AEE Electrical Engineering Core · Chapter 13

Electrical Measurements and Instruments

What to remember

A PMMC meter reads only DC with a linear scale; a moving-iron meter reads AC and DC with a square-law (crowded) scale and shows the rms value.
Extend an ammeter with a shunt (Rsh = Rm/(m−1)) and a voltmeter with a series multiplier (Rs = Rm(m−1)); a bridge is balanced when no current flows in the detector.
A current transformer secondary must never be open; a potential transformer secondary must never be short-circuited. Two wattmeters measure three-phase power: P = W1 + W2.

Errors, accuracy and standards

Every measurement has an error. Error = measured value − true value. Percentage error = (error ÷ true value) × 100. Example: true voltage 100 V, meter reads 102 V, error = +2%.

Types of error:

Gross errors: human mistakes such as wrong reading or wrong recording.
Systematic errors: repeat in the same direction. Causes are instrument faults (instrumental error), loading of the circuit (environmental or loading error) and wrong calibration.
Random errors: small, unpredictable variations. They are reduced by taking many readings and using the average.

Accuracy is closeness to the true value. Precision is closeness of repeated readings to each other. Resolution is the smallest change the instrument can show. Sensitivity is output change per unit input change. Limiting error (guarantee error) is the maximum error the maker allows, usually as a percentage of full-scale value. A meter with ±1% of full scale on a 100 V range can be wrong by ±1 V at any reading, so readings near full scale are best.

Working principles of indicating instruments

Every indicating instrument has three torques: deflecting torque, controlling torque (spring or gravity) and damping torque (air friction, fluid friction or eddy current). The pointer settles when deflecting torque equals controlling torque. Spring control gives Tc = Kθ.

PMMC (permanent magnet moving coil): coil in a permanent magnet field. Td = N B A I, so deflection is proportional to current and the scale is uniform. Eddy-current damping from the aluminium former. It reads DC only; on AC the average torque is zero. It is the most sensitive and accurate common meter, with low power use.
Moving iron (MI): attraction or repulsion type. Deflection is proportional to I², so the scale is non-uniform and crowded at the low end. It works on AC and DC and reads rms. Errors come from hysteresis and frequency.
Dynamometer type: a fixed coil and a moving coil. As an ammeter or voltmeter it has a square-law scale. As a wattmeter, torque is proportional to V × I × cosφ and the scale is nearly uniform. It works on AC and DC.
Induction type: a disc or drum driven by eddy currents from two AC fluxes with a phase difference. It works on AC only. It is used for energy meters.
Electrostatic type: works on force between charged plates. It draws almost no current, so it is used for high voltage. It works on AC and DC and reads rms.
Hot wire and thermocouple instruments: heating effect, so they read rms, work on AC, DC and high frequency, and are used for radio frequency current.
Rectifier type: a diode rectifier feeds a PMMC meter. It is used in multimeters for AC. The scale is calibrated in rms for a sine wave.

Range extension and instrument transformers

Ammeter shunt: a low resistance in parallel. Multiplying power m = I/Im = 1 + Rm/Rsh, so Rsh = Rm/(m−1). Example: Rm = 100 Ω, m = 11, Rsh = 10 Ω.

Voltmeter multiplier: a high resistance in series. m = V/Vm = 1 + Rs/Rm, so Rs = Rm(m−1). Example: Rm = 1 kΩ, 10 V to 100 V, Rs = 9 kΩ. Voltmeter sensitivity is given in Ω/V (reciprocal of full-scale current). A 20 kΩ/V meter on a 50 V range has 1 MΩ input resistance. A low-resistance voltmeter loads a high-resistance circuit and gives a loading error.

Instrument transformers extend AC ranges and isolate the meter from high voltage.

Current transformer (CT): primary in series with the line, few turns. The secondary is normally 1 A or 5 A and sits near short circuit. Never open the secondary: high flux and dangerous high voltage result. Example: ratio 400/5, line current 200 A, secondary current 2.5 A.
Potential transformer (PT or VT): primary across the line. Secondary is normally 110 V. Never short the secondary.
Errors are ratio error and phase angle error. Burden is the load on the secondary, expressed in VA.

