6.08 Temperature Dependence of Resistivity
Like in the case of most physical properties, resistivity also varies with temperature as a variation of resistivity with temperature. When we observe different conducting mediums, we see that the resistivity varies almost linearly with temperature. In other words, the resistivity increases with increasing temperature.
For such linear relations one can write an empirical approximation that is basically good enough for most engineering purposes. And this empirical equation for the resistivity is in the form of ρ minus ρ0 is equal to ρ0 times some constant, α, times T minus T0, where T0 is a selected reference temperature, and in general we select this temperature as room temperature.
Let’s see, T0 is room temperature and it is equal to 293 Kelvin. ρ0 represents the resistivity at temperature T0, at this reference temperature, and hence ρ represents the resistivity at temperature T. Here the temperatures are in Kelvin and the constant α is called “temperature coefficient of resistivity”. This quantity is tabulated for different conducting mediums in tables so that one can easily find the associated resistivity for that specific medium.
For example, the resistivity for copper, let me put it as the temperature coefficient of the resistivity for copper is equal to 4.3 times 10 to the -3, inverse Kelvin. And the resistivity at room temperature for copper, 0 0, is 1.69 times 10-19 ohm meter. In a similar way, temperature coefficient and as well as the resistivity at room temperature for different conducting mediums or different materials are listed in the tables so that one can find them in order to calculate the resistivity of that medium at a different temperature.
Now, since resistivity and resistance are directly proportional, one can also write down an empirical equation for the resistance or the temperature dependence of resistance, simply by replacing the ρ and ρ0 with R and R0. Therefore we can also easily calculate how much the resistance of an object is going to be changing with temperature.