An ideal differentiator has \(H(j\omega) = j\omega\). On a Bode magnitude plot, its magnitude response:

Rises with frequency at a slope of +20 dB/decade

Stays flat at 0 dB across all frequencies

Falls with frequency at a slope of −20 dB/decade

Rises with frequency at a slope of +40 dB/decade

A transfer function with a single zero at the origin, \(H(s) = s/(s + 10)\), behaves like a:

Pure delay, which adds phase lag only

Low-pass filter that blocks high frequencies

A continuous-time LTI system is BIBO stable when all poles of its transfer function lie:

In the left half of the s-plane

In the right half of the s-plane

An ideal integrator, \(H(s) = 1/s\), responds to a unit step input with:

A ramp that grows linearly with time

The transfer function \(H(s) = (s + 3)/[(s + 1)(s + 2)]\) has a zero at:

s = +3, on the positive real axis

FE · 5% of the exam

Linear Systems practice questions

10 free Linear Systems questions for the FE Electrical and Computer Exam (FE) exam, each with the correct answer and an explanation for every option.

Start the questions Free 10-question FE quiz

What this domain covers

How linear circuits and systems respond over time and frequency: transient and frequency response, resonance, Laplace transforms and transfer functions.

Exam weight: 5%
On a real exam: ≈ 6 questions
In our bank: 30 questions

Topics that come up most

First- and second-order transient response
Resonance and bandwidth
Laplace transforms and inverse transforms
Transfer functions, poles and zeros
Two-port network parameters

How to study it

Learn the RC and RL time-constant solutions and the second-order damping cases well enough to sketch the response before you calculate it.

Sample Linear Systems questions

Try each one before opening the answer. Original questions written to the official exam objectives.

