GATE 2018 IN Q.22: solution and answer

GATE 2018 · INQ.22 · 1 mark · NAT

As shown in the figure, temperature $θ$ is measured using a K type thermocouple. It has a sensitivity of $40 μ V /^{\circ} C$ . The gain ( $G$ ) of the ideal instrumentation amplifier is 25. If the output $V_{o}$ is 96 mV, then the value of $θ$ (in $^{\circ}$ C) is ____.

GATE 2018 IN question 22: Two thermocouple junctions in series opposition. — Figure from the GATE 2018 IN paper. It is part of the question.

Answer and solution

ANSWER

$θ = 96^{\circ} C$

Official answer: 95 to 97Source: Official answer key, GATE 2018 IN (IIT Guwahati)

The two thermocouple junctions (M-N at $θ$ and N-M at $θ_{r e f} = 0^{\circ} C$ ) are connected in series opposition through the joined N legs. Every other joint (the N-N link and the M leads meeting the amplifier terminals) is at room temperature, and by the law of intermediate metals and temperatures these add no net emf. The net emf is therefore $E = S (θ - θ_{r e f})$ .
The reference junction is at $0^{\circ} C$ and $S = 40 μ V /^{\circ} C$ , so $E = S θ$ .
The ideal instrumentation amplifier has gain $G = 25$ and the emf is applied across its inputs, so $V_{o} = G E$ .
The input emf is $E = \frac{V _{o}}{G} = \frac{96 mV}{25} = 3.84 mV$
The temperature is $θ = \frac{E}{S} = \frac{3.84 \times 1 0 ^{- 3} V}{40 \times 1 0 ^{- 6} V / ^{\circ} C} = 96^{\circ} C$

KEY IDEA

With the reference junction at $0^{\circ} C$ , the thermocouple emf is $S θ$ . An ideal amplifier of gain $G$ gives $V_{o} = G S θ$ , so $θ = V_{o} / (G S)$ . Joints at room temperature in the circuit add no net emf.

WATCH OUT FOR

Forgetting to divide $V_{o}$ by the amplifier gain, or mixing mV with $μ$ V and being off by a factor of 1000. Another slip is to subtract room temperature from $θ$ , even though the reference junction here is held at $0^{\circ} C$ .

From the GATE 2018 IN paper. Every question of this paper · Download the full paper · All 5 Temperature questions, with notes

GATE 2018 IN Q.22: solution and answer

Answer and solution

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