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GATE 2025 BT – Question 42

Fundamentals of Biological Engineering · Process Control: Measurement devices, valves, first and second order systems, feedback and feed forward control, P, I and D controllers and tuning · 2 marks · Multiple choice

A thermometer measuring body temperature follows a first-order response with a time constant of 40 seconds. The instrument will reach 95% of its steady-state output at __________ seconds. (Round off to the nearest integer)

  1. 60
  2. 80
  3. 120
  4. 160

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Correct answer: (C) 120

Explanation

The step response of a first-order system is $1 - e^{-t/\tau}$. Setting it to 0.95 gives $t = -\tau\ln 0.05 = 2.996\tau = 3 \times 40 \approx 120$ s.