Question 1
Convolving any signal f(t) with a unit impulse δ(t) gives:
- AThe derivative of f(t)
- BZero
- Cf(t) itself
- DA unit step
Show answer and explanation
Answer: C) f(t) itself
- AIncorrect. That uses the derivative of the impulse.
- BIncorrect. The result isn't zero.
- CCorrect. The impulse is the identity for convolution.
- DIncorrect. That isn't the result.
Question 2
An ideal differentiator has \(H(j\omega) = j\omega\). On a Bode magnitude plot, its magnitude response:
- AStays flat at 0 dB across all frequencies
- BFalls with frequency at a slope of −20 dB/decade
- CRises with frequency at a slope of +20 dB/decade
- DRises with frequency at a slope of +40 dB/decade
Show answer and explanation
Answer: C) Rises with frequency at a slope of +20 dB/decade
For H(jω) = jω the magnitude is ω, a straight line rising at +20 dB/decade that crosses 0 dB at ω = 1 rad/s. The phase stays constant at +90°.
- AIncorrect. |H(jω)| = ω changes with frequency. Only the phase is constant (+90°). The magnitude is 0 dB only at ω = 1 rad/s.
- BIncorrect. This is the response of an ideal integrator, H(jω) = 1/(jω).
- CCorrect. |H(jω)| = ω, so 20·log10(ω) rises by 20 dB for every tenfold increase in frequency. This is why differentiators amplify high-frequency noise.
- DIncorrect. A +40 dB/decade slope corresponds to a double differentiator, H(jω) = (jω)², not a single factor of jω.
Question 3
In the Laplace domain, delaying a signal by T seconds multiplies its transform by:
- A\(sT\)
- B\(e^{sT}\), a time advance
- C\(1/(s + T)\)
- D\(e^{-sT}\)
Show answer and explanation
Answer: D) \(e^{-sT}\)
- AIncorrect. That isn't the property.
- BIncorrect. A delay uses a negative exponent.
- CIncorrect. That isn't the property.
- DCorrect. This is the time-shift property.
Question 4
A transfer function with a single zero at the origin, \(H(s) = s/(s + 10)\), behaves like a:
- APure delay, which adds phase lag only
- BLow-pass filter that blocks high frequencies
- CPure integrator
- DHigh-pass filter
Show answer and explanation
Answer: D) High-pass filter
- AIncorrect. That's \(e^{-sT}\).
- BIncorrect. It passes high frequencies.
- CIncorrect. That's 1/s.
- DCorrect. It blocks DC and passes high frequencies.
Question 5
A continuous-time LTI system is BIBO stable when all poles of its transfer function lie:
- AIn the right half of the s-plane
- BIn the left half of the s-plane
- COn the imaginary axis
- DAt the origin
Show answer and explanation
Answer: B) In the left half of the s-plane
- AIncorrect. Those grow without bound.
- BCorrect. Negative real parts.
- CIncorrect. That's marginal stability.
- DIncorrect. That's marginal stability.
Question 6
An ideal integrator, \(H(s) = 1/s\), responds to a unit step input with:
- AAn impulse
- BA unit step, unchanged
- CA ramp that grows linearly with time
- DA decaying exponential
Show answer and explanation
Answer: C) A ramp that grows linearly with time
- AIncorrect. That's the derivative of a step.
- BIncorrect. The integrator accumulates.
- CCorrect. Integrating a constant gives a ramp.
- DIncorrect. That's a first-order lag response.
Question 7
The Laplace transform of the unit ramp \(t\,u(t)\) is:
- A\(2/s^3\)
- B\(1/s\)
- C\(s\)
- D\(1/s^2\)
Show answer and explanation
Answer: D) \(1/s^2\)
- AIncorrect. That's for \(t^2\).
- BIncorrect. That's the unit step.
- CIncorrect. That's a derivative operator.
- DCorrect. A standard transform pair.
Question 8
The impulse response of a system with transfer function \(1/s\) is:
- AA ramp
- BA unit impulse
- CA unit step
- DA decaying exponential
Show answer and explanation
Answer: C) A unit step
- AIncorrect. That's the step response.
- BIncorrect. That's a transfer function of 1.
- CCorrect. 1/s is an integrator.
- DIncorrect. That's 1/(s + a).
Question 9
Using the final value theorem, the step response of \(H(s) = 5/(s + 2)\) settles to:
- A0
- B5
- C2
- D2.5
Show answer and explanation
Answer: D) 2.5
- AIncorrect. The system has nonzero DC gain.
- BIncorrect. Evaluate H(0).
- CIncorrect. Evaluate H(0) = 5/2.
- DCorrect. \(\lim_{s\to0} s \cdot H(s)/s = 5/2\).
Question 10
The transfer function \(H(s) = (s + 3)/[(s + 1)(s + 2)]\) has a zero at:
- As = +3, on the positive real axis
- Bs = −1 and s = −2
- Cs = −3
- Ds = 0
Show answer and explanation
Answer: C) s = −3
- AIncorrect. The zero is at −3.
- BIncorrect. Those are poles.
- CCorrect. Zeros make the numerator zero.
- DIncorrect. The numerator isn't zero there.

Linear Systems: FAQs

How much of the FE exam is Linear Systems?

Linear Systems is 5% of the FE exam by the official exam guide's weighting, which on a 110-question form works out to roughly 6 questions. The real exam's exact split varies by form.

What does the Linear Systems domain cover?

How linear circuits and systems respond over time and frequency: transient and frequency response, resonance, Laplace transforms and transfer functions.

How should I study Linear Systems for FE?

Learn the RC and RL time-constant solutions and the second-order damping cases well enough to sketch the response before you calculate it.

Where can I practise more Linear Systems questions?

This page has 10 free Linear Systems questions with answers. The ExamWize FE question bank has 30 questions in this domain. Every practice exam result breaks your score down by domain, and Review Mode re-drills the questions you missed.

Get Linear Systems exam-ready

The full FE bank has 30 Linear Systems questions. Timed practice exams match the real exam's length and domain weights, every result shows your score per domain, and Review Mode re-drills the questions you missed.

See the full FE practice exams Take the free diagnostic

Not affiliated with NCEES; questions are original, written from the official exam outline, and never copied from the real exam.