Question

Define electrical conductivity of a conductor and give its S.I. unit. On what factors does it depend ?

Answer 1

Hint:Resistivity of a conductor is a measure of its ability to resist the flow of current in a given cross section of area of conductor. The reciprocal of resistivity is defined as conductivity of material. It is the measure of tendency of material to allow the flow of charge through them. It is denoted by’\[\sigma \]’.

Formula used:
Resistance of a conductor is given by:
\[R = \rho \dfrac{l}{A}\]
where, \[\rho = \dfrac{m}{{n{e^2}\tau }}\]is resistivity of conductor, \[l\] is length and $A$ is the area of cross section. Resistance has unit ohm (\[\Omega \]) and resistivity has unit \[\Omega m\].

Complete step by step answer:
As defined above conductivity is numerically equal to inverse of resistivity:
\[\sigma = \dfrac{1}{\rho }\]
S.I. unit of conductivity is \[oh{m^{ - 1}}{m^{ - 1}}\](\[{\Omega ^{ - 1}}{m^{ - 1}}\]).
As, \[\rho = \dfrac{m}{{n{e^2}\tau }}\], conductivity becomes \[\sigma = \dfrac{{n{e^2}\tau }}{m}\], where, $m$ is mass of electron, $n$ is number of electron density, \[\tau \] is relaxation time and $e$ is charge on electron.

Factors on which conductivity of conductor depends:
Relaxation time the interval between two consecutive collisions between the electrons when current goes through it, conductivity is proportional relaxation time. Conductivity is proportional to number density of electron, also on charge of electron and inversely proportional to mass of electron.

Note:Conductivity decreases with increase in temperature. When temperature of conductor is increased the electrons present in it vibrates with more energy due to which collision between them increases and relaxation time decreases. As conductivity depends directly on relaxation time conductivity also decreases.