Figure P2.16 Each resistor has a value of 1 Q.
Sometimes, we can use symmetry considerations to find the resistance of a circuit that
cannot be reduced by series or parallel combinations. A classic problem of this type is illustrated
in Figure P2.16. Twelve 1-Ω resistors are arranged on the edges of a cube, and terminals a and
b are connected to diagonally opposite corners of the cube. The problem is to find the resistance
between the terminals. Approach the problem this way: Assume that 1 A of current enters terminal a and exits through terminal b. Then, the voltage between terminals a and b is equal tothe unknown resistance. By symmetry considerations, we can find the current in each resistor.Then, using KVL, we can find the voltage between a and b.
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