Question

A wire is bent into a circle. The effective resistance across the diameter is 8 $\Omega$. Find the resistance of the wire.

Answer 1

Given: A wire is bent into a circle. The effective resistance across the diameter is $8\Omega$

To find the resistance of the wire.

Solution:

As a wire is bent in the circular form, diameter divides into two equal parts as shown in the above figure.

Let Resistance of each part =$R_1\Omega$

And resistance across the diameter given is $R_{AB}=8\Omega$

Hence from figure,

$R_{AB}=\frac{R_1\times R_1}{R_1+R_1}⟹8=\frac{R_1\times R_1}{2R_1}⟹8=\frac{R_1}{2}⟹R_1=16\Omega$

Resistance of each part, is $16\Omega$

So, the total resistance of the entire wire=$2R_1=2\times 16=32\Omega$