A regular hexagon is formed by six wires each of resistance r Ω and the corners are joined to 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
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Question

A regular hexagon is formed by six wires each of resistance r Ω and the corners are joined to 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

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G1 Physics · Accepted Answer

Let the current enter at corner A and leave at the opposite corner B. Because the network is symmetric about the line AB, the two vertices symmetrically placed above and below AB have equal potentials in pairs. Take the resistance of every wire as r. Set V(A) = V, V(B) = 0. Let the two symmetric vertices adjacent to A each have potential x, the two symmetric vertices adjacent to B each have potential y, and the centre have potential z. Applying Kirchhoff's current law at one vertex adjacent to…