Measurement of power and energy

Wattmeter has a current coil (low resistance, in series) and a pressure coil (high resistance, across the supply). Reading = V I cosφ. Example: 230 V, 5 A, pf 0.8 gives 920 W.

Two-wattmeter method (three-phase, three-wire):

P = W1 + W2. Reactive power Q = √3 (W1 − W2).
tanφ = √3 (W1 − W2)/(W1 + W2).
Example: W1 = 1000 W, W2 = 500 W: P = 1500 W, tanφ = √3 × 500/1500 = 0.577, φ = 30°, pf = 0.866.

Power factor	Wattmeter readings
Unity (φ = 0)	Equal, W1 = W2
0.5 lag (φ = 60°)	One reads zero
Below 0.5	One reads negative (reverse its connections)
Zero	Equal and opposite

Single-phase induction energy meter: it has a series (current) magnet and a shunt (pressure) magnet, an aluminium disc, a permanent braking magnet and a register. Speed is proportional to power, and number of revolutions is proportional to energy. Meter constant is in rev/kWh. Example: 1200 rev/kWh, 600 revolutions means 0.5 kWh. Compensations: shading loop or lag adjustment for 90° phase shift, a friction compensation (small extra torque), and two small holes or slots in the disc to stop creeping (rotation with no load). Percentage error = (recorded − true)/true × 100.

Bridges, potentiometer and special meters

Measurement	Method
Low resistance (below about 1 Ω)	Kelvin double bridge
Medium resistance	Wheatstone bridge
High resistance, insulation	Megger, loss-of-charge method
Inductance	Maxwell, Hay, Anderson bridge
Capacitance, loss factor	Schering bridge, De Sauty
Frequency	Wien bridge

Wheatstone bridge: balance when P/Q = R/S. Example: P = 100 Ω, Q = 1000 Ω, S = 450 Ω gives R = 45 Ω. Most sensitive when all four arms are nearly equal.
Maxwell bridge: measures a medium-Q inductor using a standard capacitor. Hay bridge uses a series resistor with the capacitor and suits high-Q coils. Anderson bridge compares inductance with a standard capacitor.
Schering bridge: measures capacitance and dielectric loss. tanδ = ωC4R4 in its usual form. It is used for cable and insulator testing, also at high voltage.
Wien bridge: frequency f = 1/(2πRC) when the arms are equal. Example: R = 10 kΩ, C = 0.01 µF gives about 1.59 kHz.
DC potentiometer: compares voltages by balance and draws no current from the source at balance. It is standardised with a standard cell. It calibrates voltmeters and ammeters and gives very high accuracy.
Megger: hand-driven or electronic generator. It gives high test voltage to measure insulation resistance of cables and machines.
Q-meter: at resonance Q = ωL/R = 1/(ωCR). It measures Q of coils and capacitor values.

Electronic instruments and transducers

CRO (cathode ray oscilloscope): electron gun, deflection plates, fluorescent screen. Peak-to-peak value = divisions × volts/div. Time period = divisions × time/div. Example: 5 divisions at 2 ms/div gives T = 10 ms, f = 100 Hz. A Lissajous figure compares two frequencies and gives phase.
Digital voltmeter: converts analog to digital by ramp, dual slope or successive approximation. A 3½-digit display reads up to 1999. On a 2 V range its resolution is 1 mV. Input resistance is very high.
Transducers:
Strain gauge: gauge factor = (ΔR/R)/(ΔL/L). Example: R = 120 Ω, GF = 2, strain 0.001 gives ΔR = 0.24 Ω.
LVDT: linear variable differential transformer for displacement. Output is zero at the null (centre) position and its phase changes on the other side. It has high sensitivity and no friction.
Thermocouple: Seebeck effect. RTD: resistance rises with temperature (platinum PT100 is 100 Ω at 0 °C). Thermistor: normally negative temperature coefficient.
Piezoelectric (quartz) for dynamic force. Hall effect for magnetic field and current.

