Ohm's law: Difference between revisions
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'''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, | '''Ohm's law''' is the name of the relationship between an electric current ''I'' flowing through a conductor and the voltage difference ''V'' between the ends of the conductor causing the current, | ||
:<math> | :<math> | ||
V = I R,\, | V = I R,\, | ||
</math> | </math> | ||
where ''R'' is the [[resistance]] of the conductor. The law was discovered by [[Georg Simon Ohm]] in 1826. | 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, 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]] <math>\vec J</math> and [[electric field]] <math>\vec E</math> that is observed in many materials (especially metals), | |||
:<math> | :<math> | ||
J_\alpha = \sum_{\beta=x,y,z} \sigma_{\alpha \beta}\, E_\beta, \qquad\alpha=x,y,z . | J_\alpha = \sum_{\beta=x,y,z} \sigma_{\alpha \beta}\, E_\beta, \qquad\alpha=x,y,z . | ||
</math> | </math> | ||
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 σ<sub>0</sub> times a 3×3 [[identity matrix]] | 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 σ<sub>0</sub> times a 3×3 [[identity matrix]]. The scalar σ<sub>0</sub> is the [[conductivity coefficient]] and is the inverse of the [[resistivity]] ρ of the (isotropic) material, | ||
:<math> | |||
\rho = \frac{E}{J} = \frac{1}{\sigma_0} | |||
</math> | |||
<math>\rho = \frac{E}{J} | |||
== | ==Reference== | ||
*H.D. Young & R.A. Freedman (2004). ''University Physics 11th Edition. International Edition''. Addison Wesley, ISBN 0-321-20469-7 | *H.D. Young & R.A. Freedman (2004). ''University Physics 11th Edition. International Edition''. Addison Wesley, ISBN 0-321-20469-7 | ||
Revision as of 09:01, 28 August 2009
Ohm's law is the name of the relationship between an electric current 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, 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