A wire of resistance 4 R is bent in the form of a circle. The equivalent resistance between two points diametrically opposite on the circle will be

$R$

The correct answer is Option (1) → $R$

Given:

Total resistance of wire = $4R$

When the wire is bent into a circle, and the resistance is measured between two diametrically opposite points, the circle is divided into two equal semicircular parts.

Each semicircular part has resistance:

$R_1 = R_2 = \frac{4R}{2} = 2R$

These two semicircular resistors are in parallel.

Hence, equivalent resistance:

$\frac{1}{R_{eq}} = \frac{1}{2R} + \frac{1}{2R} = \frac{2}{2R} = \frac{1}{R}$

$R_{eq} = R$

Final Answer: $R_{eq} = R$