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(D) The resistance $R$ of a wire is given by the formula $R = \rho \frac{l}{A}$,where $\rho$ is the resistivity,$l$ is the length,and $A = \pi r^2$ is

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$20$

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(D) The resistance $R$ of a wire is given by the formula $R = ho \frac{l}{A}$,where $ho$ is the resistivity,$l$ is the length,and $A = \pi r^2$ is the cross-sectional area.Since the material and temperature are the same,$ho$ remains constant.Thus,$R \propto \frac{l}{r^2}$.Given $R_1 = 1\,\Omega$,$l_1 = 5\,m$,$r_1 = 1\,mm$ and $R_2 = 1\,\Omega$,$r_2 = 2\,mm$.We have the ratio: $\frac{R_1}{R_2} = \frac{l_1}{l_2} 	imes \frac{r_2^2}{r_1^2}$.Substituting the values: $\frac{1}{1} = \frac{5}{l_2} 	imes \left(\frac{2}{1}ight)^2$.$1 = \frac{5}{l_2} 	imes 4$.$l_2 = 5 	imes 4 = 20\,m$.

$A$ wire of length $5\,m$ and radius $1\,mm$ has a resistance of $1\,\Omega$. What length of the wire of the same material at the same temperature and of radius $2\,mm$ will also have a resistance of $1\,\Omega$?

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