Question

A wire of resistance $12\Omega$ per meter is bent to form a complete circle of radius 10cm. The resistance between its two diametrically opposite points,A and B is

• A. $3\pi \Omega$
• B. $60\pi \Omega$
• C. $0.6\pi \Omega$
• D. $6\pi \Omega$

Answer 1

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

Given: A wire of resistance $12\Omega$ per meter is bent to form a complete circle of radius $10cm$.

To find the resistance between its two diametrically opposite points,A and B

Solution:

Length of the wire = $2\times \pi \times 10cm=0.2\pi m$

Resistance of the wire when it is a straight line

$=12\times 0.2\pi =2.4\pi \Omega$

When the wire is bent in the form of a complete circle as shown in above figure.

Resistance between points A and B is

$\frac{R_1{R}_2}{R_1+R_2}⟹=\frac{1.2\pi \times 1.2\pi }{1.2\pi +1.2\pi }⟹=\frac{1.44\pi }{2.4}⟹=0.6\pi \Omega$

is the resistance between its two diametrically opposite points,A and B