Question

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

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

Answer 1

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

Length of semi-circle $L=\pi r=\pi \left(0.1\right)$

$\therefore$ Resistance of each semi-circle $R=12\times 0.1\pi =1.2\pi \Omega$

Equivalent resistance between point A and B $R_{eq}=1.2\pi \parallel 1.2\pi =\frac{1.2\pi }{2}=0.6\pi \Omega$