Q.
A wire of resistance 12 ohms per meter is bent to form a complete circle of radius $10\ cm.$ The resistance between its two diametrically opposite points $A$ and $B$ as shown in the figure, is
A) $0.6\ \pi\ \Omega$
B) $3\ \Omega$
C) $6\ \pi\ \Omega$
D) $6\ \Omega$
Explanation
(a) Length of wire $= 2\pi r = 2\pi(0.1) = 0.2\pi m$
Resistance of complete wire $= 12 \times 0.2\pi = 2.4\pi\Omega$
$\therefore$ Resistance of each semicircle $= 1.2\pi\Omega$
Hence equivalent resistance $R_{AB} = \frac{1.2\pi}{2} = 0.6\pi\Omega$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.