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# Thermal Time Constant

The thermal time constant indicates a time required for a thermistor to respond to a change in its ambient temperature.
When the ambient temperature is changed from T1 to T2, the relationship between the time elapsed during the temperature change t (sec.) and the thermistor temperature T can be expressed by the following equation.

τ (tau in sec.) in the equation denotes the thermal time constant.

Now, assuming t and τ (tau) are equal (t = τ), the equation can be expressed as follows.

This shows that the constant τ (sec.) is defined as a time for the thermistor to reach 63.2% of the total difference between its initial and final body temperatures.
The thermistor body temperature does not reach its ambient temperature when a time period defined by τ is elapsed.

The temperature change rate at n times the constant τ (sec.) is as follows, showing that the thermistor body temperature reaches its ambient temperature approximately within 7 times the constant.

τ = 63.2%, 2τ = 86.5%, 3τ = 95.0%, ・・・・ 7τ ≒ 100%

Generally, the smaller the size of the thermistor, the faster the thermal response, and thus the smaller the constant τ will be. The constant varies significantly depending on thermistor assemblies. It is necessary to select materials having a high thermal conductivity considering the environment where the thermistor is used.