Electrical and Electronic Measuring Instruments

What to remember

• Every analogue pointer instrument needs three torques: deflecting, controlling and damping. The pointer rests where deflecting torque equals controlling torque, and damping stops it from oscillating.
• PMMC works on d.c. only and is the most accurate; moving iron works on both a.c. and d.c. An ammeter has a very low resistance and goes in series. A voltmeter has a very high resistance and goes in parallel.
• Digital meters convert the signal into numbers with an ADC, and the CRO shows a waveform against time. Frequency from a CRO is 1/period.

Basics of measurement

Measurement means comparing an unknown quantity with a standard. An instrument is a device that does this.

• Absolute instruments give the value from the instrument constants (for example, a tangent galvanometer). Secondary instruments are calibrated against a standard and are used in daily work.
• Analogue instruments show a pointer on a scale. Digital instruments show numbers.
• Key terms: accuracy (closeness to the true value), precision (closeness of repeated readings), resolution (smallest change that can be read), sensitivity (deflection per unit input) and range (lowest to highest value that can be measured).
• Error = measured value − true value. Percentage error = (error ÷ true value) × 100.
• Types of error: gross (human mistakes), systematic (instrument, environmental or observational faults) and random (small, unpredictable variations).

Torques in analogue instruments

• Deflecting torque moves the pointer. It is produced by the magnetic, heating, electrostatic or induction effect of the current.
• Controlling torque brings the pointer to a steady position. It is given by spiral springs or by gravity. In indicating instruments the pointer stops where the two torques are equal.
• Damping torque removes oscillations. Methods: air friction (a light vane in a closed chamber), fluid friction, and eddy currents (a metal former or disc moving in a magnetic field). Eddy current damping is the most efficient.
• Critical damping brings the pointer to rest in the shortest time without overshoot.

Main types of indicating instruments

• A PMMC instrument measuring a.c. directly shows zero because the torque reverses every half cycle. With a rectifier it can read the average value of a.c. and is then scaled in rms.
• MI instruments respond to the rms value because deflection is proportional to the square of the current.
• The dynamometer type can be used as an ammeter, voltmeter or wattmeter.

Ammeters, voltmeters and range extension

• Ammeter: very low internal resistance, connected in series.
• Voltmeter: very high internal resistance, connected in parallel across the component.
• Shunt (low resistance in parallel with the meter) extends the ammeter range:

Rsh = Im·Rm ÷ (I − Im), where Im is the full-scale meter current, Rm the meter resistance and I the new full-scale current. Multiplying power m = I/Im = 1 + Rm/Rsh.

• Multiplier (high resistance in series with the meter) extends the voltmeter range:

Rs = V/Im − Rm.

• Sensitivity of a voltmeter = 1/Ifsd in ohm per volt. Input resistance on a range = sensitivity × range.
• Loading effect: a voltmeter of low resistance draws current and gives a lower reading across a high-resistance circuit. A higher ohm-per-volt value means less loading.
• Worked example 1: Rm = 99 Ω, Im = 1 mA, new range 100 mA. Rsh = (0.001 × 99) ÷ (0.1 − 0.001) = 0.099 ÷ 0.099 = 1 Ω.
• Worked example 2: Im = 1 mA, Rm = 100 Ω, range 10 V. Rs = 10/0.001 − 100 = 9,900 Ω.
• Worked example 3: FSD of 20 µA gives 1/20 µA = 50 kΩ/V. On a 100 V range the resistance is 5 MΩ.

Other measuring instruments

• Wheatstone bridge: at balance the galvanometer shows zero current and P/Q = X/R, so X = (P/Q) × R. Example: P = 1000 Ω, Q = 100 Ω, R = 25 Ω gives X = 250 Ω.
• Wattmeter: P = V × I × cos φ. For 200 V, 5 A and power factor 0.8, P = 800 W.
• Energy meter: the disc speed is proportional to power, so revolutions are proportional to energy. With 600 rev/kWh, a 1 kW load for 2 h (2 kWh) gives 1,200 revolutions.
• Instrument transformers: a current transformer (CT) extends ammeter range, with the secondary usually 5 A or 1 A, and its secondary must never be opened. A potential transformer (PT) extends voltmeter range, with the secondary usually 110 V. Example: a CT of 100/5 A with the ammeter reading 4 A means a primary current of 80 A. A PT of 11,000/110 V with the voltmeter reading 105 V means 10,500 V.

