Q. 124.3( 9 Votes )

(a) Define the term ‘conductivity’ of a metallic wire. Write its SI unit.

(b) Using the concept of free electrons in a conductor, derive the expression for the conductivity of a wire in terms of number density and relaxation time. Hence obtain the relation between current density and the applied electric field E.

Answer :

a) Conductivity of a wire is defined as the reciprocal of resistivity ρ . Its S.I units is mho/m.



b) As we know that resistance R of a conductor is defined as



Where ρ = resistivity of conductor


l = length of conductor


A = area of cross section of conductor


According to ohm’s law V = IR


Where V = voltage across conductor and I = current through conductor.


Substituting the value of R in ohm’s law



Now



So, voltage becomes


V = j ρ l ….(i)


We know that electric field E is given as



Therefore V = E l.


So, equation (i) becomes


E l = j ρ l


E = j ρ


Now we know that



Therefore j = σ E


The average drift velocity of electron is given as



Where e = charge of electron


E = electric field


m = mass of electron


τ = relaxation time


If n is the number of free electrons per unit volume, the current I is given by


I = neA |Vd|




Now




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