A regular hexagon is formed by six wires each of resistance r Ω and… | JEE Main 2026 (24 Jan, Shift 2)

Q6JEE Main 2026 · 24 JAN · SHIFT 2Difficult

Combination of Resistors

A regular hexagon is formed by six wires each of resistance $r\ \Omega$ 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

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Answer: (b)

Number corners 1 to 6, current in at 1, out at 4. Take $V_1 = 1$ , $V_4 = 0$ ; by symmetry centre $= \tfrac12$ , $V_2 = V_6 = x$ , $V_3 = V_5 = 1 - x$ .
KCL at 2: $(x - 1) + (x - (1-x)) + (x - \tfrac12) = 0 \Rightarrow x = \tfrac58$
Current from 1 (in units of $1/r$ ): $2\left(1 - \tfrac58\right) + \tfrac12 = \tfrac54$
$R_{eq} = \dfrac{1}{5/4}\,r = \dfrac{4}{5}r$ . So the answer is (b).

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Combination of Resistors question from JEE Main 2026 (24 Jan, Shift 2)

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