JEE Main 2025 — Current Electricity Question with Solution

$$\text{Each side of the triangle has a resistance of }{R}_{\text{side}}=\frac{9\Omega }{3}=3\Omega .$$

When measuring the equivalent resistance between any two vertices, there are two paths:

A direct path along one side with resistance:

$$R_1=3\Omega .$$

An indirect path passing through the other two sides in series:

$$R_2=3\Omega +3\Omega =6\Omega .$$

These two paths are in parallel, so the equivalent resistance is calculated by:

$$\frac{1}{R_{\text{eq}}}=\frac{1}{R_1}+\frac{1}{R_2}=\frac{1}{3\Omega }+\frac{1}{6\Omega }=\frac{2}{6\Omega }+\frac{1}{6\Omega }=\frac{3}{6\Omega }.$$

Thus,

$$R_{\text{eq}}=\frac{6\Omega }{3}=2\Omega .$$

The equivalent resistance across any two vertices of the equilateral triangle is therefore:

$$2\Omega .$$