Obtain the macrscopic form of Ohm's law form its microscopic form and discuss its limitation.

Explanation

Ohm.s law: The Ohm.s law can be derived from the equation `J=sigma E`. Consider a segment of wire of length `l` and cross sectional area A.
When a potential difference V is applied across the wire, a net electric field is created in the wire which constitutes the current. For simplicity, we assume that the electric field is uniform in the entire length of the wire, the potential difference (voltage V) can be written as
`V=El`
As we know, the magnitude of current density
`J=sigmaE=sigma (V)/(l)" " ...(1)`
But `J=(I)/(A)`, so we wire the equation as
`(I)/(A)=sigma(V)/(l)`
by rearranging the above equation, we get
`V=I((l)/(sigmaA))" " ...(2)`
The quantity `(l)/(sigmaA)` is called resistance of the conductor and it is denoted as R. Note that the resistance is directly proportional to the length of the conductor and inversely proportional to area of cross section.
Therefore, the macroscopic form of Ohm.s law can be stated as
`V=IR" "...(2)`