Question

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

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

Answer 1

The correct option is A $3\Omega$

Resistance of the wire, $R=12\Omega$

As the length of each segment is half of the complete wire, thus the resistance of each segment, $R^{\prime }=\frac{12}{2}=6\Omega$

Effective resistance between P and Q ($R^{\prime }$ in parallel), $R_{eq}$

$\frac{1}{R_{eq}}=\frac{1}{R_1}+\frac{1}{R_2}$

$\frac{1}{R_{eq}}=\frac{1}{R^{\prime }}+\frac{1}{R^{\prime }}$

$\frac{1}{R_{eq}}=\frac{2}{R^{\prime }}$

$R_{eq}=\frac{6}{2}$

$R_{eq}=3\Omega$