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Question

Which of the following sensors has excellent linearity ?

This question was previously asked in
UGC NET 2014 Paper 2 History Question Paper (28-Dec-2014)
The correct answer is

Si based IC chip

 The IC temperature sensor is linear by construction, not by approximation — option 4.

Where its linearity comes from. It does not rely on any bulk material property. Two transistors are run at different current densities, and the difference in their base-emitter voltages is

\(\Delta V_{BE}=\dfrac{kT}{q}\ln\left(\dfrac{J_{1}}{J_{2}}\right)\)

The logarithm is a fixed ratio set by the geometry of the chip, so \(\Delta V_{BE}\) is exactly proportional to absolute temperature — a PTAT voltage. On-chip amplification scales it to a convenient 10 mV/°C, and no linearisation is needed at all.

SensorLawLinearity
RTD\(R_{T}=R_{0}\left(1+\alpha T+\beta T^{2}\right)\)Good, slightly curved
ThermocouplePolynomial, several termsModerate
Radiation pyrometer\(W=\sigma T^{4}\)Fourth power — the worst
Si IC sensor\(V=10\ \text{mV}/^{\circ}\text{C}\times T\)Excellent

Why option 1 is the strong rival. A platinum RTD is the most linear of the classical sensors and is used as an interpolation standard, but the Callendar-Van Dusen equation carries a quadratic term: over 0 to 600 °C the departure from a straight line reaches several degrees, and accurate work must correct for it. "Good" is not "excellent".

Why option 3 is the worst possible answer. A radiation pyrometer measures emitted power, and the Stefan-Boltzmann law makes that vary as the fourth power of absolute temperature. It is the most non-linear device in the list by a wide margin — and it depends on the target's emissivity as well.

What the IC sensor gives up is range. Being a silicon circuit, it works only from about −55 to +150 °C, and cannot approach the RTD's 600 °C, the thermocouple's 1500 °C, or the pyrometer's ability to measure a furnace without touching it. Its virtues are linearity, a large calibrated output that needs no cold-junction compensation or bridge, and a price of a few rupees.

Hence, the sensor with excellent linearity is the Si based IC chip.

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