What do FE Electrical practice problems actually look like?

Mostly multiple choice with four options, usually phrased 'most nearly', with options close enough that you cannot eliminate them by inspection. Many carry a figure: a circuit schematic, a spectrum sketch, a block diagram, a logic diagram. NCEES gives 110 questions in a 6-hour appointment, of which 5 hours 20 minutes is exam time, so the working time per question is under three minutes once you allow for reading, a handbook lookup and a check. NCEES also uses alternative item types (multiple correct answers, point-and-click, drag-and-drop and fill-in-the-blank), each scored right or wrong with no partial credit.

Is there really that much math on the FE Electrical exam?

Mathematics is tied with Circuit Analysis for the largest knowledge area at 11-17 questions, and FE Electrical and Computer is the only FE exam where mathematics is the largest area at all. It is also the largest mathematics allocation on any FE exam: around 40% more than FE Civil or FE Other Disciplines at 8-12, and roughly double FE Environmental at 5-8. On every other FE exam the biggest block is a subject area: water resources, thermodynamics, fluid mechanics, material and energy balances. Here it is the mathematics itself.

How many questions are on each FE Electrical topic?

Mathematics and Circuit Analysis lead at 11-17 each. Power Systems and Digital Systems follow at 8-12, then Electronics at 7-11 and Control Systems at 6-9. Linear Systems, Signal Processing, Communications, Computer Systems and Engineering Economics get 5-8 each; Probability and Statistics, Ethics and Professional Practice, Properties of Electrical Materials, Electromagnetics, Computer Networks and Software Engineering get 4-6 each. That is 17 knowledge areas, and the ranges sum to between 100 and 154 against an exam of 110 questions.

Do I need to know computer science for the FE Electrical exam?

Yes. Digital Systems at 8-12, Computer Systems at 5-8, Software Engineering at 4-6 and Computer Networks at 4-6 are all on the same exam as power systems and electromagnetics. Our companion guide works through what that split means in practice and why it is the defining feature of this exam.

What reference material do you get on the FE Electrical exam?

The exam is closed book with an electronic reference: the NCEES FE Reference Handbook is supplied on-screen as a searchable PDF, and no personal copies or outside material are allowed. With 17 knowledge areas spanning power engineering through software, searching it quickly is a substantial part of the skill. Practice with the searchable PDF rather than a printed copy.

FE Electrical practice problems: the math is the exam

Mathematics is tied for the largest knowledge area on the FE Electrical and Computer exam, at 11 to 17 of the 110 questions, and this is the only FE exam where that is true. On every other one the biggest block is a subject: water resources, thermodynamics, fluid mechanics. The three problems below make the point a second way. All three are electrical, and six of the nine wrong answers are math slips.

Updated October 6, 2026 · by the FE → PE Prep team

110

Questions

5h 20m

Exam time

Knowledge areas

11–17

Mathematics

The arithmetic is rarely the difficulty

Work through the three problems below and check what each wrong answer actually is. A load left out. A fold you stopped one step short of. A virtual ground ignored. Most of the nine are decisions about what the circuit or the sampler is doing, made before any arithmetic starts, and that is the shape of this exam.

The electrical step is usually one line. Corner frequency is one division. Op-amp gain is one ratio. Aliasing is one subtraction, done twice. The points are in deciding what goes into that one line.
A conversion you performed correctly is still an answer. In the RC problem, the corner at 7667 rad/s is right, necessary, and on the option list as 7670 Hz. Writing it down means forgetting only that the question said hertz.
Doing the right operation too few times is the subtlest failure. In the aliasing problem, one fold leaves the tone still above the baseband limit, so it has to fold again. Stopping after the first fold feels like finishing.
The clock is the same as every FE. Six hours sounds generous, but only 5 hours 20 minutes is exam time. The rest is a nondisclosure agreement, a tutorial and a scheduled break. Across 110 questions that is under three minutes each.

Three practice problems

One from Linear Systems, one from Signal Processing, one from Electronics, all drawn from our free FE Electrical set, and none of them the three worked in the companion guide. Try each before opening the solution, and read the distractor notes.

