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

Explanation

Let us consider a segment of wire of length 1 and cross sectional area A.

When a potential dillcrence across the wire, a net clectric field is created in the wire that constitutes the current. For simplicity, it is assumed that the clcctric field is uniform in the entire length of the wire the potential difference (voltage V) is given by
V = El
As we know, the magnitude of current density
`J = sigma E = sigma V/l " ...(1)"`
But ` J = I/A` so let us rewrite the equation (1) as
`I/A = sigma V/I`
By rearranging the above equation we get,
`V = i (l/(sigam A))`
The quantity `l /(sigma A)`
is called resistance of the conductor and it is denoted as R. So the resistance is directly proportional to the length of the conductor and inversely proportional to area of cross-section.
Hence the macroscopic form of Ohm.s law can be stated as
`V = IR`
From the above equation, the resistance is the ratio of potential difference across the given conductor to the current passing through the conductor.
`R = V/I`