Information AboutElectrical Resistivity |
| CATEGORIES ABOUT RESISTIVITY | |
| electronics | |
| physical quantity | |
| materials science | |
|
DEFINITIONS The electrical resistivity ρ ('' Rho '') of a material is given by : where ρ R A Electrical resistivity can also be defined as : where E J Finally, electrical resistivity is also defined as the inverse of the Conductivity ''σ'' ('' Sigma ''), of the material, or : TABLE OF RESISTIVITIES This table shows the resistivity and Temperature Coefficient of various materials. The values are correct at 20 °C (68 °F )
TEMPERATURE DEPENDENCE In general, electrical resistivity of Metal s increases with Temperature , while the resistivity of Semiconductor s decreases with increasing temperature. In both cases, electron- Phonon interactions can play a key role. At high temperatures, the resistance of a metal increases linearly with temperature. As the temperature of a metal is reduced, the temperature dependence of resistivity follows a power law function of temperature. Mathematically the temperature dependence of the resistivity ρ of a metal is given by the Bloch-Gruneissen formula : where is the residual resistivity due to defect scattering, A is a constant that depends on the velocity of electrons at the fermi surface, the Debye radius and the number density of electrons in the metal. is the Debye temperature as obtained from resistivity measurements and matches very closely with the values of Debye temperature obtained from specific heat measurements. n is an integer that depends upon the nature of interaction: #n=5 implies that the resistance is due to scattering of electrons by Phonon s (as it is for simple metals) #n=3 implies that the resistance is due to s-d electron scattering (as is the case for transition metals) #n=2 implies that the resistance is due to electron-electron interaction. As the temperature of the metal is sufficiently reduced (so as to 'freeze' all the phonons), the resistivity usually reaches a constant value, known as the residual resistivity. This value depends not only on the type of metal, but on its purity and thermal history. The value of the residual resistivity of a metal is decided by its impurity concentration. Some materials lose all electrical resistivity at sufficiently low temperatures, due to an effect known as Superconductivity . An even better approximation of the temperature dependence of the resistivity of a semiconductor is given by the Steinhart-Hart Equation : : where ''A'', ''B'' and ''C'' are the so-called Steinhart-Hart coefficients. This equation is used to calibrate Thermistor s. COMPLEX RESISTIVITY When analysing the response of materials to alternating Electric Field s, as is done in certain types of Tomography , it is necessary to replace resistivity with a Complex quantity called ''impeditivity'', in analogy to Electrical Impedance . Impeditivity is the sum of a real component, the resistivity, and an imaginary component, the ''reactivity'' ( Reactance ) {Link without Title} . SOURCES SEE ALSO EXTERNAL LINKS
|
|
|