Q 12-03-071JEE MainJEE Main 2025 (28 Jan, Shift 1)Medium
A wire of resistance $R$ is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is
Answer: (C) $32/27$
Triangle: each side is $R/3$. Across one edge, $R/3$ is in parallel with $2R/3$:
$$R_\triangle = \frac{(R/3)(2R/3)}{R} = \frac{2R}{9}$$
Square: each side is $R/4$. Across one edge, $R/4$ is in parallel with $3R/4$:
$$R_\square = \frac{(R/4)(3R/4)}{R} = \frac{3R}{16}$$
$$\frac{R_\triangle}{R_\square} = \frac{2/9}{3/16} = \frac{32}{27}$$
Solution by Sreeraj P, M.Sc Physics