Question

Six equal resistors of 1 ohm each are connected to form the sides of a hexagon ABCDEF. Calculate the resistance offered by the combination if the current enters at A and leaves it at D.

Answer 1

From figure it is clear that there are two sets of parallel resistances between A and D. Each group has three resistances of 1Ω each, in series.
Equivalent resistance R₁ of one group (AB, BC and CD) = 1Ω + 1Ω + 1Ω = 3Ω

Similarly equivalent resistance R² of the other group (AF, FE, ED)

= 1Ω + 1Ω + 1Ω = 3Ω

As the two groups are in parallel, we have

`1/"R" = 1/"R"_1 + 1/"R"_2 = 1/3 + 1/3 = 2/3`

where R is the equivalent resistance of the whole combonation.

∴ R = `3/2` Ω or 1.5 Ω.