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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.
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Solution
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.
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