Measurements, Instrumentation and Controls is 5-8 questions on the FE Mechanical exam. Along with Electricity and Magnetism it is the area mechanical candidates most often skip, usually because controls was one course taken once and never revisited.
Skipping it is expensive. Five to eight questions is a similar block to electricity, and much of the content overlaps with statistics and dynamics you are already studying.
Exam weight: NCEES lists Measurements, Instrumentation, and Controls 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 Measurements, Instrumentation, and Controls
The specification covers sensors and measurement devices, measurement uncertainty, control systems and their components, and dynamic system response. Expect a strain gauge or thermocouple question, a propagation-of-uncertainty calculation, a block-diagram reduction, and identification of first- or second-order system behaviour from a response curve.
Dynamic response items ask for a time constant, a settling behaviour, or the effect of damping ratio on overshoot. These are the same second-order relationships that appear in the vibrations part of Dynamics, expressed in control language.
5 Free Measurements, Instrumentation, and Controls 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. Sensors and transducers
A Resistance Temperature Detector (RTD) operates on the principle that:
A) Two dissimilar metals generate a voltage when heated
B) Light intensity varies with temperature
C) Mechanical strain produces an electric charge
D) Electrical resistance changes with temperature
Answer: D) Electrical resistance changes with temperature
An RTD operates on the principle that electrical resistance changes with temperature.
The resistance-temperature relationship is:
\(R_T = R_0[1 + \alpha(T - T_0)]\)
where \(\alpha\) is the temperature coefficient (typically 0.00385 Ω/Ω/°C for platinum).
\(\boxed{\text{Electrical resistance changes with temperature}}\)
Problem 2 — A. Sensors and transducers
A platinum RTD has \(R_{0}\) = 100 Ω at 0°C and α = 0.00385 Ω/Ω/°C. The resistance at 200°C is:
A) 177 Ω
B) 200 Ω
C) 185 Ω
D) 170 Ω
Answer: A) 177 Ω
Using the RTD equation:
\(R_T = R_0[1 + \alpha(T - T_0)]\)
\(R_{200} = 100[1 + 0.00385(200 - 0)]\)
\(R_{200} = 100[1 + 0.77] = 100 \times 1.77\)
\(\boxed{R_{200} = 177 \text{ Ω}}\)
Problem 3 — A. Sensors and transducers
An 8-bit A/D converter has a voltage range of 0-10 V. The voltage resolution is:
A) 0.020 V
B) 0.156 V
C) 0.039 V
D) 0.078 V
Answer: C) 0.039 V
Voltage resolution of an A/D converter:
\(\varepsilon_V = \frac{V_H - V_L}{2^n}\)
where \(n\) = number of bits
\(\varepsilon_V = \frac{10 - 0}{2^8} = \frac{10}{256}\)
\(\boxed{\varepsilon_V = 0.039 \text{ V}}\)
This is the smallest voltage change the converter can detect.
Problem 4 — A. Sensors and transducers
A strain gauge with GF = 2.0 and nominal resistance 120 Ω experiences a strain of 1000 με. The change in resistance is:
A) 0.024 Ω
B) 0.12 Ω
C) 2.4 Ω
D) 0.24 Ω
Answer: D) 0.24 Ω
From the gauge factor definition:
\(GF = \frac{\Delta R/R}{\varepsilon}\)
\(\Delta R = GF \times R \times \varepsilon\)
\(\varepsilon = 1000 \mu\varepsilon = 1000 \times 10^{-6} = 0.001\)
\(\Delta R = 2.0 \times 120 \times 0.001\)
\(\boxed{\Delta R = 0.24 \text{ Ω}}\)
Problem 5 — A. Sensors and transducers
A thermocouple measures temperature using:
A) Piezoelectric effect
B) The Seebeck effect (voltage generated by two dissimilar metals)
C) Change in electrical resistance
D) Optical emission spectrum
Answer: B) The Seebeck effect (voltage generated by two dissimilar metals)
A thermocouple uses the Seebeck effect:
- Two dissimilar metal conductors are joined at one end
- A temperature difference between the junction and reference creates a voltage
- Common types: J (Iron-Constantan), K (Chromel-Alumel), T (Copper-Constantan)
Thermocouples can measure a wide temperature range but require a reference junction.
Using the FE Reference Handbook for Measurements, Instrumentation, and Controls
The Measurement and Controls material is spread rather than concentrated, so know the two anchors: the uncertainty propagation expression and the standard second-order response parameters. Search the handbook for uncertainty and for damping ratio during practice, because hunting for these while the clock runs is what makes candidates abandon the area.
Four Mistakes That Cost Points
- Adding uncertainties linearly. Independent random uncertainties combine in quadrature, as the square root of the sum of squares. Straight addition overstates the result and is always offered as an option.
- Confusing accuracy with precision. A systematically biased instrument can be highly repeatable and consistently wrong. Concept questions in this area turn on exactly that distinction, and calibration corrects bias rather than scatter.
- Reducing a block diagram without the feedback sign. A negative feedback loop gives forward gain over one plus loop gain; positive feedback gives one minus. Getting the sign wrong changes stability conclusions entirely.
- Reading a time constant as the time to reach final value. One time constant brings a first-order system to about 63 percent of its final change, not to completion. Practical settling takes roughly four to five time constants.
Frequently Asked Questions
How many measurements and controls questions are on the FE Mechanical exam?
NCEES specifies 5-8 questions from Measurements, Instrumentation and Controls out of 110, about 5-7 percent. It carries the same weight as Electricity and Magnetism.
How much control theory is required?
Substantially less than a controls course. You need block-diagram reduction, the behaviour of first- and second-order systems, and the roles of proportional, integral and derivative action. Root locus, Bode design and state-space methods are outside the usual scope.
What sensors should I know?
Strain gauges, thermocouples, RTDs, pressure transducers and encoders cover most of what appears. Know the physical principle behind each and its typical output signal rather than manufacturer specifications.
Is measurement uncertainty the same as the statistics area?
It draws on it. Uncertainty propagation is applied statistics, so studying Probability and Statistics first makes this area substantially shorter. The two together are worth 9-14 questions, which is why treating them as one study block is efficient.
Keep Going
These topics feed into each other on the exam:
- FE Mechanical Electricity and Magnetism practice problems — 5-8 questions on the exam
- FE Mechanical Probability and Statistics practice problems — 4-6 questions on the exam
- FE Mechanical Dynamics, Kinematics, and Vibrations 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.