The equivalent resistance between A and B of the network shown in… | JEE Main 2023 (1 Feb, Shift 1)

Q34JEE Main 2023 · 1 FEB · SHIFT 1Medium

Combination of Resistors

The equivalent resistance between $A$ and $B$ of the network shown in figure;

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Answer: (b)

Redraw as a Wheatstone bridge: arms $R$ and $3R$ on one side, $2R$ and $6R$ on the other, with $9R$ as the bridge.
$\dfrac{R}{3R} = \dfrac{2R}{6R}$ , so the bridge is balanced and $9R$ carries no current.
$R_{AB} = (R + 3R) \parallel (2R + 6R) = \dfrac{4R \times 8R}{12R} = \dfrac{8R}{3}$
So the answer is (b) $\dfrac{8}{3}R$ .

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