# 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,



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  and electric field  that is observed in many materials (especially metals),



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,



## Reference

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