Linear approximation: Difference between revisions

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The electrical resistivity of most materials changes with temperature. If the temperature ''T'' does not vary too much, a linear approximation is typically used:

:<math>\rho(T) = \rho_0[1+\alpha (T - T_0)]</math>

where <math>\alpha</math> is called the ''temperature coefficient of resistivity'', <math>T_0</math> is a fixed reference temperature (usually room temperature), and <math>\rho_0</math> is the resistivity at temperature <math>T_0</math>. The parameter <math>\alpha</math> is an empirical parameter fitted from measurement data. Because the linear approximation is only an approximation, <math>\alpha</math> is different for different reference temperatures. For this reason it is usual to specify the temperature that <math>\alpha</math> was measured at with a suffix, such as <math>\alpha_{15}</math>, and the relationship only holds in a range of temperatures around the reference.<ref>{{cite book |first=M. R. |last=Ward (|year=1971) ''|title=Electrical Engineering Science'', pp. |pages=36–40, |publisher=McGraw-Hill. |isbn=0-07-094255-2 }}</ref> When the temperature varies over a large temperature range, the linear approximation is inadequate and a more detailed analysis and understanding should be used.

==See also==