of 4.

Each layer in this case has 2 rows in parallel with each other. Each row in turn has 2 x 1 ohm resistors in series = 2 ohms.

As you have 2 x rows in parallel the net resistance (of the layer) is 1 ohm

Since you have 2 layers in parallel the net result is 0.5 ohm.

You can see that in doubling the side length that the resistance is lowered and this keeps going as you increase the length using this logic showing the inverse proportion.

Note: As said before my answer was simplified, the actual answer is 0.83333 ohm as a cube is a 3D solid meaning there is also vertical resistances as well but note the resistance still decreases with increase in side length.