Near room temperature, the electric resistance of a typical metal increases linearly with rising temperature, while the electrical resistance of a typical semiconductor decreases with rising temperature. The amount of that change in resistance can be calculated using the temperature coefficient of resistivity of the material using the following formula:
![R = R_0 [\alpha (T - T_0) + 1]\,\!](http://upload.wikimedia.org/math/b/5/e/b5e510a563967b7edb98ee8e8ed1b280.png)
where T is its temperature, T0 is a reference temperature (usually room temperature), R0 is the resistance at T0, and α is the percentage change in resistivity per unit temperature. The constant α depends only on the material being considered. The relationship stated is actually only an approximate one, the true physics being somewhat non-linear, or looking at it another way, α itself varies with temperature. For this reason it is usual to specify the temperature that α was measured at with a suffix, such as α15 and the relationship only holds in a range of temperatures around the reference.[4]
At lower temperatures (less than the Debye temperature), the resistance of a metal decreases as T5 due to the electrons scattering off of phonons. At even lower temperatures, the dominant scattering mechanism for electrons is other electrons, and the resistance decreases as T2. At some point, the impurities in the metal will dominate the behavior of the electrical resistance which causes it to saturate to a constant value. Matthiessen's Rule (first formulated by Augustus Matthiessen in the 1860s; the equation below gives its modern form) [5][6] says that all of these different behaviors can be summed up to get the total resistance as a function of temperature,
E-Store