1. Corner frequency of a loaded RC low-pass filter

This is the handbook's own first-order RC cell, drawn the way the handbook draws it: with a load across the output. The arithmetic is one time constant and one division. The work is deciding which resistance belongs in the time constant.

1
medium
A. Transient/frequency response, resonance, Laplace & transfer functions
The first-order RC low-pass filter shown has $R_1 = 1.5$ kΩ and $C = 0.1$ µF, and it drives a load resistor $R_2 = 10$ kΩ connected across its output. The corner (−3 dB) frequency of the loaded filter is most nearly:
Figure — drag or pinch to move around
1. 138 Hz
2. 1060 Hz
3. 1220 Hz
4. 7670 Hz
Show the answer & worked solution
Answer: C.1220 Hz
With the source replaced by a short, the capacitor sees $R_1$ and the load $R_2$ in parallel — the handbook's first-order RC low-pass cell (Analog Filter Circuits, p. 384): $R_P=\dfrac{R_1R_2}{R_1+R_2}=\dfrac{1.5\times10}{1.5+10}=1.304$ kΩ, so $\omega_c=\dfrac{1}{R_P C}=\dfrac{1}{(1304.3\ \Omega)(0.1\times10^{-6}\ \text{F})}=7667$ rad/s and $f_c=\dfrac{\omega_c}{2\pi}=1220$ Hz. Distractors: $R_1$ and $R_2$ added in series instead of combined in parallel, the $R_S=R_1+R_2$ the handbook uses in its RC high-pass and RL low-pass cells (138 Hz); the load left out, so the capacitor is charged through $R_1$ alone (1060 Hz, the unloaded filter); and $\omega_c = 1/(R_P C)$ in rad/s reported as if it were hertz (7670 Hz).

What the distractors teach

With the source shorted, the capacitor sees R₁ and the 10 kΩ load in parallel: 1.304 kΩ, which gives 7667 rad/s and 1220 Hz. Ignore the load and you get the unloaded filter's 1060 Hz, a comfortable-looking answer 13% low. Add the two resistors in series instead and you get 138 Hz. Forget to divide ω by 2π and you get 7670 Hz, the number you computed on the way. Two of the three wrong answers are decisions about the circuit, not slips of arithmetic, and the most tempting one is the circuit you studied rather than the one you were given.

2. Alias frequency of an under-sampled tone

An 18 kHz tone sampled at 10 kHz. Everyone who has met Nyquist knows this will alias. The alias frequency is still easy to get wrong the first time, and the reason is arithmetic rather than signal theory.

2
medium
A. Sampling, analog & digital filters, Z-transforms
An 18 kHz sinusoidal tone is sampled at $f_s = 10$ kHz (see the spectrum sketch). The apparent (alias) frequency of the tone in the sampled signal is most nearly:
Figure — drag or pinch to move around
1. 2 kHz
2. 3 kHz
3. 8 kHz
4. 18 kHz
Show the answer & worked solution
Answer: A.2 kHz
Sampled images appear at $|f-kf_s|$ : $|18-10|=8$ kHz and $|18-20|=2$ kHz. Only 2 kHz lies in the baseband $[0,\ f_s/2=5\ \text{kHz}]$ , so the tone appears at 2 kHz. Distractors stop after one subtraction ( $f-f_s=8$ kHz, which still exceeds $f_s/2$ and must fold again), repeatedly subtract $f_s/2$ as if the spectrum replicated every half sample rate (3 kHz), and report the original 18 kHz tone as if sampling preserved it.

What the distractors teach

The trap is stopping too early. Subtract once (18 minus 10) and you get 8 kHz, which looks like a finished answer. It is not: 8 kHz still sits above the 5 kHz baseband limit, so it has to fold again, landing at 10 minus 8, or 2 kHz. The other two options are cruder: subtract half the sample rate repeatedly and you get 3 kHz, or report the original 18 kHz as though sampling had preserved it. This is the single most instructive question in our free FE Electrical set, because the wrong answer is what you get from doing the right operation one time too few.