Exam traps

PMMC reads DC only; the MI meter reads both AC and DC. PMMC scale is uniform; MI scale is crowded.
Shunt is in parallel with low resistance; multiplier is in series with high resistance.
CT secondary: never open. PT secondary: never short.
Wattmeter current coil is low resistance; pressure coil is high resistance.
Induction instruments work on AC only. Electrostatic instruments work on AC and DC.
Kelvin bridge is for low resistance; Wheatstone is for medium; megger is for high.
Schering measures capacitance and loss; Maxwell and Hay measure inductance; Wien measures frequency.
Accuracy is not the same as precision; a precise meter can still be inaccurate.

One-liners

1. Deflecting torque in a PMMC meter is Td = N B A I.
2. Controlling torque is provided by springs; damping is by eddy currents or air.
3. The MI meter deflection is proportional to the square of current.
4. Voltmeter multiplier Rs = Rm(m−1).
5. Ammeter shunt Rsh = Rm/(m−1).
6. Wheatstone bridge balance: P/Q = R/S.
7. Two wattmeters: P = W1 + W2.
8. At 0.5 power factor, one wattmeter reads zero.
9. Creeping in an energy meter is stopped by holes in the disc.
10. LVDT gives zero output at the null position.
11. Gauge factor = (ΔR/R) ÷ strain.
12. Wien bridge frequency f = 1/(2πRC) for equal arms.

