Question

1m and radius 1mm has rasistance ,
of 100ohms

find the specific, resistance ofthe material
​

Answer 1

Need to FinD :-

• The Specific Resistance of the material .

$\red{\frak{Given}}\begin{cases}\sf Length (\ell ) = 1m \\\\\sf Radius ( r ) = 1 mm = 10^{-3} m \\\\\sf Resistance ( R) = 100\Omega \end{cases}$

We know that , the resistance R of a material having a length l cross section area A is given by ,

$\sf\longrightarrow R = \rho \dfrac{\ell}{A}$

• Where $\rho$ is the specific resistance of the material.
• Transposing the terms ,

$\sf\longrightarrow \rho = \dfrac{ A . R }{\ell }$

• Since the wire is cylindrical , its cross sectional area will be same as that of circle πr².

$\\\sf\longrightarrow \rho = \dfrac{ \pi r^2 . R }{\ell }$

• Put on the respective values ,

$\\\sf\longrightarrow \rho = \dfrac{ 3.14 \times ( 10^{-3})^2 * 100 }{1 m } \\\\\\\sf\longrightarrow \underline{\underline{\red{ \rho = 3.14 \times 10^{-4} \ \Omega . m^{-1} }}}$