Javalab [Javalab] Lars Drud Nielsen
ldn@oersted.dtu.dk

Resistor cube

The circuit topology corresponds to a cube with resistors along all of the 12 cube edges. Each of the 8 nodes (cube corners) are thus connected by resistors to its 3 nearest neighbours. The voltage source is connected across a space diagonal of the cube.

With all resistances having a common value R, the symmetry of the circuit will establish two groups of each three nodes with a common potential. The resulting load resistance as seen from the voltage source will then be RL = (1/3+1/6+1/3)·R = (5/6)·R.

Other highly symmetrical (and thereby easily verifyable) situations will occur when proper symmetrical selections among the resistance values are set to zero.

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