Question

A regular $n$ sided polygon is made from a uniform wire of resistance $R$. Given $n$ is even, find the resistance of the polygon between any two adjacent corners.

• A. $\frac{R}{n^2}$
• B. $n-1)R^2$
• C. $\frac{(n-1)R}{n^2}$
• D. $(n-1)R$

Answer 1

The correct option is C $\frac{(n-1)R}{n^2}$

In a polygon made up of a uniform wire, each side has resistance $\frac{R}{n}$

Let us consider a side $\text{AB}$, across which let us find out the equivalent resistance of the system of resistors.


From the figure,

$R_{AB}^{\prime }=\frac{R}{n}$ and $R_{AB}^{\prime \prime }=\frac{R(n-1)}{n}$

Equivalent resistance across $\text{AB}$ is given by $R_{AB}=\frac{R_{AB}^{\prime }{R}_{AB}^{\prime \prime }}{R_{AB}^{\prime }+R_{AB}^{\prime \prime }}$

Substituting the data obtained we get,

$R_{AB}=\frac{(n-1)R}{n^2}$

Hence, option (c) is the correct answer.