What length of a copper wire of cross$-$sectional area $0.01\ mm^2$ will be needed to prepare a resistance of $1\text{k}\Omega?$ Resistivity of copper $=1.7\times10^{-8}\Omega\text{-m}.$
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$\text{f}_\text{cu}=1.7\times10^{-8}\Omega\text{-m}$
$\text{A}=0.01\text{mm}^2=0.01\times10^{-6}\text{m}^2$
$\text{R}=1\text{K}\Omega=10^3\Omega$
$\text{R}=\frac{\text{f}\ell}{\text{a}}$
$\Rightarrow10^3=\frac{1.7\times10^{-8}\times\ell}{10^{-6}}$
$\Rightarrow\ell=\frac{10^3}{1.7}=0.58\times10^3\text{m}=0.6\text{km}.$
$\text{A}=0.01\text{mm}^2=0.01\times10^{-6}\text{m}^2$
$\text{R}=1\text{K}\Omega=10^3\Omega$
$\text{R}=\frac{\text{f}\ell}{\text{a}}$
$\Rightarrow10^3=\frac{1.7\times10^{-8}\times\ell}{10^{-6}}$
$\Rightarrow\ell=\frac{10^3}{1.7}=0.58\times10^3\text{m}=0.6\text{km}.$
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