Ohm's Law

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.