3. Output of an inverting op-amp

Electronics carries 7–11 questions and this is its most fundamental configuration. Two resistors, one ratio, one virtual ground. The distractors are a catalog of the ways that ratio and that virtual ground go wrong.

3
medium
A. Diodes, transistors, op-amps, instrumentation & power electronics
The ideal inverting op-amp circuit shown (±15 V supplies) has input resistor $R_1=10$ k $\Omega$ and feedback resistor $R_f=47$ k $\Omega$ . With $v_{in}=0.2$ V applied, the output voltage is most nearly:
Figure — drag or pinch to move around
1. -1.14 V
2. -0.94 V
3. -0.165 V
4. -0.0426 V
Show the answer & worked solution
Answer: B.-0.94 V
The + input is grounded, so the ideal op-amp holds the − input at 0 V (a virtual ground): the input current $v_{in}/R_1$ flows on through $R_f$ and the output swings negative. The handbook's inverting case of the two-source circuit, $v_0=-(R_2/R_1)\,v_a$ with $R_2=R_f$ (Operational Amplifiers, p. 386), gives $v_{out}=-\dfrac{R_f}{R_1}v_{in}=-\dfrac{47}{10}\times0.2=-0.94$ V, well inside the ±15 V supplies. Distractors: keep the minus sign but use the non-inverting magnitude, $-(1+R_f/R_1)v_{in}=-1.14$ V; ignore the virtual ground and send the input current through $R_1$ and $R_f$ in series, $-v_{in}R_f/(R_1+R_f)=-0.165$ V; and invert the resistor ratio, $-(R_1/R_f)v_{in}=-0.0426$ V.

What the distractors teach

Every option is negative, so the minus sign gives nothing away; the magnitude is the whole question. Use the non-inverting gain 1 + Rf/R1 and keep the minus sign and you get −1.14 V: the right polarity on the gain of a different circuit, which makes it the most tempting wrong answer. Forget the virtual ground and run the input current through R1 and Rf in series and you get −0.165 V. Invert the resistor ratio to −R1/Rf and you get −0.0426 V. The inverting gain is −Rf/R1 = −4.7, and −4.7 × 0.2 V = −0.94 V.

Where the 110 questions come from

Seventeen knowledge areas, tied for the most of any FE exam. Read the first row before anything else.

FE Electrical and Computer knowledge areas and question counts, per the NCEES specification
Knowledge area	Questions
MathematicsTied for the largest area on the exam, and the largest mathematics allocation on any FE exam. Algebra and trigonometry, complex numbers, discrete mathematics, analytic geometry, calculus, differential equations, linear algebra, vector analysis.	11–17
Probability and StatisticsMeasures of central tendency and dispersion, probability distributions including conditional probability, expected value.	4–6
Ethics and Professional PracticeCodes of ethics and the NCEES Model Law and Rules, intellectual property, safety (grounding, PPE, radiation protection).	4–6
Engineering EconomicsTime value of money, cost estimation, risk identification, analyses.	5–8
Properties of Electrical MaterialsSemiconductor materials (energy bands, doping, p-n theory), electrical properties such as resistivity and permittivity, thermal properties.	4–6
Circuit Analysis (DC and AC Steady State)Tied with Mathematics for the largest area. KCL and KVL, series/parallel equivalents, Thevenin and Norton, node and loop analysis, waveform analysis, phasors, impedance.	11–17
Linear SystemsFrequency and transient response, resonance, Laplace transforms, transfer functions.	5–8
Signal ProcessingSampling (aliasing, Nyquist), analog filters, digital filters (difference equations, Z-transforms).	5–8
ElectronicsModels and characteristics of diodes and transistors, amplifiers, operational amplifiers, instrumentation, power electronics.	7–11
Power SystemsSingle and three-phase power, transmission and distribution, voltage regulation, transformers, motors and generators, power factor correction.	8–12
ElectromagneticsElectrostatics and magnetostatics, Maxwell equations and wave propagation, high-frequency transmission lines.	4–6
Control SystemsBlock diagrams, Bode plots, closed-loop and open-loop response, stability, controller performance.	6–9
CommunicationsAM, FM and PCM modulation, Fourier transforms and series, multiplexing, digital communications.	5–8
Computer NetworksRouting and switching, topologies, network types and models (OSI, TCP/IP), intrusion detection, security.	4–6
Digital SystemsNumber systems, Boolean logic, logic gates and circuits, logic minimization, flip-flops and counters, state machines, timing, programmable logic devices.	8–12
Computer SystemsMicroprocessors, memory technology and systems, interfacing.	5–8
Software EngineeringAlgorithms and big-O complexity, data structures, software implementation and testing.	4–6