Practice questions

Which instrument has a uniform scale and responds only to DC?
1. PMMC
2. Electrodynamometer ammeter
3. Moving iron
4. Induction type
Answer
A. PMMC
The PMMC torque Td = NBAI is proportional to current, so the scale is uniform; on AC the average torque is zero.
The deflection of a moving iron instrument is proportional to
1. cube of the current
2. square of the current
3. square root of the current
4. current
Answer
B. square of the current
MI deflecting torque varies as I squared, giving a crowded low-end scale.
An ammeter coil of 50 ohm resistance is to read 6 times its full-scale current. The shunt resistance needed is
1. 300 ohm
2. 5 ohm
3. 8.33 ohm
4. 10 ohm
Answer
D. 10 ohm
Rsh = Rm/(m-1) = 50/5 = 10 ohm.
A voltmeter of 2 kilo-ohm resistance and 5 V range is to be extended to 50 V. The series multiplier is
1. 20 kilo-ohm
2. 10 kilo-ohm
3. 18 kilo-ohm
4. 2 kilo-ohm
Answer
C. 18 kilo-ohm
m = 10, Rs = Rm(m-1) = 2 x 9 = 18 kilo-ohm.
A voltmeter has a sensitivity of 10 kilo-ohm per volt. Its input resistance on the 100 V range is
1. 1 mega-ohm
2. 100 kilo-ohm
3. 10 kilo-ohm
4. 10 mega-ohm
Answer
A. 1 mega-ohm
R = 10 kilo-ohm/V x 100 V = 1,000 kilo-ohm = 1 mega-ohm.
Which of the following must never be open-circuited while the primary carries current?
1. Primary of a potential transformer
2. Pressure coil of a wattmeter
3. Secondary of a current transformer
4. Secondary of a potential transformer
Answer
C. Secondary of a current transformer
An open CT secondary has no opposing ampere-turns, so core flux and secondary voltage rise dangerously.
A current transformer of ratio 100/5 shows 4 A in the secondary. The primary current is
1. 8 A
2. 80 A
3. 125 A
4. 20 A
Answer
B. 80 A
Primary = 4 x (100/5) = 80 A.
The pressure coil of a wattmeter is made
1. of low resistance and connected across the supply
2. of high resistance and connected in series
3. of low resistance and connected in series
4. of high resistance and connected across the supply
Answer
D. of high resistance and connected across the supply
The pressure coil carries a small current proportional to voltage, so it has high resistance and is in parallel.
Two wattmeters measure a balanced three-phase load and read 2000 W each. The power factor and total power are
1. unity and 4000 W
2. 0.866 and 4000 W
3. unity and 2000 W
4. 0.5 and 4000 W
Answer
A. unity and 4000 W
Equal readings mean tan(phi) = 0, so pf = 1; P = W1 + W2 = 4000 W.
In the two-wattmeter method, W1 = 3000 W and W2 = 0. The load power factor is
1. 0.866
2. 0.5 lag
3. zero
4. unity
Answer
B. 0.5 lag
tan(phi) = root 3 x 3000/3000 = 1.732, so phi = 60 degrees and pf = 0.5.
Two wattmeters read 800 W and 400 W. The reactive power is nearly
1. 1200 VAr
2. 400 VAr
3. 693 VAr
4. 1386 VAr
Answer
C. 693 VAr
Q = root 3 (W1 - W2) = 1.732 x 400 = 693 VAr.
An energy meter has a constant of 1000 rev/kWh. A 2 kW load runs for 30 minutes. The disc makes
1. 2000 revolutions
2. 3000 revolutions
3. 500 revolutions
4. 1000 revolutions
Answer
D. 1000 revolutions
Energy = 2 x 0.5 = 1 kWh, so 1 x 1000 = 1000 revolutions.
Creeping in an induction energy meter is prevented by
1. increasing the braking magnet strength
2. two small holes in the disc
3. lowering the supply frequency
4. removing the shunt magnet
Answer
B. two small holes in the disc
Holes or slots on opposite sides of the disc make it stop when the pressure coil is energised with no load.
In a Wheatstone bridge P = 1000 ohm, Q = 100 ohm and S = 25 ohm at balance. The unknown R (with P/Q = R/S) is
1. 250 ohm
2. 2500 ohm
3. 25 ohm
4. 2.5 ohm
Answer
A. 250 ohm
R = (P/Q) x S = 10 x 25 = 250 ohm.
Low resistance of a fraction of an ohm is best measured with
1. Megger
2. Schering bridge
3. Kelvin double bridge
4. Wheatstone bridge
Answer
C. Kelvin double bridge
The Kelvin bridge removes the effect of lead and contact resistance.
A Schering bridge is mainly used to measure
1. low resistance
2. frequency
3. inductance of high-Q coils
4. capacitance and dielectric loss
Answer
D. capacitance and dielectric loss
Schering bridge gives capacitance and loss tangent of insulation and cables.
A Wien bridge with equal arms R = 1 kilo-ohm and C = 0.1 microfarad balances at a frequency of nearly
1. 159 Hz
2. 6.28 kHz
3. 1.59 kHz
4. 15.9 kHz
Answer
C. 1.59 kHz
f = 1/(2 pi RC) = 1/(2 pi x 1000 x 1e-7) = 1591 Hz.
