Measurements, Instrumentation, and Controls – Medium Difficulty
ARE YOU READY?
LET’S PRACTICE!
Results
#1. A metallic strain gauge has a nominal resistance of 350 Ω and a gauge factor of 2.1. If the strain gauge is subjected to a strain of 800 microstrain (800 × 10⁻⁶), what is the change in resistance?
#2. A strain gauge with a gauge factor of 2.0 and initial resistance of 120 Ω experiences a resistance change of 0.24 Ω. What is the strain in microstrain?
#3. A full-bridge strain gauge configuration has four active gauges, each with a gauge factor of 2.05. If the excitation voltage is 5 V and each gauge experiences 600 microstrain, what is the bridge output voltage?
#4. A Type J thermocouple has a Seebeck coefficient of approximately 50 µV/°C. If the hot junction is at 400°C and the cold junction is at 0°C, what is the approximate EMF output?
#5. A Type K thermocouple with a Seebeck coefficient of 40 µV/°C produces an output of 12.8 mV. If the reference junction is at 25°C, what is the hot junction temperature?
#6. A thermocouple measuring system shows 8.2 mV output. The Type E thermocouple has a Seebeck coefficient of 68 µV/°C, and the reference junction is at 20°C. What is the measured temperature?
#7. A PT1000 RTD has a resistance of 1000 Ω at 0°C with α = 0.00385/°C. Using R = R₀(1 + αT), what is the resistance at 75°C?
#8. An RTD shows a resistance of 154 Ω. If R₀ = 100 Ω at 0°C and α = 0.00385/°C, what is the temperature?
#9. A nickel RTD has R₀ = 100 Ω at 0°C with α = 0.00672/°C. What is the resistance at 50°C?
#10. An LVDT has a sensitivity of 40 mV/mm and is displaced 2.25 mm from the null position. What is the output voltage?
#11. An LVDT produces an output of 156 mV when the core is displaced from null. If the sensitivity is 52 mV/mm, what is the displacement?
#12. Four independent measurement uncertainties are ±0.2, ±0.3, ±0.4, and ±0.5 units. What is the combined uncertainty using RSS?
#13. A measurement has systematic uncertainty of ±0.5% and random uncertainty of ±0.3%. What is the total uncertainty using RSS?
#14. A first-order system has a time constant τ = 0.8 seconds. What percentage of final value is reached after 2.4 seconds?
#15. A first-order thermal system reaches 63.2% of its final temperature after 12 seconds. What is the time constant?
#16. A first-order system with time constant τ = 0.4 s is subjected to a step input. At what time does the output reach 98.2% of the final value?
#17. A second-order system has the transfer function G(s) = 64/(s² + 6s + 64). What are ωₙ and ζ?
#18. A second-order underdamped system has ωₙ = 12 rad/s and ζ = 0.5. What is the damped natural frequency ωd?
#19. A second-order system has ζ = 0.3 and ωₙ = 15 rad/s. What is the 2% settling time using ts ≈ 4/(ζωₙ)?
#20. A second-order underdamped system has ζ = 0.25. What is the percent overshoot for a step input?
#21. A pressure transmitter outputs 4-20 mA for a 0-200 psi range. What is the output current at 140 psi?
#22. A 4-20 mA transmitter outputs 11.2 mA. If the measurement range is 0-400 kPa, what is the pressure?
#23. A pressure sensor with range 0-1000 kPa produces 1-5 V output. What voltage corresponds to 650 kPa?
#24. A control system has G(s) = 20/(s + 4) and H(s) = 0.25. What is the closed-loop transfer function?
#25. Two blocks G₁(s) = 4/(s + 2) and G₂(s) = 3/(s + 5) are in series. What is the overall transfer function?
#26. Two parallel blocks G₁(s) = 6/(s + 3) and G₂(s) = 4/(s + 3) have what equivalent transfer function?
#27. A piezoelectric force sensor has a charge sensitivity of 4 pC/N. If a force of 250 N is applied, what is the charge output?
#28. A piezoelectric accelerometer outputs 2.5 nC when subjected to acceleration. If the sensitivity is 25 pC/g, what is the acceleration?
#29. A capacitive proximity sensor’s capacitance varies from 15 pF to 12 pF as an object moves away. By what factor did the gap increase?
