Question

A uniform wire of resistance $18\Omega$ is bent in the form of a circle. The effective resistance across the points a and b is :

• A. $3\Omega$
• B. $2\Omega$
• C. $2.5\Omega$
• D. $6\Omega$

Answer 1

Answer: (C)

$2.5\Omega$

Given,

Resistance per unit radian, $\mu =\frac{18}{2\pi }$

Resistance in ${60}^o$.

$R_1=\mu \frac{\pi }{3}=\frac{18}{2\pi }\times \frac{\pi }{3}=3\Omega$

Resistance in remaining is $R_2=18-R_1=18-3=15\Omega$

And both resistance are in parallel

$R_T=\frac{R_1{R}_2}{R_1+R_2}=\frac{3\times 15}{15+3}=2.5\Omega$

Hence, effective resistance is $2.5\Omega$