Question

A wire of resistance $12\Omega /\text{m}$ is bent to form a complete circle of radius $10\text{cm}$. The resistance between its two diametrically opposite points, $A$ and $B$ as shown in the figure is -

• A. $6\Omega$
• B. $0.6\pi \Omega$
• C. $3\Omega$
• D. $6\pi \Omega$

Answer 1

The correct option is B $0.6\pi \Omega$


Resistance of each semicircular part,

$R=\frac{2\pi \times 0.10}{2}\times 12=1.2\pi \Omega$

Therefore,

$R_{AB}=\frac{1.2\pi \times 1.2\pi }{1.2\pi +1.2\pi }=0.6\pi \Omega$

​​​​​​​Hence, option $\left(B\right)$ is the correct answer.