Resistivity¶
Resistivity is the electrical resistance of a conductor of unit cross-sectional area and unit length. A characteristic property of each material, resistivity, is useful in comparing various materials on the basis of their ability to conduct electric currents. High resistivity designates poor conductors.
Resistivity, commonly symbolized by the Greek letter rho, ρ, is quantitatively equal to the resistance R of a specimen such as a wire, multiplied by its cross-sectional area A, and divided by its length l; ρ = RA/l. The unit of resistance is the ohm-metre.
The value of resistivity depends also on the temperature of the material; tabulations of resistivities usually list values at 20° C. Resistivity of metallic conductors generally increases with a rise in temperature; but resistivity of semiconductors, such as carbon and silicon, generally decreases with temperature rise.
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\(\rho_T = \rho_0 [ 1 + \alpha (T – T_0)\) is the equation that shows the relation between the temperature and the resistivity of a material. \(\rho_0\) is the resistivity at a standard temperature, \(\rho_T\) is the resistivity at \(t^o\) C, \(T_0\) is the reference temperature and α is the temperature coefficient of resistivity.
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