Calculate the resistance of a copper wire 1.0km long and 0.50mm diameter if the resistivity of copper is $1.7\times10\Omega\ \text{m}.$
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I = 1km = 1000m
$\text{r}=\frac{\text{d}}{2}=\frac{0.5}{2}\text{mm}=0.25\text{mm}=0.25\times10^{-3}\text{m}$
$\rho=1.7\times10^{-8}\Omega\text{m}$
$\text{R}=\rho\frac{\text{I}}{\text{A}}=\rho\frac{\text{l}}{\pi\text{r}^2}$
$\text{R}=1.7\times10^{-8}\times\frac{1000}{3.14\times(0.25\times10^{-3})^2}=86.6\Omega$
$\text{r}=\frac{\text{d}}{2}=\frac{0.5}{2}\text{mm}=0.25\text{mm}=0.25\times10^{-3}\text{m}$
$\rho=1.7\times10^{-8}\Omega\text{m}$
$\text{R}=\rho\frac{\text{I}}{\text{A}}=\rho\frac{\text{l}}{\pi\text{r}^2}$
$\text{R}=1.7\times10^{-8}\times\frac{1000}{3.14\times(0.25\times10^{-3})^2}=86.6\Omega$
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