(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.

(a) Conductivity of a metallic wire is defined as its ability to allow electric charges or heat to
pass through it.
Numerically, conductivity of a material is reciprocal of its resistivity.
SI unit : ohm^-1 m^-1 or mho m^-1 or Siemen m^-1 
(b) Consider a potential difference V be applied across a conductor of length l and cross
section A.
Electric field inside the conductor, E = v / I.
Due to the external field the free electrons inside the conductor drift with velocity Vd.
Let, number of electrons per unit volume = n,
charge on an electron = e
Total electrons in length, l = nAl
And,
total charge, q = neAl