Resistance of a wire of length 1 m is 35 Ω at 20°C. If the diameter of the wire is 0.2 mm, determine the resistivity of the material of the wire at…

$\displaystyle \mathrm{R}=35 \Omega$Diameter $\displaystyle (2 \mathrm{r})=0 \cdot 2 \mathrm{~mm}=2 \times 10^{-4} \mathrm{~m} \quad \therefore r=10^{-4} \mathrm{~m}$Length of the wire $\displaystyle =1 \mathrm{~m}$$\displaystyle R=\rho \frac{l}{A}$Area of cross section, $\displaystyle \mathrm{A}=\pi r^{2}$Resistivity, $\displaystyle \rho=\frac{\mathrm{RA}}{l}=\frac{35 \times \dfrac{22}{7} \times\left(10^{-4}\right)^{2}}{1}$$\displaystyle =110 \times 10^{-8} \Omega \mathrm{m}$Resistivity of the wire will not changeas it is a characteristic property of the material which does not depend on the dimensions of the wire.