| Since .1 did not explain how the result was achieved, let me point out that
the voltage at each of the three vertices adjacent to one of the vertices
is identical, by symmetry. Hence, connecting these three vertices with wires
will not change anything. Similarly, connecting the three vertices adjacent
to the diagonally opposite vertex will not change anything. This leaves
us with a simple arrangement: three one-ohm resistances in parallel, followed
serially by six in parallel, followed by three in parallel.
For parallel resistances, the combined resistance is the reciprocal of the sum
of the resistances (for three one-ohm resistances, 1/(1/1+1/1+1/1) = 1/3,
for six, 1/6). For serial resistances, the combined resistance is the sum
of the resistances (1/3+1/6+1/3 = 5/6).
-- edp
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