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  • Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of resistance R would be:Option: 1 <img alt="\frac{n^

Equivalent resistance between the adjacent corners of a regular n-sided polygon of uniform wire of resistance R would be:

Option: 1

\frac{n^2 R}{n-1}


Option: 2

\frac{(n-1) R}{n}


Option: 3

\frac{(n-1) R}{n^2}


Option: 4

\frac{(n-1) R}{(2 n-1)}


Answers (1)

best_answer

When, a uniform wire of resistance R is shaped into a regular n-sided polygon, the resistance of each side will be

$$ \frac{\mathrm{R}}{\mathrm{n}}=\mathrm{R}_1
Let R_1 \& R_2  be the resistance between adjacent corners of a regular polygon
\therefore The resistance of (n-1)$ side, $R_2=\frac{(n-1) R}{n}
Since two parts are parallel, therefore R_{\mathrm{eq}}
$$ \begin{aligned} & R_{\mathrm{eq}}=\frac{R_1 R_2}{R_1+R_2}=\frac{\left(\frac{R}{n}\right)\left(\frac{n-1}{n}\right) R}{\left(\frac{R}{n}\right)+\left(\frac{\mathrm{n}-1}{n}\right) R} \\ & R_{\mathrm{eq}}=\frac{(n-1) R^2}{n^2} \times \frac{n}{R+n R-R} \\ & R_{\mathrm{eq}}=\frac{(n-1) R}{n^2} \end{aligned}

Posted by

Irshad Anwar

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