#30. A parallel plate capacitor sensor has C = 20 pF at gap distance d. If the gap is reduced by half, what is the new capacitance?
#31. An incremental encoder produces 2048 pulses per revolution. With quadrature decoding, what is the angular resolution?
#32. A rotary encoder with 1000 PPR and 4× quadrature decoding measures a shaft rotating at 3600 RPM. What is the pulse frequency?
#33. A load cell rated at 10,000 N has sensitivity of 2.5 mV/V. With 12 V excitation and 8000 N applied load, what is the output?
#34. A load cell outputs 8.4 mV with 10 V excitation at 70% of rated capacity. What is the sensitivity?
#35. Six measurements yield: 42.1, 42.5, 41.8, 42.3, 42.0, 42.3 mm. What is the range (repeatability)?
#36. A measurement process has σ = 4 units. If 16 measurements are averaged, what is the standard error of the mean?
#37. Eight measurements have a sample standard deviation of 1.2 units. What is the Type A standard uncertainty of the mean?
#38. A Wheatstone bridge has R₁ = R₂ = R₃ = 350 Ω and R₄ = 350.35 Ω. With 5 V excitation, what is the output voltage?
#39. A balanced Wheatstone bridge has R₁ = 150 Ω, R₂ = 300 Ω, and R₄ = 600 Ω. What value of R₃ balances the bridge?
#40. A linear potentiometer has 5 kΩ total resistance and 50 mm stroke. With 10 V excitation and wiper at 18 mm, what is the output?
#41. A rotary potentiometer spans 270° with 10 kΩ resistance. At 90° rotation from zero, what is the resistance?
#42. A DC tachometer has sensitivity of 0.08 V/(rad/s). What is the output at 2400 RPM?
#43. A tachometer outputs 6.28 V when the shaft rotates at 600 RPM. What is its sensitivity?
#44. A 10-bit ADC has an input range of 0-5 V. What is the resolution (1 LSB)?
#45. A 12-bit DAC with 10 V reference receives input 101010101010 (binary). What is the analog output?
#46. A 16-bit ADC with ±10 V input range has maximum quantization error of:
#47. An NTC thermistor has R = 5 kΩ at 25°C and β = 3500 K. What is the resistance at 40°C?
#48. A thermistor shows R = 2.5 kΩ at temperature T and R₀ = 10 kΩ at T₀ = 25°C with β = 4000 K. What is T?
#49. A first-order system has G(s) = 50/(0.02s + 1). What is the bandwidth (-3 dB frequency)?
#50. A system has bandwidth of 100 rad/s. At ω = 100 rad/s, the gain magnitude is:
#51. At the phase crossover frequency, |G(jω)H(jω)| = 0.5. What is the gain margin?
#52. At the gain crossover frequency, the phase angle is -150°. What is the phase margin?
#53. A Type 1 system has velocity error constant Kᵥ = 50. For ramp input r(t) = 2t, what is the steady-state error?
#54. A unity feedback system requires steady-state error ≤ 5% for unit step input. What is minimum Kp?
#55. A Type 2 system subjected to a ramp input r(t) = 3t has steady-state error of:
#56. A PI controller has Kp = 3 and Ki = 0.8. At error e = 5 with ∫e dt = 10, what is the output?
#57. A PD controller with Kp = 4, Kd = 0.2 has error e = 8 and de/dt = -5. What is the output?
#58. A PID controller has Kp = 2.5, Ki = 1.0, Kd = 0.3. With e = 4, ∫e dt = 8, de/dt = -3, what is u?
#59. An ultrasonic sensor measures round-trip time of 8.5 ms. If sound velocity is 340 m/s, what is the distance?
#60. An ultrasonic level sensor indicates 2.5 m to liquid surface. If sound speed is 345 m/s, what is the pulse round-trip time?
#61. An orifice meter has Cd = 0.61, diameter 40 mm, ΔP = 30 kPa, fluid density 900 kg/m³. What is Q using Q = Cd·A·√(2ΔP/ρ)?
#62. A magnetic flowmeter with B = 0.04 T, D = 80 mm, produces E = 9.6 mV. What is the fluid velocity using E = B×D×v?
