Question

a wire is 1.0m long ,0.2mm in diameter and resistance of 10 ohms.calculate the resistivity of its material.​

Answer 1

$\huge{\mathfrak{\blue{\underline{\underline{Solution:-}}}}}$

${\mathtt{\underline{Given:-}}}$

$\sf{I = 1m}$

$\sf{d=0.2mm} \\ \\ \sf{r=0.1mm}$

$\sf{R=10\;ohm}$

$\sf{Using\;R=\frac{\rho\;l}{A}}$

$\sf{=\frac{\rho\;l}{\pi \;r^{2}}}$

$\sf{\rho = \frac{R\pi\;r^{2}}{l} = \frac{10\times 3.14\times(0.1\times 10^{-3})^{2}}{1}}$

$\sf{= 10\times 3.14\times 0.1\times 0.1\times 10^{-6}}$

$\sf{= 0.314 \times 10^{-6}}$

${\boxed{\boxed{\sf{\red{= 3.14\times 10^{-7}\;ohm}}}}}$