Test Yourself - First-Order Unity Feedback System

1. What is the time constant \( T \) in a first-order system?

a) Time to reach 50% of the final value b) Time to reach 63.2% of the final value c) Time to reach 100% of the final value d) Time to reach 0% of the final value

2. For a unit-step input, the output response of a first-order system is:

a) \( C(t) = 1 - e^{-t/T} \) b) \( C(t) = e^{-t/T} \) c) \( C(t) = 1 + e^{-t/T} \) d) \( C(t) = 1 - e^{t/T} \)

3. The transfer function of a first-order system is:

a) \( \frac{1}{sT + 1} \) b) \( \frac{1}{sT - 1} \) c) \( \frac{1}{s + T} \) d) \( \frac{1}{s - T} \)