What is meant by ohms law and resistivity and derivation of resistivity

Hello Student

Ohm's law is the relation between the potential difference applied to the ends of the conductor and current flowing through the conductor.This law was expressed by George Simon Ohm in 1826.

Statement of Ohm's Law
'if the physical state of the conductor (Temperature and mechanical strain etc) remains unchanged ,then current flowing through a conductor is always directly proportional to the potential difference across the two ends of the conductor
Mathematically
V α I
or
V=IR
Where constant of proportionallity R is called the electric resistance or simply resistance of the conductor
Value of resistance depends upon the nature ,dimension and physically dimensions of the conductor
Law
From Ohm's Law
V=IR or R=V/I
Thus electric resitance is the ratio of potential difference across the two ends of conductor and amount of current flowing through the conductor
electric resistance of a conductor is the obstraction offered by the conductor to the flow of the current through it.
SI unit of resistance is ohm (Ω) where
1 Ohm=1 volt/1 Ampere
or1Ω=1VA-1

Now from equation
R=ρl/A
And from ohm law R=V/I
Therefore
ρ=(V/I)(A/L)
=(V/L) / (I/A)
=E/J
Where E=V/L is the electric field at any point inside the wire and J=I/A is current density at any point in the wire. Unit of resistivity is ohm-meter.