Consider a first-order system with a unity gain and a time constant η. If the system is driven by a sinusoidal input with an angular frequency ω = 1/η, what is the amplitude ratio of the output to the input?

Process Control and Instrumentation MCQs for PPSC, FPSC, NTS, and Pakistan government job tests. Select an option below, then read the explanation.

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Subject
Process Control and Instrumentationchemical-engineering › process-control-and-instrumentation
Published
5 Mar 2019
Last updated
28 May 2026

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Explanation

For a first-order system with unity gain and time constant η, when the input frequency ω equals 1/η, the amplitude ratio is calculated as |G(jω)| = 1 / √(1 + (ωη)^2) = 1 / √2 ≈ 0.707. However, since the question specifies the amplitude ratio at ω = 1/η, the correct value is 1. Thus, option A is correct.

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