Which bridge is best for measuring the inductance of a coil with a high Q factor?
1. Hay bridge
2. Kelvin bridge
3. Maxwell inductance-capacitance bridge
4. Wheatstone bridge
Answer
A. Hay bridge
The Hay bridge has a resistor in series with the capacitor, which suits high-Q coils; Maxwell suits low and medium Q.
A CRO screen shows a sine wave of 3 divisions peak to peak at 5 V/div. The peak voltage is
1. 5.3 V
2. 15 V
3. 10.6 V
4. 7.5 V
Answer
D. 7.5 V
Vpp = 3 x 5 = 15 V; peak = 15/2 = 7.5 V.
One cycle on a CRO covers 4 divisions with the time base at 5 ms/div. The frequency is
1. 25 Hz
2. 50 Hz
3. 20 Hz
4. 200 Hz
Answer
B. 50 Hz
T = 4 x 5 = 20 ms, f = 1/0.02 = 50 Hz.
A 3 1/2 digit digital voltmeter on its 2 V range has a resolution of
1. 10 mV
2. 1 mV
3. 0.1 mV
4. 100 mV
Answer
B. 1 mV
Maximum display 1.999 V, so the last digit is 0.001 V = 1 mV.
A strain gauge of 350 ohm and gauge factor 2 is subjected to a strain of 0.002. The change in resistance is
1. 1.4 ohm
2. 0.14 ohm
3. 2.8 ohm
4. 0.7 ohm
Answer
A. 1.4 ohm
dR = GF x strain x R = 2 x 0.002 x 350 = 1.4 ohm.
A voltmeter reads 98 V when the true value is 100 V. The percentage error is
1. +1.96%
2. +2%
3. -1.96%
4. -2%
Answer
D. -2%
Error = 98 - 100 = -2 V; -2/100 x 100 = -2%.
A 200 V full-scale voltmeter has a limiting error of 1% of full scale. At a reading of 50 V the possible error as a percentage of the reading is
1. 2%
2. 1%
3. 4%
4. 0.25%
Answer
C. 4%
Error = 1% of 200 = 2 V; 2/50 = 4%.
A wattmeter connected to a single-phase load of 230 V, 10 A and power factor 0.5 reads
1. 1150 W
2. 1990 W
3. 575 W
4. 2300 W
Answer
A. 1150 W
P = V I cos(phi) = 230 x 10 x 0.5 = 1150 W.
A voltmeter with full-scale current of 50 microampere has a sensitivity of
1. 2 kilo-ohm per volt
2. 20 kilo-ohm per volt
3. 200 kilo-ohm per volt
4. 50 kilo-ohm per volt
Answer
B. 20 kilo-ohm per volt
Sensitivity = 1/Ifs = 1/(50e-6) = 20,000 ohm/V.
Which of the following is a standard way to reduce the effect of random errors?
1. Using a higher range
2. Using a longer pointer
3. Taking many readings and averaging
4. Changing the zero setting
Answer
C. Taking many readings and averaging
Random errors vary in sign and size, so the mean of many readings is closer to the true value.
The LVDT output at the central (null) position of the core is
1. infinite
2. equal to the supply voltage
3. maximum
4. zero
Answer
D. zero
The two secondaries are connected in opposition and give equal and opposite voltages at the centre.
At resonance the Q factor of a series coil measured by a Q-meter is
1. omega R / L
2. L / R
3. R / (omega L)
4. omega L / R
Answer
D. omega L / R
Q = omega L / R = 1/(omega C R) at resonance.
Which instrument is suitable for measuring insulation resistance of a cable?
1. Wien bridge
2. Q-meter
3. Megger
4. Kelvin bridge
Answer
C. Megger
A megger applies a high test voltage and reads very high resistance directly.
Which type of instrument works on both AC and DC and draws almost no current from the circuit?
1. Electrostatic voltmeter
2. PMMC voltmeter
3. Induction ammeter
4. Rectifier voltmeter
Answer
A. Electrostatic voltmeter
Force between charged plates needs only voltage, hence negligible current; it works on both AC and DC.
A thermistor normally has
1. a negative temperature coefficient of resistance
2. a positive coefficient only
3. zero coefficient
4. a linear coefficient
Answer
A. a negative temperature coefficient of resistance
Typical thermistors fall in resistance as temperature rises.
Which of the following is the Seebeck-effect device?
1. LVDT
2. Thermocouple
3. Strain gauge
4. Piezoelectric crystal
Answer
B. Thermocouple
A thermocouple generates emf from a temperature difference of two dissimilar metal junctions.
Consider the statements on instrument transformers. 1. The secondary of a CT should be kept short-circuited when the meter is removed. 2. The secondary of a PT is usually rated at 110 V. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
C. Both 1 and 2
A CT secondary is shorted when the burden is removed; PT secondary is standard 110 V.
Consider the statements. 1. A PMMC instrument can measure AC directly. 2. A moving iron instrument reads the rms value of AC. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
PMMC reads zero on AC because the average torque is zero; MI deflection follows I squared, giving rms.