Mathematics at 11–17 is the largest mathematics allocation on any FE exam: about 40% more than FE Civil or FE Other Disciplines at 8–12, and roughly double FE Environmental at 5–8. It is also the only case where mathematics outranks every subject area on its own exam. Candidates who plan their study around circuits and power tend to discover this in the wrong room.

The other defining feature of this exam, that it is really two professions on one exam, is covered in the companion guide, along with the pass rate: how hard is the FE Electrical and Computer exam?

Common questions

What do FE Electrical practice problems actually look like?: Mostly multiple choice with four options, usually phrased 'most nearly', with options close enough that you cannot eliminate them by inspection. Many carry a figure: a circuit schematic, a spectrum sketch, a block diagram, a logic diagram. NCEES gives 110 questions in a 6-hour appointment, of which 5 hours 20 minutes is exam time, so the working time per question is under three minutes once you allow for reading, a handbook lookup and a check. NCEES also uses alternative item types (multiple correct answers, point-and-click, drag-and-drop and fill-in-the-blank), each scored right or wrong with no partial credit.
Is there really that much math on the FE Electrical exam?: Mathematics is tied with Circuit Analysis for the largest knowledge area at 11-17 questions, and FE Electrical and Computer is the only FE exam where mathematics is the largest area at all. It is also the largest mathematics allocation on any FE exam: around 40% more than FE Civil or FE Other Disciplines at 8-12, and roughly double FE Environmental at 5-8. On every other FE exam the biggest block is a subject area: water resources, thermodynamics, fluid mechanics, material and energy balances. Here it is the mathematics itself.
How many questions are on each FE Electrical topic?: Mathematics and Circuit Analysis lead at 11-17 each. Power Systems and Digital Systems follow at 8-12, then Electronics at 7-11 and Control Systems at 6-9. Linear Systems, Signal Processing, Communications, Computer Systems and Engineering Economics get 5-8 each; Probability and Statistics, Ethics and Professional Practice, Properties of Electrical Materials, Electromagnetics, Computer Networks and Software Engineering get 4-6 each. That is 17 knowledge areas, and the ranges sum to between 100 and 154 against an exam of 110 questions.
Do I need to know computer science for the FE Electrical exam?: Yes. Digital Systems at 8-12, Computer Systems at 5-8, Software Engineering at 4-6 and Computer Networks at 4-6 are all on the same exam as power systems and electromagnetics. Our companion guide works through what that split means in practice and why it is the defining feature of this exam.
What reference material do you get on the FE Electrical exam?: The exam is closed book with an electronic reference: the NCEES FE Reference Handbook is supplied on-screen as a searchable PDF, and no personal copies or outside material are allowed. With 17 knowledge areas spanning power engineering through software, searching it quickly is a substantial part of the skill. Practice with the searchable PDF rather than a printed copy.

Build your study plan

Tell us how long you have. We'll budget your hours across every knowledge area using the official NCEES question weights. The heaviest areas get the most time, which is the opposite of how most people study.

Work through seven more

Ten free FE Electrical and Computer problems in total: a loaded voltage divider, power factor correction, network topology, AM spectra, cascade feedback, transmission-line reflection. Each comes with the figure and the full worked solution. No signup.

Try the free FE Electrical set Explore FE Electrical

Format, knowledge areas and appointment length are from the NCEES FE Electrical and Computer specification. The per-question time and the comparisons drawn against other FE specifications are ours, not NCEES figures. Specifications and fees change over time; confirm current specifics at ncees.org. Independent study resource; not affiliated with, endorsed by, or sponsored by NCEES.