Ohm's law

Ohm's law is the name of the relationship between an electric current I flowing through a conductor and the voltage difference V causing the current,

$V=IR,\,$

where R is the resistance of the conductor. The law was discovered by Georg Simon Ohm in 1826.

Later the law was generalized to the proportionality of current density ${\vec {J}}$ and electric field ${\vec {E}}$ that is observed in many materials (especially metals),

$J_{\alpha }=\sum _{\beta =x,y,z}\sigma _{\alpha \beta }\,E_{\beta },\qquad \alpha =x,y,z.$

The symmetric tensor σ is the conductivity tensor, which in general depends on temperature and is specific for the material. For homogeneous and isotropic materials the tensor is a real number σ₀ times a 3×3 identity matrix). The scalar σ₀ is the conductivity coefficient of the material.

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.

References

• H.D. Young & R.A. Freedman (2004). University Physics 11th Edition. International Edition. Addison Wesley, ISBN 0-321-20469-7