Difficulty: Easy
Correct Answer: increases exponentially from zero to the final value
Explanation:
Introduction / Context:Lag networks (first-order RC circuits) are widely used in control and communication systems for shaping frequency response. Understanding their time-domain step response helps correlate time and frequency domain behavior.
Given Data / Assumptions:
Concept / Approach:The step response of a first-order low-pass network is exponential. It starts at 0 V and asymptotically approaches the final steady-state value equal to the input amplitude (here, 1 V).
Step-by-Step Solution:
Transfer function H(s) = 1 / (1 + sRC).Laplace of input: 1/s.Output: Y(s) = (1/s)(1 / (1 + sRC)).Inverse Laplace: y(t) = 1 − e^(−t/RC).Hence, y(t) rises exponentially from 0 to 1 as t → ∞.Verification / Alternative check:
Compare with capacitor charging curve; matches physical intuition.Why Other Options Are Wrong:
Constant from start: wrong, no system can instantaneously jump to final.Decreasing from 1 to 0: describes discharge, not step input.Oscillation: absent in first-order lag networks.Common Pitfalls:
Confusing lag network with lead or resonant circuits; forgetting exponential charging law.Final Answer:
increases exponentially from zero to the final value
Discussion & Comments