As discussed in Resistance and Ohm's Law, it is the thermal velocity which dominates setting the mean time betwen electron-atom collisions.
As temperature goes up, resistance goes up in most resistive materials.
At higher temperatures, there's greater thermal energy, leading to higher electron velocity. This leads to more frequent collisions (reducing $t_{\text{collision}}$), which reduces the peak drift velocity reached before a collision occurs. This causes reduced current flow for the same external electric field, which manifests itself as higher resistance.
The linearized model of resistivity has a material-dependent temperature coefficient $\alpha_{\text{material}}$:
$$\rho_T = \rho_{ref} + \alpha_{\text{material}} * (T - T_{ref})$$
While this is a linearized model, the real behavior is highly nonlinear. This is just an approximation over a small range.
Most materials have a positive temperature coefficient (PTC), $\alpha > 0$.
Some materials, however, have a negative temperature coefficient (NTC).
In many consumer, industrial, and other situations, we often want a zero temperature coefficient, so that our circuit's performance doesn't change over our operating temperature range.
Since resistance changes with temperature, we may be able to use a resistor as a temperature sensor.
A resistor, in normal operation, turns electrical energy into heat. The mass of the resistor heats up.
For a positive-temperature-coefficient resistor, the resistance also rises as the temperature goes up.
Normally, a new equilibrium is found. This equilibrium is at a temperature higher than ambient, and (for a PTC resistor) at a resistance higher than the resistance at ambient.
If a PTC resistor is driven by a constant current source, then when temperature goes up, so does the power dissipation (since $P = i^2 R$ and $R$ is increasing). This can lead to destructive runaway.
If a PTC resistor is driven by a constant voltage source, then when temperature goes up, the power dissipation goes down (since $P = \frac {v^2} {R}$).
In any case, using any resistor as a temperature sensor always involves running a current through it, so there will always be self-heating, which can bias the measurement.
As discussed in the Practial Resistors: Power Rating (Wattage) section, it is possible that no equilibrium is reached before the resistor material heats up to a point where the material changes dramatically and possibly fails permanently.
There are three common types of resistors used as temperature sensors:
Thermistors are often used intentionally with self-heating effects for current limiting or as self-resetting fuses.
RTDs are often used for precision temperature measurement.
In the next section, Practical Resistors: Potentiometers, we'll discuss mechanically adjustable resistors, also known as potentiometers.
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