Imagine a conductor through which a current

**is flowing and let***I***be the potential difference between the ends of the conductor. Then Ohm’s law states that***V***or**

*V α I*

*V = R I*
where the constant of proportionality

**is called the***R***resistance of the conductor**. The SI unit of resistance is ohm, and is denoted by the symbol**.***Ω*
The resistance R not only depends on the material of the
conductor but also on the dimensions of the conductor.

In general, then the resistance

**is inversely proportional to the cross-sectional area and length of the conductor.***R*
Current per unit area (taken normal to the current), I/A, is
called current density and is denoted by j.

The SI units of the current density are A/m

^{2}.
If E is the magnitude of uniform electric field in the conductor
whose length is l, and then the potential difference V across its ends is El.

where

**σ≡1/ρ is called the conductivity**.
Exact definition of Ohm's Law : The resistivity ( or conductivity ) of a material is independent of the magnitude and direction of the applied electric field.

ReplyDeleteThe text book definition is an inference of this definition. So it is better to derive from j = sigma E to V = iR. j = i/A ; sigma = i / tau ; E = V / length.