Imagine a conductor through which a current I
is flowing and let V be the potential difference between the ends of the
conductor. Then Ohm’s law states that
V α I or V = R
I
where the constant of proportionality R is called the 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 R is inversely
proportional to the cross-sectional area and length of the conductor.
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/m2.
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.