#63. A Coriolis meter has 1° phase shift per 4 kg/min. At 6.5° phase shift, what is the mass flow rate?
#64. An instrument has accuracy ±0.5% FS with range 0-500 units. What is maximum error at any reading?
#65. A sensor has ±0.2% of reading plus ±0.1% FS accuracy. At 300 reading (FS = 1000), what is total error?
#66. A transducer has 0.8% hysteresis of span. For span 0-250 units, what is maximum hysteresis error?
#67. At mid-range (50% FS), a sensor’s ideal output is 2.5 V but actual is 2.44 V. What is nonlinearity error as % FS (output range 0-5 V)?
#68. A sensor produces 0-50 mV. An ADC requires 0-10 V input. What amplifier gain is needed?
#69. An instrumentation amplifier with gain 500 amplifies a 2 mV signal. What is the output?
#70. A data acquisition system samples at 2 kHz. What is the Nyquist frequency?
#71. An 800 Hz signal is sampled at 1200 Hz. At what frequency does aliasing occur?
#72. To avoid aliasing of signals up to 5 kHz, minimum sampling rate should be:
#73. A Hall current sensor has sensitivity 60 mV/A and offset 2.0 V. At output 3.8 V, what is current?
#74. A Hall sensor with 50 mV/A sensitivity measures 25 A. If offset is 2.5 V, what is output voltage?
#75. For characteristic equation s³ + 5s² + 8s + K = 0, what range of K ensures stability?
#76. Characteristic equation s³ + 3s² + 4s + 12 = 0. Is the system stable?
#77. A system has G(s) = 40/(s + 8), H = 0.1. What is the closed-loop DC gain?
#78. Unity feedback system has G(s) = 100/(s + 5). The closed-loop DC gain is:
#79. A feedback system has G = 200, H = 0.02. What is sensitivity S = 1/(1 + GH)?
#80. A capacitive level sensor reads 30 pF empty (εᵣ = 1). Full with liquid (εᵣ = 1.8), what is capacitance?
#81. A MEMS accelerometer has sensitivity 250 mV/g, zero-g offset 1.25 V. At output 1.75 V, what is acceleration?
#82. A resolver outputs V_sin = V_max·sin(θ) and V_cos = V_max·cos(θ). At θ = 60°, with V_max = 4 V, what is V_sin?
#83. Using Ziegler-Nichols, Ku = 10, Tu = 1.5 s. For P-only controller, what is Kp?
#84. Ziegler-Nichols tuning: Ku = 12, Tu = 2 s. For PI controller, Kp and Ti are:
#85. For G(s)H(s) = K/[s(s + 6)], the breakaway point on real axis is at:
#86. A lag compensator Gc(s) = (s + 0.5)/(s + 0.05) has DC gain of:
#87. A lead compensator Gc(s) = (s + 1)/(s + 5). Maximum phase lead occurs at ω =:
#88. Using Wien’s law (λ_max·T = 2898 µm·K), peak wavelength at 500°C is:
#89. Characteristic equation s² + 4s + 13 = 0. The poles are:
#90. An inductive sensor has 10 mm sensing distance for steel. Correction factor for copper is 0.35. What is sensing distance for copper?
#91. A process step test: input step = 5, output change = 15, time to 63.2% = 8 s. What is process gain K?
#92. First-order process with K = 2.5, τ = 4 s responds to step input of 6. Final steady-state output change is:
#93. An equal-percentage valve has rangeability R = 40, Q/Q_max = R^(x-1). At x = 0.75, what % of max flow?
#94. An amplifier has CMRR = 100 dB, differential gain = 1000. With 1 V common-mode input, what is CM error at output?
#95. State space: A = [-2, 0; 0, -3], B = [1; 1], C = [1, 1], D = 0. The system has poles at:
#96. A pressure sensor linearity error is 0.3% FS. With span 0-1500 kPa, the maximum linearity error is:
#97. An optical tachometer counts 180 pulses from a 6-blade target in 0.5 seconds. What is the shaft speed?
#98. A 14-bit ADC with 0-5 V range has a quantization step size of:
#99. A proximity switch with 5 ms response time can reliably detect objects moving at maximum frequency of:
#100. A torque sensor with range 0-100 N·m produces 4-20 mA output. At 65 N·m, the output is:
