A first-order process with gain 2.0 and time constant 5 min receives a unit step. Output after 5 min is most nearly:
- (A)0.632
- (B)1
- (C)1.01
- (D)1.26
Show worked solution
Answer: (D)
After one time constant, response is K(1-e^-1)=1.264.
A first-order step response approaches final gain exponentially.
At t=tau and unit step, the normalized fraction is 0.632.
FE Reference Handbook — Process Control: First-Order Dynamics
Why the other choices appear
- (A)Using unit process gain gives the normalized response only.
- (B)Assuming output reaches half or full unit after one time constant ignores gain and exponential response.
- (C)Applying an unsupported 20% final scaling understates the result obtained from the governing relation.