Measurements, Instrumentation, and Controls practice questions

Answer: A) 2 kHz

• ACorrect. The Nyquist rate is twice the highest frequency.
• BIncorrect. Sample at more than twice the frequency.
• CIncorrect. That causes aliasing.
• DIncorrect. That causes aliasing.

Answer: A) It uses the measured output to correct for disturbances

Closed-loop control measures the output, compares it with the setpoint, and acts on the error, so it can reject disturbances. That requires a sensor and introduces stability concerns.

• ACorrect. A feedback loop compares the measured output with the setpoint and acts on the error. This lets it compensate for disturbances and changes in the plant.
• BIncorrect. Driving the actuator from the setpoint alone, without measuring the output, is the definition of open-loop control.
• CIncorrect. Feedback control needs a sensor to measure the controlled variable so it can be compared with the setpoint.
• DIncorrect. Feedback can make a system unstable if the gain is too high. Stability has to be checked, for example with root locus or the Routh criterion.

Answer: C) Straightening of a curved, flattened tube whose free end moves a pointer

A Bourdon tube is a curved elastic tube with an elliptical cross section. Internal pressure makes it straighten, and a linkage turns that tip movement into pointer movement on the dial.

• AIncorrect. This is how an electrical strain-gauge pressure transducer works, not a mechanical Bourdon gauge.
• BIncorrect. This is the principle of a manometer, which balances pressure against a liquid column's hydrostatic head.
• CCorrect. Pressure inside the C-shaped tube makes its elliptical cross section rounder, so the curve straightens. The tip's movement, which is roughly proportional to pressure, is linked to the pointer.
• DIncorrect. This is a piezoelectric pressure sensor, which is mainly used for dynamic pressure measurements.

Answer: D) Detect small resistance changes

• AIncorrect. It detects resistance changes.
• BIncorrect. It detects small resistance changes.
• CIncorrect. That's a rectifier.
• DCorrect. Converting them to a measurable voltage.

Answer: A) Displacement of the core along the coil axis

An LVDT is an inductive transducer. The position of its movable core changes the differential voltage across two secondary coils, so it measures displacement.

• ACorrect. Moving the core changes the coupling between the primary coil and the two secondary coils. The differential output is proportional to the core's position along its axis.
• BIncorrect. That is how a thermocouple works (the Seebeck effect), not a transformer-coupled core device.
• CIncorrect. That describes a bonded resistance strain gage, which is usually read with a Wheatstone bridge.
• DIncorrect. That describes a vortex flowmeter, which senses how often vortices shed off a bluff body.

Answer: C) 0.001

• AIncorrect. Recheck the powers of ten.
• BIncorrect. Multiply by the gauge factor.
• CCorrect. \(\Delta R/R = GF \cdot \varepsilon = 2(500\times10^{-6})\).
• DIncorrect. Recheck the units.

Answer: C) Increases overshoot after a step input

• AIncorrect. That isn't the effect.
• BIncorrect. Lower damping increases it.
• CCorrect. Lightly damped systems oscillate more.
• DIncorrect. Damping controls overshoot.

Answer: C) 9.8 mV

• AIncorrect. Recheck the division.
• BIncorrect. A 10-bit ADC has 1,024 levels.
• CCorrect. 10 V/1,024 steps.
• DIncorrect. That's an 8-bit converter.

Answer: B) Calibration

• AIncorrect. That's path-dependent error.
• BCorrect. It corrects systematic error.
• CIncorrect. That's a slow change over time.
• DIncorrect. That's signal processing.

Answer: C) 10

An ideal non-inverting op-amp amplifier has gain 1 + Rf/Ri, so the gain here is 1 + 90 kΩ/10 kΩ = 10.

• AIncorrect. 9 is just Rf/Ri, which is the size of an inverting amplifier's gain. A non-inverting amplifier's gain is 1 + Rf/Ri, so the 1 is missing.
• BIncorrect. 1.11 comes from 1 + Ri/Rf, which flips the resistor ratio.
• CCorrect. For an ideal non-inverting amplifier, Vout/Vin = 1 + Rf/Ri = 1 + 90/10 = 10.
• DIncorrect. 0.90 is Rf/(Rf + Ri), which treats the resistors as a passive voltage divider. A non-inverting amplifier boosts the signal; its gain is at least 1.