A wire of resistance R is bent into a triangular pyramid as shown in… | JEE Main 2025 (7 Apr, Shift 1)

Q10JEE Main 2025 · 7 APR · SHIFT 1Medium

Combination of Resistors

A wire of resistance $R$ is bent into a triangular pyramid as shown in figure with each segment having same length. The resistance between points $A$ and $B$ is $R/n$ . The value of $n$ is:

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Answer: (c)

The pyramid (tetrahedron) has 6 equal edges, each of resistance $r = \dfrac{R}{6}$ .
By symmetry the other two vertices are at the same potential, so the edge joining them carries no current.
Paths: direct $r$ , plus two paths of $2r$ each, all in parallel: $\dfrac{1}{R_{AB}} = \dfrac{1}{r} + \dfrac{1}{2r} + \dfrac{1}{2r} = \dfrac{2}{r}$
$R_{AB} = \dfrac{r}{2} = \dfrac{R}{12}$ , so $n = 12$ .
So the answer is (c) 12.

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