Discussion
The time constant of a first-order sensor determines
Answer: C
The time constant determines the speed of response.
A first-order sensor, such as a thermometer or thermistor, follows a step input exponentially:
\[ y(t) = K\left(1 - e^{-t/\tau}\right) \]
The time constant tau is the time to reach 63.2% of the final value, and the output is within about 1% after 5 tau. A smaller tau means a faster sensor.
Sensitivity is the static gain K, linearity describes how straight the input-output relation is, and range is the span of inputs. All three are static characteristics, while tau describes the dynamic response.
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