Ohm's law

Ohm's law is the name of the relationship between current density and electric field of some materials (especially metals), discovered by Georg Simon Ohm in 1826. The law states that at a given temperature and given certain materials, the current density ${\vec {J}}$ in a conductor is almost directly proportional to the electric field ${\vec {E}}$. In addition, the ratio of the magnitudes $E$ and $J$ is constant.

Resistivity

Ohm's law is used to define the resistivity of a material or a conductor. The equation for Ohm's law is

$\rho ={\frac {E}{J}}$

where $\rho$ is the resistivity of the material.

Ohm's law in circuit theory

In circuit theory, Ohm's law often refers to the relationship between voltage, current and resistance. This relationship is mathematically expressed as

$R={\frac {V}{I}}$

where $R$ is the resistance of the conductor, $V$ is the potential difference between the ends of the conductor and $I$ is the current through the conductor.

The validity of the equation requires that the resistance of the conductor is constant, implying that the resistivity is constant. While a resistor is an ohmic conductor, a semiconductor diode is not as its resistance varies with the voltage applied.