Question

A wire of resistance $12ohm/meter$is bent to form a complete circle of radius $10cm$. The resistance between its two diametrically opposite points, A and B as shown in the figure is?

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

Answer 1

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

Total length of wire, $l=2\pi \times 0.1=0.2\pi m$

Resistance per unit length, $r=12\Omega /m$

Let us assume two semicircular part of wire connected in parallel between $A$ and $B$

Resistance of each part $,R=r\times l=12\times \frac{0.2\pi }{2}=1.2\pi \Omega$

Two equal resistors (R) are connected in parallel between A and B so equivalent resistance is equal to $R/2$.

$\therefore$ Resistance between $A$ and $B=\frac{R}{2}=\frac{1.2\pi }{2}=0.6\pi \Omega$

Hence, option $\left(D\right)$ is correct.