Electronic and digital instruments

• Digital multimeter (DMM): has a high input resistance (typically 10 MΩ), no parallax error and an auto-ranging option. Display digits: a "3½ digit" display shows up to 1999 (the half digit can only be 0 or 1) and a "4½ digit" display shows up to 19999. Resolution of a 3½ digit meter on a 2 V range is 1 mV.
• ADC (analogue to digital converter) converts the input voltage into a binary number. An n-bit ADC has 2ⁿ levels, so an 8-bit ADC has 256 levels. Common types: dual-slope (accurate, used in DMMs), successive approximation and flash (fastest).
• Digital frequency counter counts input pulses in a fixed gate time. Digital storage oscilloscope samples and stores the waveform.
• Transducers change one form of energy into another, for example a thermocouple (temperature to voltage), strain gauge (strain to resistance change), LVDT (displacement to voltage) and thermistor (temperature to resistance).

Cathode ray oscilloscope (CRO)

• Main parts: electron gun, deflection plates (vertical and horizontal), fluorescent screen, time base generator and amplifiers.
• The vertical (Y) plates carry the signal. The horizontal (X) plates carry the sawtooth voltage from the time base, which sweeps the beam from left to right.
• The CRO can measure voltage, time period, frequency and phase difference.
• Frequency f = 1/T. Example: 4 divisions at 5 ms/div gives T = 20 ms and f = 50 Hz.
• Peak-to-peak voltage = divisions × volts/div. Example: 6 divisions at 2 V/div gives 12 V peak to peak, so peak = 6 V.
• Lissajous figures (signals on both X and Y) are used to compare frequencies and measure phase. A circle shows equal frequency and a phase difference of 90° with equal amplitudes.
• A dual trace CRO displays two signals together.

Exam traps

• PMMC is for d.c. only. MI is for both a.c. and d.c. Do not mix them.
• Ammeter in series with low resistance. Voltmeter in parallel with high resistance. An ideal ammeter has zero resistance and an ideal voltmeter has infinite resistance.
• A shunt is parallel (for current). A multiplier is series (for voltage).
• Megger measures insulation resistance. Wheatstone bridge measures medium resistance. Kelvin bridge measures low resistance.
• A CT secondary must never be left open. A PT secondary must never be short-circuited.
• Accuracy is closeness to the true value. Precision is repeatability. A meter can be precise but not accurate.
• Controlling torque is by springs. Damping torque is by air, fluid or eddy currents. Damping does not set the final position.
• A "3½ digit" display means three full digits plus a half digit that can only show 0 or 1.

One-liners

• 1. Deflecting, controlling and damping torques are needed in an analogue instrument.
• 2. PMMC has a uniform scale and works only on d.c.
• 3. Moving iron instruments show the rms value of a.c.
• 4. Induction instruments are used as energy meters.
• 5. Shunt resistance Rsh = Im·Rm ÷ (I − Im).
• 6. Multiplier resistance Rs = V/Im − Rm.
• 7. Voltmeter sensitivity = 1/Ifsd (ohm per volt).
• 8. A megger measures insulation resistance.
• 9. A wattmeter has a current coil and a pressure coil.
• 10. A clamp meter measures a.c. current without breaking the circuit.
• 11. An n-bit ADC has 2ⁿ levels.
• 12. Time base voltage in a CRO is a sawtooth wave, and frequency = 1/period.

Practice questions

1. Which instrument is used to measure insulation resistance?

   1. Wheatstone bridge
   2. Kelvin bridge
   3. Wattmeter
   4. Megger
   Answer

   D. Megger

   A megger gives a high d.c. test voltage and reads insulation resistance in megohms.

2. An ammeter must be connected in ___ with the circuit and should have ___ resistance.

   1. series, very high
   2. parallel, very low
   3. parallel, very high
   4. series, very low
   Answer

   D. series, very low

   An ammeter carries the full circuit current, so it is in series with low resistance to avoid a voltage drop.

