. The resistance of all the wires between any two adjacent
dots is R. Then equivalent resistance between A and B as
shown in the figure is
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Here the equivalent resistance of each triangle is R
eq1
=
(R+R)+R
(R+R)R
=(2/3)R
Now reduce the side by connecting resistance in series as shown in figure.
Here, R
eq2
=(2/3)R+(2/3)R=(4/3)R
Now the circuit is a balanced Wheatstone bridge. So middle resistor R is not working.
Thus, R
AB
=
[(4/3)R+R]+[(4/3)R+R]
[(4/3)R+R][(4/3)R+R]
= 67r
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