Resistance of a wire of length $\displaystyle 1$ m is $\displaystyle 35 \Omega$ at $\displaystyle 20$°C. If the diameter of the wire is $\displaystyle 0.2$ mm , determine the resistivity of the material of the wire at that temperature. How will the resistivity of the wire change if the length and diameter of the wire both are doubled ? Justify your answer. \[\text { (Given that } \pi=\frac{22}{7} \text { ) } \]

$\displaystyle \mathrm{R}=35 \Omega$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.