3. Which instrument works on d.c. only?

   1. Electrostatic instrument
   2. PMMC (moving coil) instrument
   3. Moving iron instrument
   4. Dynamometer instrument
   Answer

   B. PMMC (moving coil) instrument

   The torque of a PMMC instrument reverses with the current, so it reads only d.c.

4. Which torque brings the pointer to rest quickly without oscillation?

   1. Gravity torque
   2. Controlling torque
   3. Deflecting torque
   4. Damping torque
   Answer

   D. Damping torque

   Damping torque removes the oscillations about the final position.

5. Which instrument is used as a domestic energy meter?

   1. Induction type
   2. Hot wire type
   3. Electrostatic type
   4. PMMC type
   Answer

   A. Induction type

   The induction disc meter works on a.c. and records energy in kWh.

6. Which bridge is used to measure medium resistance?

   1. Q meter
   2. Wheatstone bridge
   3. Schering bridge
   4. Maxwell bridge
   Answer

   B. Wheatstone bridge

   The Wheatstone bridge balances when P/Q = R/S.

7. Which bridge is used to measure capacitance and dielectric loss?

   1. Wheatstone bridge
   2. Kelvin bridge
   3. Maxwell bridge
   4. Schering bridge
   Answer

   D. Schering bridge

   Schering bridge is used for capacitance and loss angle (insulation testing).

8. What does a clamp meter measure without breaking the circuit?

   1. A.C. current
   2. Frequency of a signal
   3. Insulation resistance
   4. Capacitance
   Answer

   A. A.C. current

   A clamp meter works like a current transformer around the conductor.

9. Frequency of a signal in a CRO is obtained from

   1. Peak voltage divided by period
   2. 1 divided by the time period
   3. Rms voltage multiplied by period
   4. Time period multiplied by 2
   Answer

   B. 1 divided by the time period

   f = 1/T.

10. Which part of a CRO produces the sawtooth sweep voltage?

    1. Electron gun
    2. Vertical amplifier
    3. Fluorescent screen
    4. Time base generator
    Answer

    D. Time base generator

    The time base sweeps the beam horizontally at a steady rate.

11. A 3½ digit digital voltmeter can show a maximum reading of

    1. 1999
    2. 9999
    3. 19999
    4. 999
    Answer

    A. 1999

    The half digit can only be 0 or 1, so the highest count is 1999.

12. An 8-bit ADC has how many output levels?

    1. 64
    2. 256
    3. 512
    4. 128
    Answer

    B. 256

    2^8 = 256.

13. A galvanometer has Rm = 99 Ω and full-scale current 1 mA. The shunt needed to read 100 mA full scale is

    1. 1 Ω
    2. 0.99 Ω
    3. 10 Ω
    4. 9.9 Ω
    Answer

    A. 1 Ω

    Rsh = 0.001 × 99 ÷ (0.1 − 0.001) = 0.099 ÷ 0.099 = 1 Ω.

14. A meter has Im = 1 mA and Rm = 100 Ω. The series multiplier needed for a 10 V range is

    1. 10,100 Ω
    2. 10,000 Ω
    3. 9,000 Ω
    4. 9,900 Ω
    Answer

    D. 9,900 Ω

    Rs = V/Im − Rm = 10/0.001 − 100 = 9,900 Ω.

15. A voltmeter movement of full-scale current 20 µA has a sensitivity of

    1. 50 kΩ/V
    2. 5 kΩ/V
    3. 20 kΩ/V
    4. 100 kΩ/V
    Answer

    A. 50 kΩ/V

    Sensitivity = 1/Ifsd = 1/(20 × 10^-6) = 50,000 Ω/V.

16. On a 100 V range, the voltmeter of 50 kΩ/V sensitivity has an input resistance of

    1. 50 kΩ
    2. 5 MΩ
    3. 50 MΩ
    4. 500 kΩ
    Answer

    B. 5 MΩ

    Resistance = 50,000 × 100 = 5,000,000 Ω.

17. A voltmeter reads 98 V when the true value is 100 V. The percentage error is

    1. +0.98%
    2. −1.96%
    3. +2%
    4. −2%
    Answer

    D. −2%

    Error = 98 − 100 = −2 V, and −2/100 × 100 = −2%.

