Ohm's Law and Limitations of Ohm's Law

Ohm’s Law:

It states:

“Current passing-through a conductor is directly proportional to the potential difference across its ends provided the temperature and the other physical conditions remain same”.

So current (I) and p.d. (V) across it are related as:

V α I

or V = IR

where R is constant called as the resistance which quantifies the obstruction to the flow of electrons (due to collisions with the stationary ions). The S.I unit of resistance is ohm, denoted by Ω. One ohm can be understood as obstruction which allows passage of current of 1A through it, when a potential difference of I V is maintained across its ends.

Ohm's Law in Microscopic form:

Expressing ohm’s law in terms of the driving electric field E and the current density j at any point within a conductor we get:

For uniform field  and from Ohm's Law, V = iR

Substituting j = i/A,

E = ρ j

j = σ E(σ = 1/ρ)