Ram is bored, so he decides to use his collection of uniform thin copper rods, each of resistance $R = 1.00Ω$ , to create a rigid compound shape shown below. The copper rods form seven regular hexagons. The effective resistance $R_{A B}$ between points A and B is $\frac{α}{160} Ω$ . The value of $α$ is:

Question

TestHub · Accepted Answer

The seven hexagons form a network of 24 vertices and 30 unit-resistance rods. Set the potentials at A and B to 0 and 1 V.

At each other vertex i, Kirchhoff’s current law is

$de g (i) V_{i} - \sum_{j \sim i} V_{j} = 0$

Solving these node equations gives the three neighbours of B at potentials

$\frac{134}{153}, \frac{37}{51}, \frac{134}{153} V$

Thus the current drawn from B is

$I = 2 (1 - \frac{134}{153}) + (1 - \frac{37}{51}) = \frac{80}{153} A$

$R_{A B} = \frac{1}{I} = \frac{153}{80} = \frac{306}{160} Ω$

$α = 306$

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JEE Advanced 2027 (Class 12+)