18. On a CRO, one cycle of a signal covers 4 divisions with the time base at 5 ms/div. The frequency is

    1. 200 Hz
    2. 20 Hz
    3. 50 Hz
    4. 25 Hz
    Answer

    C. 50 Hz

    T = 4 × 5 ms = 20 ms, so f = 1/0.02 = 50 Hz.

19. A CRO shows a sine wave of 6 divisions peak to peak at 2 V/div. The peak voltage is

    1. 6 V
    2. 24 V
    3. 3 V
    4. 12 V
    Answer

    A. 6 V

    Peak to peak = 6 × 2 = 12 V, so peak = 12/2 = 6 V.

20. A wattmeter in a 200 V, 5 A circuit at power factor 0.8 reads

    1. 640 W
    2. 1000 W
    3. 800 W
    4. 1250 W
    Answer

    C. 800 W

    P = V × I × cos φ = 200 × 5 × 0.8 = 800 W.

21. An energy meter has a constant of 600 rev/kWh. A 1 kW load runs for 2 hours. The number of revolutions is

    1. 600
    2. 2,400
    3. 300
    4. 1,200
    Answer

    D. 1,200

    Energy = 2 kWh, so revolutions = 2 × 600 = 1,200.

22. In a Wheatstone bridge, P = 1000 Ω, Q = 100 Ω and R = 25 Ω at balance. The unknown resistance X = (P/Q) × R is

    1. 2,500 Ω
    2. 250 Ω
    3. 25 Ω
    4. 2.5 Ω
    Answer

    B. 250 Ω

    X = (1000/100) × 25 = 250 Ω.

23. A CT of ratio 100/5 A is used and the ammeter reads 4 A. The primary current is

    1. 100 A
    2. 8 A
    3. 80 A
    4. 20 A
    Answer

    C. 80 A

    Primary = 4 × (100/5) = 80 A.

24. A PT of ratio 11,000/110 V is used and the voltmeter reads 105 V. The line voltage is

    1. 11,550 V
    2. 10,500 V
    3. 1,050 V
    4. 105,000 V
    Answer

    B. 10,500 V

    Ratio is 100, so voltage = 105 × 100 = 10,500 V.

25. Which instrument can be used as an ammeter, voltmeter and wattmeter?

    1. Dynamometer type
    2. PMMC type
    3. Induction type
    4. Hot wire type
    Answer

    A. Dynamometer type

    Fixed and moving coils carrying currents allow the dynamometer type to serve for all three.

26. What is the main reason for using a shunt with a PMMC ammeter?

    1. To increase damping
    2. To extend the voltage range
    3. To reduce friction
    4. To extend the current range
    Answer

    D. To extend the current range

    A shunt bypasses most of the current, so the movement can measure larger currents.

27. Eddy current damping is produced when

    1. a metal former moves in a magnetic field
    2. a spring is wound tightly
    3. a vane moves in air
    4. a piston moves in oil
    Answer

    A. a metal former moves in a magnetic field

    Motion of a conductor in a magnetic field induces eddy currents that oppose the motion.

28. The scale of a moving iron instrument is generally

    1. uniform
    2. non-uniform, crowded at the lower end
    3. logarithmic with no crowding
    4. uniform only for a.c.
    Answer

    B. non-uniform, crowded at the lower end

    The deflection varies with the square of the current, which crowds the lower end of the scale.

29. Which statement about the input resistance of a digital multimeter is correct?

    1. It is the same as that of a PMMC voltmeter always
    2. It is very low, so it acts like an ammeter
    3. It is high, so loading of the circuit is small
    4. It is zero on voltage ranges
    Answer

    C. It is high, so loading of the circuit is small

    A high input resistance (about 10 MΩ) reduces the loading effect.

30. Which bridge is best suited to measure a very low resistance?

    1. Wheatstone bridge
    2. Schering bridge
    3. Maxwell bridge
    4. Kelvin bridge
    Answer

    D. Kelvin bridge

    The Kelvin double bridge removes the effect of lead and contact resistance.

31. A voltmeter of low resistance connected across a high-resistance circuit will

    1. read lower than the true value because of loading
    2. read exactly the true value
    3. read higher than the true value
    4. burn out immediately
    Answer

    A. read lower than the true value because of loading

    It draws current and lowers the voltage across the circuit.

