Question

The resistance of the wire of length 10m is 2ohm. If the area of cross section of the wire is 2 x 10 ^-7 m^2 , determine its
(I) Resistivity
(II) Conductance
(III) Conductivity

Answer 1

Given :

$\text{Length, L = 10\:m}$

$\text{Resistance, R = 2\:ohm}$

$\text{Area, A = }2\times 10^{-7}m^2$

To Find :

(I)$\text{Resistivity}$

(II)$\text{Conductance}$

(III)$\text{Conductivity}$

Formula Applied :

$\text{Resistivity}$,  $\rho = \frac{RA}{L}$

$\text{Conductance}, G = \frac{1}{R}$

$\text{Conductivity},$ $\sigma = \frac {1}{p}$

Solution :

(I) Resistivity :

$\text{Resistivity}= \frac{Resistance\: \times\: Area }{Length}$

$\rho = \frac{2 \times 2 \times 10^{-7}}{10}$

$\implies \frac{4 \times 10 ^{-8}}{10}$

$\boxed {\text{Resistivity = }4 \times 10 ^{-8}\Omega m}$

(II) Conductance :

$\text{Conductance = } \frac{1}{\text{Resistance}}$

$G = \frac{1}{R}$

$\implies \frac{1}{2}$

$\boxed{\text{Conductance = } 0.5 \: \text{mho}}$

(III) Conductivity :

$\text{Conductance = } \frac{1}{Resistivity}$

$\sigma = \frac{1}{\rho}$

$\implies \frac{1}{4 \times 10^{-8}}$

$\boxed{\text{Conductivity = }0.25 \times 10^{-8}\:\text{mho}\:m^{-1}}$