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A sensor requires 30 s to indicate 90% of the response to a step input. If the sensor is a first-order system, the time constant is [given, loge (0.1) = -2.3]

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  1. 15 s
  2. 13 s
  3. 21 s
  4. 28 s

Answer (Detailed Solution Below)

Option 2 : 13 s
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Detailed Solution

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The standard equation for a step input is,

c(t) = 1 – e-t/τ

Where τ is time constant.

At c(t) = 0.9 and t = 30s

⇒ 0.9 = 1 – e-30/τ

⇒ τ = 13 sec
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