32. Which device is an example of a transducer that changes displacement into an electrical signal?

    1. Rectifier
    2. LVDT
    3. Shunt
    4. Multiplier
    Answer

    B. LVDT

    A linear variable differential transformer gives a voltage proportional to displacement.

33. Which statements about PMMC and moving iron instruments are correct? 1. PMMC has a uniform scale. 2. Moving iron instruments read only d.c.

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    A. 1 only

    PMMC has a uniform scale. Moving iron instruments work on both a.c. and d.c.

34. Which statements are correct? 1. A CT secondary should never be left open. 2. A PT secondary is usually rated about 110 V.

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    An open CT secondary produces a dangerously high voltage. The standard PT secondary is 110 V.

35. Which statements are correct? 1. A voltmeter is connected in series. 2. A higher ohm-per-volt rating reduces the loading effect.

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    B. 2 only

    A voltmeter is connected in parallel. A higher ohm-per-volt rating draws less current.

36. Which statements are correct? 1. Accuracy means closeness to the true value. 2. Precision means repeatability of readings.

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    C. Both 1 and 2

    Both are standard definitions.

37. Which statements are correct? 1. Damping torque decides the final steady position of the pointer. 2. Controlling torque is usually supplied by spiral springs.

    1. 1 only
    2. 2 only
    3. Both 1 and 2
    4. Neither 1 nor 2
    Answer

    B. 2 only

    The final position is where deflecting and controlling torques balance. Damping only stops the oscillation.

38. Match the instrument with its use: (a) Megger (b) Q meter (c) Wattmeter (d) Clamp meter. Which pairing is correct?

    1. (a) capacitance, (b) power
    2. (c) quality factor, (d) insulation resistance
    3. (a) frequency, (c) energy
    4. (a) insulation resistance, (b) quality factor of a coil
    Answer

    D. (a) insulation resistance, (b) quality factor of a coil

    A megger tests insulation resistance and a Q meter finds the quality factor of a coil.

39. A galvanometer of 100 Ω resistance and 10 mA full scale is shunted by 10 Ω. The shunted meter's full-scale current is

    1. 1.1 A
    2. 100 mA
    3. 11 mA
    4. 110 mA
    Answer

    D. 110 mA

    Multiplying power = 1 + 100/10 = 11, so full scale = 10 × 11 = 110 mA.

40. A moving coil meter of 50 Ω and 2 mA full scale is to read 100 V full scale. The series resistance required is

    1. 49,950 Ω
    2. 49,900 Ω
    3. 50,000 Ω
    4. 5,000 Ω
    Answer

    A. 49,950 Ω

    Total = 100/0.002 = 50,000 Ω, so series resistance = 50,000 − 50 = 49,950 Ω.

41. The total resistance of a voltmeter on its 10 V range is 100 kΩ. Its sensitivity is

    1. 100 kΩ/V
    2. 0.1 kΩ/V
    3. 1 kΩ/V
    4. 10 kΩ/V
    Answer

    D. 10 kΩ/V

    Sensitivity = 100 kΩ ÷ 10 V = 10 kΩ/V.

42. Two equal-frequency signals applied to X and Y of a CRO show a circle. This indicates that the signals

    1. have equal amplitude and a 90° phase difference
    2. are in phase with unequal amplitude
    3. have different frequencies
    4. are of opposite polarity only
    Answer

    A. have equal amplitude and a 90° phase difference

    A circle Lissajous figure arises from equal frequency, equal amplitude and a 90° phase shift.

43. Which type of instrument has a uniform scale and high accuracy for d.c. measurement?

    1. Moving iron
    2. Hot wire
    3. PMMC
    4. Induction
    Answer

    C. PMMC

    The torque in PMMC is proportional to current, giving a uniform scale.

44. The standard unit of electrical energy recorded by a house energy meter is

    1. watt-second per minute
    2. kilowatt
    3. volt-ampere
    4. kilowatt-hour
    Answer

    D. kilowatt-hour

    Energy meters record energy in kWh (units).

45. Which instrument measures voltage, current and resistance in one case?

    1. Megger
    2. Multimeter
    3. Clamp meter only
    4. Q meter
    Answer

    B. Multimeter

    A multimeter has switchable ranges for V, I and R.