Ohm's Law

Ohm's law was named after George Simon Ohm (1787 — 1854). It states that for many materials (including most metals), the ratio of the current density to the electric field is a constant,  that is independent of the electric field producing the current. A courant density  and an electric field E are established in a conductor when potential difference is maintained across the conductor. If the potential difference is constant, the current is also constant. Very often, the current density is proportional to the electric field:

Where the constant of proportionality  is called conductivity of the conductor.

A form of Ohm's law useful in practical applications can be obtained by considering a segment of a straight wire of cross-sectional area A and length l.  A protential difference V = Vb - Va is maintained across the wire, creating an electric field in a wire and current.  If the electric field in the wire is assumed to be uniform, the potential difference is related to the electric field through the relationship

A form Therefore, the magnitude of the current density in the wire can be expressed as

Since, the potential diffence can be written

The quantity  l A is called the resistance R of the conductor.  It is defined as the ratio of the potential difference across the conductor to the current

This relationship is referred to as the basic law in electric circuits, the Ohm's law. The SI unit of resistance (R), which is called the ohm , is in fact a derived unit, related to the voltage and current units through