Electricity and Magnetism is 5-8 questions on the FE Mechanical exam. For most mechanical candidates it is the least familiar area on the paper, and the one most often written off as a loss.
That is a poor trade. The scope is narrow, the questions are shallow relative to an electrical engineer's version of them, and five to eight questions is more than dynamics is worth on the FE Civil exam. A weekend on circuits recovers most of these points.
Exam weight: NCEES lists Electricity and Magnetism at 5-8 questions (5-7%) of the 110-question FE Mechanical exam. Work each problem below on paper first, then reveal the worked solution — reading a solution you have not attempted builds recognition, not recall.
What NCEES Tests in Electricity and Magnetism
The specification covers charge, current, voltage, resistance and power, along with DC circuit analysis, AC circuit fundamentals, and motors and generators. Expect equivalent resistance of a series-parallel network, a voltage divider, power dissipated in a resistor, and an RMS-versus-peak conversion.
The motor and generator items are conceptual more often than computational: efficiency, power factor, and the relationship between electrical input and mechanical output. These sit naturally alongside the mechanical power questions elsewhere on the exam.
5 Free Electricity and Magnetism Practice Problems
Each problem below comes from the PECivilClick FE Mechanical question bank and matches the style, difficulty and format of the real exam. Attempt each one under a three-minute limit — roughly the pace the exam demands.
Problem 1 — A. Electrical fundamentals
A charge of 15 coulombs passes through a wire in 3 seconds. What is the current flowing through the wire?
A) 0.2 A
B) 5 A
C) 12 A
D) 45 A
Answer: B) 5 A
Current is defined as the rate of charge transport:
\(i = \frac{dq}{dt} = \frac{Q}{t}\)
\(i = \frac{15 \text{ C}}{3 \text{ s}}\)
\(\boxed{i = 5 \text{ A}}\)
Problem 2 — A. Electrical fundamentals
A 12 V battery supplies 3 A of current for 2 hours. How much energy is delivered?
A) 36 Wh
B) 24 Wh
C) 6 Wh
D) 72 Wh
Answer: D) 72 Wh
Energy = Power \(\times\) Time
\(P = VI = 12 \times 3 = 36 \text{ W}\)
\(E = P \times t = 36 \times 2\)
\(\boxed{E = 72 \text{ Wh}}\)
Problem 3 — A. Electrical fundamentals
A conductor has a resistance of 20 ohms at 20°C. If the temperature coefficient of resistance is 0.004/°C, what is the resistance at 70°C?
A) 22 ohms
B) 26 ohms
C) 24 ohms
D) 28 ohms
Answer: C) 24 ohms
Using the temperature-resistance relationship:
\(R = R_0[1 + \alpha(T - T_0)]\)
\(R = 20[1 + 0.004(70 - 20)]\)
\(R = 20[1 + 0.2] = 20 \times 1.2\)
\(\boxed{R = 24 \text{ ohms}}\)
Problem 4 — A. Electrical fundamentals
The energy stored in a 50 µF capacitor charged to 200 V is most nearly:
A) 0.5 J
B) 0.01 J
C) 1.0 J
D) 2.0 J
Answer: C) 1.0 J
Energy stored in a capacitor:
\(E = \frac{1}{2}CV^2\)
\(E = \frac{1}{2}(50 \times 10^{-6})(200)^2\)
\(E = \frac{1}{2}(50 \times 10^{-6})(40000) = \frac{1}{2}(2)\)
\(\boxed{E = 1.0 \text{ J}}\)
Problem 5 — A. Electrical fundamentals
A copper wire has a resistivity of \(1.7 \times 10^{-8}\) ohm-m, length of 100 m, and cross-sectional area of \(2 \times 10^{-6}\) m\(^{2}\). What is its resistance?
A) 0.085 ohms
B) 0.85 ohms
C) 8.5 ohms
D) 85 ohms
Answer: B) 0.85 ohms
Using the resistance formula:
\(R = \frac{\rho L}{A}\)
\(R = \frac{(1.7 \times 10^{-8})(100)}{2 \times 10^{-6}}\)
\(R = \frac{1.7 \times 10^{-6}}{2 \times 10^{-6}}\)
\(\boxed{R = 0.85 \text{ ohms}}\)
Using the FE Reference Handbook for Electricity and Magnetism
The Electrical and Computer Engineering chapter is larger than what you need, so anchor on three things: the resistor combination rules, the impedance definitions for inductors and capacitors, and the RMS relationships. Search the handbook for impedance and for RMS during practice so you land on those pages directly rather than reading around them.
Four Mistakes That Cost Points
- Adding parallel resistors as if they were in series. Two 10-ohm resistors in parallel give 5 ohms, not 20. Under time pressure the series habit takes over, and both answers appear among the options.
- Mixing peak and RMS values. AC power questions expect RMS unless stated otherwise, and the ratio is the square root of two. Feeding a peak voltage into a power expression overstates the result by a factor of two.
- Treating impedance magnitude as an algebraic sum. Resistance and reactance combine in quadrature, not by addition. The arithmetic sum is always one of the four options.
- Losing the milli and micro prefixes. Capacitance in microfarads and current in milliamps are the norm here, and a factor of a thousand is the most common single error in this area. Convert to base units before substituting.
Frequently Asked Questions
How many electricity questions are on the FE Mechanical exam?
NCEES specifies 5-8 questions from Electricity and Magnetism out of 110, about 5-7 percent. It is comparable in weight to Measurements, Instrumentation and Controls.
How deep does the electrical content go?
Not deep. The exam tests whether a mechanical engineer can analyse a simple circuit, reason about AC quantities, and understand motor efficiency. It does not test transmission lines, semiconductor physics or three-phase analysis at the level an FE Electrical candidate would face.
Is it worth studying if I have not touched circuits since sophomore year?
Yes. Five to eight questions is a meaningful block, and the required scope is small enough to rebuild in a weekend. Start with series-parallel resistance and Ohm's law, then power, then RMS. That sequence covers the majority of what appears.
Do I need to know three-phase power?
Basic exposure is enough. Questions involving motors may reference three-phase supply, but the calculation asked is usually power or efficiency rather than a phase analysis. Focus your time on single-phase AC fundamentals first.
Keep Going
These topics feed into each other on the exam:
- FE Mechanical Measurements, Instrumentation, and Controls practice problems — 5-8 questions on the exam
- FE Mechanical Mathematics practice problems — 6-9 questions on the exam
- FE Mechanical Mechanical Design and Analysis practice problems — 10-15 questions on the exam
Browse every knowledge area from the free FE Mechanical practice problem hub, see what the full bank covers on the FE Mechanical exam prep page, or plan your schedule with the FE study timeline.