A wire of resistance $12\Omega$ is bent into a circle. What is the effective resistance between two points diametrically opposite on the circle?

Solution

1. The total resistance of the wire is $12\Omega$.
2. Bending it into a circle and picking diametrically opposite points creates two parallel arcs.
3. Each arc has a resistance of $12/2=6\Omega$.
4. The equivalent resistance is $$\begin{array}{rl}{R}_{\text{eq}}& =\frac{6\times 6}{6+6}\\ & =3\Omega \end{array}$$.
5. Hence the answer is (A).