Question

Resistivity and its mathematical expression in terms of relaxation of time

Answer 1

Resistivity is the resistance per metre. Its SI unit is ohm m.

We know that,
Resistance is directly proportional to the length of the conductor and is inversely proporional to the area of cross section.

R = l/A

Here rsistivity is taken as the constant of proportionality and is represented by p

There the mathematical expression for resistivity becomes

R = p (l/A)

p = R (A/l)

Answer 2

the formula for the conductivity σ σ is given by σ = n e 2 τ m σ=ne2τm where n n is the density, e e is the electrical charge, τ τ is the relaxation time and m m mass of the electron. From here you should be able to find the resistivity.