A linear transducer is calibrated for the ranges shown in the figure. The gain of the transducer is _______ mA/°C (rounded off to two decimal places).
Tap to open full sizeBlock diagram: a dashed box labelled 'Transducer' contains two solid blocks in series, 'Temperature Sensor' followed by 'Current Transmitter'. The input line entering the dashed box on the left is labelled '50 °C – 150 °C'. The output line leaving the dashed box on the right is labelled '4 mA – 20 mA'.
ANSWER
The gain of the transducer is 0.16 mA/°C.
Official answer: 0.15 to 0.17Source: Official answer key, GATE 2024 IN (IISc Bengaluru)
The dashed block (temperature sensor followed by current transmitter) is one linear transducer. Its gain is the slope of output against input: .
Input span: .
Output span: . The 4 mA offset at 50 °C is a zero shift and does not enter the gain.
The gain is therefore .
KEY IDEA
For a linear transducer, gain is the slope: output span divided by input span. The calibrated ranges give the spans directly, and the offset (4 mA at 50 °C) does not affect the slope.
WATCH OUT FOR
Dividing the end values (20 mA / 150 °C or 4 mA / 50 °C) instead of the spans, or counting the 4 mA live-zero offset as part of the gain.
From the GATE 2024 IN paper. Every question of this paper · Download the full paper · All 1 4-20 mA & networks questions, with notes