A regular hexagon is formed by six wires each of resistance and the corners are joined to the centre by wires of same resistance. If the current enters at one corner and leaves at the opposite corner, the equivalent resistance of the hexagon between the two opposite corners will be
Correct answer:A
Standard Method
Given: A regular hexagon is made of six wires, each of resistance , and every corner is connected to the centre by a wire of the same resistance. Current enters at one corner and leaves at the opposite corner.
Find: The equivalent resistance between the two opposite corners.
Using symmetry of the network, points placed symmetrically with respect to the line joining the entry and exit corners carry equal currents. Therefore, the current divides equally along identical branches, which allows the network to be reduced by series-parallel combinations.
The solution states that after simplifying the symmetric branches, the equivalent resistance is
Hence, the equivalent resistance between the opposite corners is .
Therefore, the correct option is A.
Assuming the current flows through only one side of the hexagon is incorrect because the network has multiple conducting paths. Use symmetry first, then combine the resulting parallel and series branches.
Combining all six outer resistors directly in series is wrong because the centre connections provide additional parallel paths. Reduce only after identifying equipotential or symmetric branches.
Ignoring symmetry leads to unnecessary complexity and often wrong combinations. In such regular resistor networks, first identify branches carrying equal current or nodes at the same potential.
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