Physics-electric current?

Question

12 equal wires are joined to form a skeleton cube.the current enters at on corner and leaves at diagonally opposite corner.find the resistance between these corners?

Answer 1

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The symmetry of the system, suggests that the current I entering a corner divides into 3 equal parts = I /3 and passes along three sides of a cube. Each of the three current is further divided into 2 equal parts = I /6. Similarly, coming along 3 sides, it leaves the opposite corner.



If R is the equivalent resistance and I is the external current, considering a loop containing the external source of emf V,
there are three one ohm resistances and the current in the middle one is half that of the curent on either side.


IR = V = I/3 *1 + I/6 *1 + I/3*1 = 5/6 I

R = 5/6 Ohm.

Answer 2

That will equal to the resistance of the wire which forms one side.
How??!!!
Let the resistance be 1 ohm for each side.
Say at bottom corner the current enters and leaves at the top opposite corner.
The top surface will have two 1 ohms in series and effective is 2 ohm, such 2 ohms are in parallel. Hence the effective will become back to one ohm along the diagonal. Same way bottom face will have diagonally one ohm.
Now, the two vertical sides and these two diagonals form the same situation as before and so the effective is once again 1 ohm.
Very interesting.

Answer 3

Take a cube. Now keeping two diagonally opposite sides fixed press down the cube to form a 2-D figure of a square with a vertical wire in the center. adding the wires that were joined in doing this as they were in a parallel combination you get an unbalanced Wheatstone bridge. Now simply calculate the resistance of this Wheatstone bridge.

This was done seeing the symmetry in the cube