Question

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

Answer 1

Answer: (D)

$0.6 \pi\,\Omega$

Answer 2

Total resistance of wire $=12\, \Omega \times 2 \pi \times 10^{-1}$
$=2.4 \pi$
Resistance of each half $=\frac{2.4 \pi}{2}=1.2 \pi$
and as about diameter both parts are in parallel
Re $=\frac{1.2 \pi}{2}=0.6\, \pi \Omega$