Question

A wire of length 1m and of radius 0.01 mm has a resistance of 100ohm .fund the resistivity of the wire?

Answer 1

Answer:

l=1 R=0.1=0.1×10ki power-3 R=0.1

Explanation:

we know that A=πrsqure

3.14×0.1×0.1×10ki power -6

3.14×10 ki power -8

p=(100×3.14×10 ki power minus 8)/1

3.14×10 ki power minus 6

Answer 2

Need to FinD :-

• The Specific Resistance of the material .

$\red{\frak{Given}}\begin{cases}\sf Length (\ell ) = 1m \\\\\sf Radius ( r ) = 0.01 mm = 10^{-5} m \\\\\sf Resistance ( R) = 100\Omega \end{cases}$

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 ,

$\\\sf\longrightarrow \rho = \dfrac{ 3.14 \times ( 10^{-5})^2 * 100 }{1 m }\\\\\\\sf\longrightarrow \rho = 3.14 \times 10^{-10 + 2} \\\\\\\sf\longrightarrow \underline{\underline{\red{ \rho = 3.14 \times 10^{-8} \ \Omega . m^{-1} }}}$