Measurement and Instrumentation: practice problems and exam questions

Measuring physical quantities with electrical circuits: Wheatstone bridges, strain gauges and load cells, amplifiers that condition small sensor signals, and the loading of a measurement by the instrument.

Practise this course for freePractise this courseTake a mock exam5 free problems every day. No card needed.

Cram pack (PDF)Formula sheets, method steps and practice problems with full solutions, ready to print.

Topics in this course

  1. Wheatstone bridge & strain gaugesbalance and node voltages · unbalanced bridges · strain gauges and load cellscalculations
  2. Data acquisition & samplingNyquist, LSB and data rates · aliasing, bits and UART frames · harmonics, SQNR and system designcalculations
  3. Op-amp circuitsinverting amplifier · non-inverting amplifier · summing amplifiercalculations
  4. Series & parallel resistors3 resistors · 4 resistors · ladder of 6 resistorscalculations
  5. Thévenin & Nortondivider network · with series resistor and load · with current source and loadcalculations

Exam tips for Measurement and Instrumentation

  • A bridge is two voltage dividers: work out each node voltage and subtract.
  • Strain is usually given in microstrain: 500 µε is 0.0005.
  • Count the active gauges: a quarter, half or full bridge changes the output by a factor of 4.

Worked examples

Wheatstone bridge & strain gaugesEasy
+−6 VR1​ = 250 ΩR2​ = 300 ΩR3​ = ?R4​ = 150 ΩabG0

The Wheatstone bridge in the diagram is balanced by adjusting R₃. R₁ = 250 Ω, R₂ = 300 Ω and R₄ = 150 Ω. Find the setting R3.

R1 = 250 ΩR2 = 300 ΩR4 = 150 Ω

Find R3 (Ω)

Show hints
  1. At balance both dividers give the same voltage: Va = Vb.
  2. R₁/R₂ = R₃/R₄.
  3. R₃ = R₁·R₄/R₂.
Show the answer and the step-by-step solution

Wheatstone bridge: two voltage dividers share one supply Vs. The left divider R1–R2 gives Va = Vs·R2/(R1 + R2) and the right divider R3–R4 gives Vb = Vs·R4/(R3 + R4); the output is Vab = Va − Vb. The bridge is balanced (Vab = 0, no current in the meter) when R1/R2 = R3/R4, that is R1·R4 = R2·R3. Seen from the output, the bridge is a Thévenin source with Rth = R1∥R2 + R3∥R4.

Balance condition

R₁·R₄ = R₂·R₃

Unknown resistor

R₃ = 250·150/300 = 125 Ω

Answer

R3 = 125 Ω

The supply voltage does not matter at balance.

Data acquisition & samplingMedium
Vin​N = 85 V2ᴺ − 101 LSB2.125 V?

An 8-bit ADC with an input range of 0 to 5 V truncates: its output code is ⌊Vin/LSB⌋ with 1 LSB = VFSR/2ᴺ. Find the decimal output code D for an input of 2.125 V.

N = 8VFSR = 5 VVin = 2.125 V

Find D

Show hints
  1. First find the size of one LSB.
  2. 1 LSB = 5/256 = 19.53 mV.
  3. Divide the input by the LSB and keep the whole part.
Show the answer and the step-by-step solution

ADC resolution: an N-bit converter divides its full-scale range VFSR into 2ᴺ codes, from 0 to 2ᴺ − 1. One step is 1 LSB = VFSR/2ᴺ: the smallest change the converter can show. A truncating ADC gives the code ⌊Vin/LSB⌋; a rounding ADC is never more than ½ LSB away from the true value, its quantisation error. Every extra bit halves the LSB and adds about 6 dB to the ideal signal-to-quantisation-noise ratio SQNR = 6.02·N + 1.76 dB for a full-scale sine. To reach a resolution r over a span, choose the smallest N with 2ᴺ ≥ span/r.

Step size

1 LSB = 5/28 = 19.53 mV

Code

Vin/LSB = 2125/19.53 = 108.8
code = ⌊108.8⌋ = 108

Answer

D = 108

In binary that is 01101100.

How practising works

  • “Practise this course” mixes problems from all its topics, like a real exam.
  • Every problem has new values, so you learn the method instead of an answer.
  • Stuck? Open a small hint first, and the full explanation only when you need it.
  • Mock exams are timed and have no hints, and you get your score and a full review at the end.

Calculators for this course

Series and parallel resistor calculatorVoltage divider calculatorOp-amp gain calculatorThévenin and Norton equivalent calculatorOhm’s law calculator (voltage, current, resistance and power)Resistor colour code calculator (4, 5 and 6 bands)

Related courses

Circuit Analysis 1Electronics 1FE Electrical and Computer exam practiceElectrical Engineering FundamentalsMechatronic SystemsCircuit Analysis 2: AC circuitsDigital ElectronicsPhysics 2: Electricity and Magnetism
Practise this course for freePractise this courseTake a mock exam5 free problems every day. No card needed.