Flow of Electrons in a Metal, Drift Velocity, Relaxation Time, Mobility and Simple Derivation of Ohm's Law

A metal wire is subjected to a constant potential difference. When the temperature of the metal wire increases, the drift velocity of the electron in it 

The density of copper is $9\times {10}^{3 }kg/m^3$ and its atomic weight is $63.5u.$ Each copper atom provides one free electron. Estimate the number of free electrons per cubic metre in copper 

A conductor wire having ${10}^{29}$ free electrons/$m^3$ carries a current of $20A.$ If the cross-section of the wire is $1 m{m}^2,$ then the drift velocity of electrons will be 

The current in a copper wire is increased by increasing the potential difference between its ends. Which one of the following statements regarding the number of charge carriers per unit volume in the wire and ${\mathrm{v}}_{\mathrm{i}}$, the drift velocity of the charge carriers is correct?

A steady current flows in a metallic conductor of non-uniform cross-section. The quantity/quantities that are constant along the length of the conductor is /are

Derive the relation between current density $\mathrm{J}$ and potential difference $\mathrm{V}$ across a current-carrying conductor of length $\mathrm{l},$ area of cross-section $\mathrm{A}$ and the number density $\mathrm{n}$ of free electron density.

Define the terms current density of a metallic conductor. Deduce the relation connecting current density $\left(\mathrm{J}\right)$ and conductivity $\left(\mathrm{\sigma }\right)$ of the conductor when an electric field $\mathrm{E}$ is applied it.

Define relaxation time of the free electrons drifting in a conductor. How is it related to the drift velocity of free electrons? Use this relation to deduce the expression for the electrical resistivity of the material.

What are relaxation time and mobility?

Explain how the process of flow of electric current through a metallic conductor can be explained from the concept of free electrons of metal. Deduce $\mathrm{Ohm}$ 's law from this picture.