Question

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, log_e (0.1) = -2.3]
1. 15 s
2. 13 s
3. 21 s
4. 28 s

Answer 1

Correct Answer - Option 2 : 13 s

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