FE Other Disciplines (NCEES Fundamentals of Engineering) — All Questions
19 questions
By the Nyquist sampling theorem, what is the minimum sampling rate needed to reconstruct a signal whose highest frequency is 1 kHz?
- a.500 Hz
- b.1 kHz
- c.4 kHz
- d.2 kHz✓
The Nyquist criterion requires a sampling rate greater than twice the highest signal frequency to avoid aliasing: f_s > 2 x 1 kHz = 2 kHz. Sampling below this rate causes higher frequencies to masquerade as lower ones (aliasing).
In a closed-loop control system, negative feedback is used primarily to:
- a.Reduce error by comparing output to the setpoint and correcting the difference✓
- b.Amplify measurement noise and progressively push the output further from its setpoint
- c.Increase steady-state error
- d.Convert the system to open-loop
Negative feedback subtracts a measurement of the output from the setpoint to form an error signal that drives the output toward the desired value, improving accuracy and stability.
In a PID controller, the derivative (D) term produces an output proportional to the:
- a.The running sum of all accumulated past error over time
- b.Constant setpoint value
- c.Square of the error
- d.Rate of change of the error✓
Derivative action responds to how fast the error is changing, adding anticipatory damping that reduces overshoot. Integral action instead addresses accumulated past error.
Which control action is chiefly responsible for eliminating steady-state (offset) error?
- a.Derivative
- b.Integral✓
- c.Proportional
- d.On-off (bang-bang)
The integral term accumulates error over time and keeps adjusting the output until the steady-state error is driven to zero, unlike pure proportional control, which leaves an offset.
A purely proportional controller applied to a process typically leaves:
- a.No error at all
- b.An unstable oscillation always
- c.A residual steady-state offset error✓
- d.Only derivative noise
Proportional-only control needs a nonzero error to produce the output that holds the process, so it settles with a residual offset. Adding integral action removes this offset.
A thermocouple generates a temperature-dependent voltage based on the:
- a.Piezoelectric effect
- b.Seebeck effect at a junction of two dissimilar metals✓
- c.A predictable change of electrical resistance with temperature
- d.Photoelectric effect
A thermocouple exploits the Seebeck effect: two dissimilar metals joined at a junction develop a voltage proportional to the temperature difference between the measuring and reference junctions.
A resistance temperature detector (RTD), such as a platinum Pt100, works because its:
- a.Voltage output rises through the thermoelectric Seebeck effect at a junction
- b.Capacitance drops with temperature
- c.Color changes with temperature
- d.Electrical resistance increases predictably with temperature✓
An RTD relies on the positive, nearly linear rise of metal resistance with temperature. Platinum RTDs are prized for stability and accuracy over wide ranges.
A common NTC thermistor differs from an RTD in that its resistance:
- a.Increases linearly with temperature
- b.Stays constant with temperature
- c.Depends only on pressure
- d.Decreases sharply and nonlinearly as temperature rises✓
A negative-temperature-coefficient (NTC) thermistor's resistance falls steeply and nonlinearly as temperature increases, giving high sensitivity over a narrow range.
A bonded metallic strain gauge measures strain by detecting the change in its:
- a.Electrical resistance as the foil stretches or compresses✓
- b.Magnetic polarity
- c.Mass
- d.Color
Stretching a strain gauge lengthens and thins its conductor, raising resistance, and vice versa. The gauge factor relates the fractional resistance change to strain.
A Wheatstone bridge is commonly used with a strain gauge to:
- a.Convert a small resistance change into a measurable voltage signal✓
- b.Generate a very high excitation voltage to drive the downstream amplifier stage
- c.Store electrical energy
- d.Rectify AC to DC
The bridge is balanced at zero strain; a small gauge-resistance change unbalances it, producing an output voltage proportional to strain that can then be amplified and read.
Industrial sensors often transmit a 4-20 mA current signal rather than a voltage mainly because current loops:
- a.Are considerably cheaper to generate than an equivalent voltage signal
- b.Eliminate the need for a power supply
- c.Cannot carry analog data
- d.Resist voltage drop over long wires and reveal a broken wire as 0 mA✓
A current signal is unaffected by wire resistance and voltage drop, so it stays accurate over long runs. The 4 mA live zero also lets 0 mA flag a broken loop or failed sensor.
A linear variable differential transformer (LVDT) is a sensor used to measure:
- a.Linear position or displacement✓
- b.Light intensity
- c.pH
- d.Temperature
An LVDT uses a movable magnetic core and paired secondary coils to produce a voltage proportional to the core's linear displacement, giving frictionless, high-resolution position sensing.
For a first-order measuring instrument, the time constant is the time to reach what percentage of a step change in the measured value?
- a.100%
- b.63.2%✓
- c.90%
- d.50%
After one time constant a first-order system reaches 63.2% (that is, 1 - e^-1) of its final value; about five time constants are needed to settle to roughly 99%.
A second-order system with a damping ratio (zeta) between 0 and 1 is:
- a.Underdamped, with an oscillatory response✓
- b.Overdamped
- c.Undamped
- d.Critically damped
For 0 < zeta < 1 the response overshoots and oscillates before settling (underdamped). zeta = 1 is critically damped (fastest without overshoot) and zeta > 1 is overdamped.
The key difference between a closed-loop and an open-loop control system is that the closed-loop system:
- a.Has no controller
- b.Ignores the measured output
- c.Uses feedback of the output to adjust its input✓
- d.Cannot correct for external disturbances acting on the process
A closed-loop (feedback) system measures its output and feeds it back to correct errors and reject disturbances; an open-loop system acts without checking the actual result.
The transfer function of a linear system is defined as the:
- a.Ratio of the Laplace transform of the output to that of the input, with zero initial conditions✓
- b.Time-domain product of the input and output signals evaluated at every instant without any transform
- c.Sum of all system poles
- d.Steady-state gain only
A transfer function G(s) = Y(s)/X(s) with zero initial conditions characterizes the system's dynamics in the s-domain, from which poles, zeros, and stability follow.
A unity-feedback loop has forward gain G = 10. What is the closed-loop gain, G/(1 + G)?
- a.11
- b.0.909✓
- c.10
- d.0.1
Closed-loop gain = G/(1 + GH) with H = 1 gives 10/(1 + 10) = 10/11 = 0.909. Feedback trades raw gain for accuracy, stability, and reduced sensitivity.
An instrument that consistently reads 5.00 g for a true 4.50 g mass, repeating within plus or minus 0.01 g, is best described as:
- a.Both accurate and precise
- b.Neither accurate nor precise
- c.Accurate but not precise
- d.Precise but not accurate✓
Precision is repeatability (the tight plus or minus 0.01 g spread) while accuracy is closeness to the true value (off by 0.50 g). The instrument is precise but inaccurate, a systematic bias error.
A continuous linear time-invariant system is stable if all poles of its transfer function lie:
- a.In the left half of the s-plane (negative real parts)✓
- b.In the right half of the s-plane, having positive real parts
- c.Exactly on the imaginary axis
- d.At the origin only
Stability requires every pole to have a negative real part (left-half s-plane), so transient terms e^(pt) decay. Any right-half-plane pole produces an unbounded, unstable response.