Question

A wire has a resistance $12\Omega$. It is bent in the form of a circle. The effective resistance between two point on any diameter is

• A. $6\Omega$
• B. $3\Omega$
• C. $12\Omega$
• D. $24\Omega$

Answer 1

The correct option is B $3\Omega$

Resistance of the wire of a semicircle $=12/2=6\Omega$ (as the length of semicircle wire is half of total length of wire and $R\propto l$)
There are two resistances $6\Omega$ and $6\Omega$ between two points on any diameter of the ring and they are in parallel.
Thus, equivalent resistance is: $R_{eq}=\frac{6\times 6}{6+6}=3\Omega$