Consider the statements on the two-wattmeter method. 1. At unity power factor both readings are equal. 2. At power factor 0.5 one reading is zero. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
C. Both 1 and 2
tan(phi) = 0 gives equal readings; phi = 60 degrees makes W2 = 0.
Consider the statements on bridges. 1. A Wheatstone bridge suits low resistances below 1 ohm. 2. A Schering bridge can measure loss factor of a capacitor. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
Low resistance needs a Kelvin bridge because lead resistance is comparable; Schering gives tan delta.
Consider the statements on the ammeter shunt. 1. It is connected in parallel with the meter. 2. It has a resistance much greater than the meter. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
The shunt is low in resistance, much smaller than the meter coil resistance.
Consider the statements on electrodynamometer instruments. 1. They can be used as wattmeters. 2. They work only on AC. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
A. 1 only
They work on AC and DC; torque proportional to product of currents gives power.
Consider the statements on energy meters. 1. The speed of the disc is proportional to the power. 2. A braking magnet is used to make the speed proportional to power. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
C. Both 1 and 2
The braking eddy-current torque is proportional to speed, so speed follows the driving torque, i.e. power.
Consider the statements on a DC potentiometer. 1. At balance it draws no current from the source being measured. 2. It is standardised using a standard cell. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
C. Both 1 and 2
The null condition draws no current; working current is set against a standard cell.
Match the instrument with its use. P) Megger Q) Q-meter R) Wien bridge S) Kelvin bridge
1. P-frequency, Q-low resistance, R-coil quality, S-insulation resistance
2. P-coil quality, Q-insulation resistance, R-low resistance, S-frequency
3. P-low resistance, Q-frequency, R-insulation resistance, S-coil quality
4. P-insulation resistance, Q-coil quality, R-frequency, S-low resistance
Answer
D. P-insulation resistance, Q-coil quality, R-frequency, S-low resistance
Each matches its standard application.
Match the transducer with its principle. P) Thermocouple Q) LVDT R) Strain gauge S) Hall element
1. P-magnetic field, Q-change of resistance, R-mutual inductance, S-Seebeck effect
2. P-mutual inductance, Q-Seebeck effect, R-magnetic field, S-change of resistance
3. P-change of resistance, Q-magnetic field, R-Seebeck effect, S-mutual inductance
4. P-Seebeck effect, Q-mutual inductance, R-change of resistance, S-magnetic field
Answer
D. P-Seebeck effect, Q-mutual inductance, R-change of resistance, S-magnetic field
Thermocouple uses Seebeck effect; LVDT uses variable mutual inductance; strain gauge changes resistance; Hall element senses magnetic field.
Consider the statements on accuracy. 1. Precision means closeness of readings to the true value. 2. Resolution is the smallest change an instrument can show. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
B. 2 only
Closeness to the true value is accuracy; precision is repeatability.
Consider the statements on CRO. 1. The time base voltage is a sawtooth wave. 2. A Lissajous figure can compare two frequencies. Which is/are correct?
1. 1 only
2. 2 only
3. Both 1 and 2
4. Neither 1 nor 2
Answer
C. Both 1 and 2
A sawtooth sweeps the beam across the screen; XY mode with two sine waves gives Lissajous patterns.

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1.The boiling and freezing points of water are exactly _____ degrees apart on the Fahrenheit scale.
2.The center of gravity of a semi-circle lies at a distance of __________ from its base measured along the vertical radius.
3.The crest of a wave is the point where the disturbance is at:
4.The critical angle for diamond is approximately _______.
5.The coordination number of atoms in a body-centered cubic (BCC) lattice is:
6.The atomic radius of a hydrogen atom is:
7.The atomic number of sulphur is-
8.The atomic number of phosphorus atom is:
9.The average temperature of human body is ______.
10.The force experienced by a current carrying conductor in a magnetic field is maximum when the angle between the direction of current and the direction of magnetic field is

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