Question 184: Current Electricity

Question

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

Accepted Answer

When, a uniform wire of resistance $\mathrm{R}$ is shaped into a regular $\mathrm{n}$-sided polygon, the resistance of each side will be,
$$
\frac{\mathrm{R}}{\mathrm{n}}=\mathrm{R}_1
$$
Let $R_1 $ and $ R_2$ be the resistance between adjacent corners of a regular polygon
$	herefore$ The resistance of $(\mathrm{n}-1)$ sides, $\mathrm{R}_2=\frac{(\mathrm{n}-1) \mathrm{R}}{\mathrm{n}}$
Since two parts are parallel, therefore,
$$
\begin{aligned}
& \mathrm{R}_{\mathrm{eq}}=\frac{\mathrm{R}_1 \mathrm{R}_2}{\mathrm{R}_1+\mathrm{R}_2}=\frac{\left(\frac{\mathrm{R}}{\mathrm{n}}ight)\left(\frac{\mathrm{n}-1}{\mathrm{n}}ight) \mathrm{R}}{\left(\frac{\mathrm{R}}{\mathrm{n}}ight)+\left(\frac{\mathrm{n}-1}{\mathrm{n}}ight) \mathrm{R}} \\
& \Rightarrow \mathrm{R}_{\mathrm{eq}}=\frac{(\mathrm{n}-1) \mathrm{R}^2}{\mathrm{n}^2} 	imes \frac{\mathrm{n}}{\mathrm{R}+\mathrm{nR}-\mathrm{R}} \\
&\Rightarrow \mathrm{R}_{\mathrm{eq}}=\frac{(\mathrm{n}-1) \mathrm{R}}{\mathrm{n}^2}
\end{aligned}
$$

Answer

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

Answer

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

Answer

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

Answer

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

Current Electricity

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

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