# Ohm's law

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

${\displaystyle V=IR,\,}$

where R is the resistance of the conductor. The law was discovered by Georg Simon Ohm in 1826. Ohm's equation implies that R is constant, i.e., independent of V. While a resistor is an ohmic conductor, a semiconductor diode is not, as its resistance varies with the voltage applied.

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

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

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 and is the inverse of the resistivity ρ of the (isotropic) material,

${\displaystyle \rho ={\frac {E}{J}}={\frac {1}{\sigma _{0}}}.}$

## Reference

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