Question

A uniform wire of resistance 20$\Omega$ having resistance 1$\Omega /m$ is bent in the form of circle as shown in fig. If the equivalent resistance between M and N is 1.8 $\Omega$ , then the length of the shorter section is :

• A. 2 m
• B. 5 m
• C. 1.8 m
• D. 18 m

Answer 1

The correct option is A 2 m

$R=20\Omega$
$L=20m$
Let the length of the shorter section be x
length of longer section is (20-x)
$R_{eq}=\frac{x(20-x)}{20}=1.8$
$20x-x^2=36$
$x^2-20x+36=0$
$(x-2)(x-18)=0$
$x=2m$
length of shorter side$=2m$