# Resistivity, Conductivity and Conductance

## Resistivity, Conductivity and Conductance

1) Resistivity: Resistivity is a measure of the resistance of a given size of a specific material to electrical conduction.

From, $$R=\rho \frac{l}{A}$$ , if $$l=1m$$, $$A=1\,{{m}^{2}}$$ then $$R=\rho$$ i.e. resistivity is numerically equal to the resistance of a substance having unit area of cross section and unit length.

i) Unit and dimension: Its SI unit is Ohm$$\times$$m and dimension is $$\left[ M{{L}^{3}}{{T}^{-3}}{{A}^{-2}} \right]$$.

ii) Its formula is: $$\rho =\frac{m}{n{{e}^{2}}\tau }$$.

iii) Resistivity is the intrinsic property of the substance. It is independent of shape and size of the body.

iv) For different substance their resistivity is also different e.g. $${{\rho }_{Silver}}=Minimum=1.6\times {{10}^{-8}}\Omega .m$$ and $${{\rho }_{Fused\,quartz}}=Maximum\approx {{10}^{-16}}\Omega .m$$.

$${{\rho }_{\begin{smallmatrix} Insulator \\ (Maximum\,for\,fused\,quartz) \end{smallmatrix}}}>{{\rho }_{alloy}}>{{\rho }_{semi-conductor}}>{{\rho }_{\begin{smallmatrix} Conductor \\ (Minimum\,for\,silver) \end{smallmatrix}}}$$.

(v) Resistivity depends on the temperature. For metals $${{\rho }_{t}}={{\rho }_{0}}\left( 1+\alpha \,\Delta t \right)$$ i.e. resistivity increases with temperature.

(vi) Resistivity increases with impurity and mechanical stress.

(vii) Magnetic field increases the resistivity of all metals except iron, cobalt and nickel.

(viii) Resistivity of certain substances like selenium, cadmium, sulphides is inversely proportional to intensity of light falling upon them.

2) Conductivity$$\left(\sigma \right)$$: Reciprocal of resistivity is called conductivity i.e.  $$\sigma =\frac{1}{\rho }$$ with mho/m and dimensions $$\left[ {{M}^{-1}}{{L}^{-3}}{{T}^{3}}{{A}^{2}} \right]$$.

3) Conductance: Reciprocal of resistance is known as conductance. $$C=\frac{1}{R}$$ its unit is $$\frac{1}{\Omega }$$ (or) $${{\Omega }^{-1}}$$ or Siemen.