Deduce ohm law from elementary concepts.

The elementary idea of ohm's law states that potential difference V across a conductoris directly proportional to the current I passing through the condutor when physical conditions of the conductor are not changed.
i.e. {tex}V\alpha I{/tex}
or {tex}\frac{V}{I} = {\text{constant}}(R){/tex}
Where R is the constant known ar resistance of the conductor.Resistance is directly proportional to the length of the conductor and inversely proportional to the area of crossection of the conductor. Therefore, {tex}R\alpha lA{/tex}, where R, l and A are resistance, length and area of crossection respectively.On removing the sign of proportionality, we get:
{tex}R = \rho lA{/tex}, where {tex}\rho {/tex} is the resistivity of the conductorof resistance R which depends on the nature of the conductor.
Now {tex}I = neAvd{/tex},
where n is the number of electrons present in unit volume of the conductor drifting with velocity vd.
But {tex}vd = eEm\tau {/tex},
so putting the value of vd in the above eqn of current, we get, {tex}I = neA \times eEm\tau {/tex} further we know that E=Vl,
so {tex}I = neA \times eVml\tau {/tex}
Again {tex}VI = R = m\ln {e^2}A\tau {/tex}
and {tex}\rho = RAl = mn{e^2}\tau {/tex}
These are the required expressions.