Match List I with List II.List IList II(a) Recording Instruments(i) C.T. and P.T.(b) Integrating Instruments(ii) Measurement of current(c) Galvanometer(iii) Watt hour Meter(d) Instrument Transformers(iv) Magnetic TapeChoose the most appropriate answer from the options given below :

The correct matching is (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i).Recording instruments keep a continuous record of a quantity over time, on a chart or magnetic tape: (iv).Integrating instruments add up a quantity over time, like the watt hour meter that totals energy: (iii).A galvanometer detects and measures small currents: (ii).Instrument transformers are the C.T. and P.T.: (i).The option ending (c)-(i), (d)-(ii) swaps the galvanometer and instrument transformers, and the options starting (a)-(iii) confuse recording with integrating instruments.

Match the pair :SET ISET II(a) Output power measurement(i) Q meter(b) High resistance measurement(ii) Calomel electrode(c) pH measurement(iii) Megger(d) Electrical properties of coil and capacitors(iv) Wattmeter

The correct matching is a-iv, b-iii, c-ii, d-i.Output power is measured with a wattmeter (iv).High resistance, such as insulation resistance, is measured with a megger (iii).pH is measured with a glass electrode against a calomel reference electrode (ii).The electrical properties of coils and capacitors, such as Q, inductance and self-capacitance, are measured with a Q meter (i).The other codes give the Q meter to power measurement or the megger to pH, which do not match the instruments' uses.

Measurement Errors and Standards Questions and Answers

Q: The solution for the unknown resistance for a Wheatstone Bridge is \(R_{4} = \frac{R_{2}R_{3}}{R_{1}}\)Where, R1 = 100 ± 0.5% ΩR2 = 1000 ± 0.5% ΩR3 = 842 ± 0.5% ΩWhat will be the limiting error in percent for Resistance R4 ?

The limiting error of \(R_{4}\) is 1.5%.When a result is a product or quotient of quantities, the limiting (worst-case) relative errors add, whichever side of the fraction each quantity is on.\[ \begin{aligned} \frac{\delta R_{4}}{R_{4}} &= \frac{\delta R_{1}}{R_{1}} + \frac{\delta R_{2}}{R_{2}} + \frac{\delta R_{3}}{R_{3}} \\ &= 0.5 + 0.5 + 0.5 = 1.5\% \end{aligned} \]The nominal value is \(R_{4} = 1000 \times 842/100 = 8420\ \Omega\), so it lies within \(8420 \pm 126.3\ \Omega\). 0.50% counts only one resistor. 1.6% and 0.16% do not follow from adding three 0.5% errors.

Q: In an experiment, the acceleration due to gravity is determined by measuring the time period of a simple pendulum. If there is an error of 1% in the measurement of time period, the error in the value of g is :

The error in g is 2%.For a simple pendulum \(T = 2\pi\sqrt{L/g}\), so \(g = 4\pi^{2}L/T^{2}\). The relative error in a quantity raised to a power is that power times the relative error:\[ \begin{aligned} \frac{\Delta g}{g} &= 2\frac{\Delta T}{T} \\ &= 2 \times 1\% = 2\% \end{aligned} \]The option 1% ignores the square, and 0.5% treats g as depending on the square root of T.

Q: Which of the following is not an instrument ?

The PID controller is not an instrument.The passage defines an instrument as "a device or mechanism used to determine the present value of the quantity under measurement". A fuel gauge shows the fuel level, a meter scale determines length, and a wrist watch determines the time, so all three fit that definition.A PID controller does not determine the present value of a quantity. It takes a measured value from an instrument, compares it with a set point and computes a control action, so it is a controller acting on measurements and not itself a measuring device.

Q: Which of the following is most accurate device for length measurement ?

The most accurate device for length measurement is the micrometer.The passage defines accuracy as closeness of a measurement to the expected value. A micrometer screw gauge normally reads to 0.01 mm, and 0.001 mm with a vernier thimble, while vernier calipers usually read to 0.02 mm or 0.05 mm, so the micrometer can resolve and report a length more closely.An odometer measures distance travelled only roughly, in tenths of a kilometre or so, and is affected by tyre wear. A calorimeter is not a length instrument at all; it measures heat. So the choice is between the two hand tools, and the micrometer wins on accuracy.

Q: Which of the following instruments has highest resolution ?

The key gives the electrometer as having the highest resolution.The passage defines resolution as the smallest change in the measured variable to which an instrument will respond. An electrometer is built to measure extremely small charges and currents, down to femtoamps, with input resistances of teraohms, so it responds to the smallest changes of the four.A galvanometer and a micro-ammeter respond to currents around a microamp or at best nanoamps, and a 6½ digit multimeter, although it has many digits, resolves about 100 nV or 1 nA on its most sensitive ranges. I did not find a published table comparing all four, so this ranking rests on the typical resolutions of each class of instrument.

Q: The difference between the indicated value and true value of a quantity is known as :

The difference between the indicated and true value is the absolute error.\[ \delta A = A_{m} - A_{t} \]where \(A_{m}\) is the measured (indicated) value and \(A_{t}\) the true value. The relative error is this difference divided by the true value, \(\delta A/A_{t}\), often expressed as a percentage.Gross errors are human blunders, such as misreading a scale or recording the wrong figure. Dynamic error is the difference between the true and indicated value of a quantity that is changing with time, caused by the instrument's slow response, rather than the general definition asked for here.

Q: A digital to analogue converter has 5.0 V full scale output voltage and an accuracy of ±0.2. The maximum error for any output voltage will be :

The maximum error is 10.0 mV.A DAC's accuracy is quoted as a percentage of full scale, so ±0.2 means ±0.2% of 5.0 V:\[ \begin{aligned} \Delta V &= 0.002 \times 5.0\ \text{V} \\ &= 0.010\ \text{V} \\ &= 10\ \text{mV} \end{aligned} \]Because the error is based on full scale, it is the same 10 mV whatever the output voltage. 5.0 mV and 20.0 mV halve or double it, and 100 mV takes 2% instead of 0.2%.

Q: The error of an instrument is normally given as percentage of :

Instrument error is normally given as a percentage of Full scale value.Manufacturers specify accuracy as a percentage of full-scale deflection, because the absolute error of a meter is roughly constant over its range. A consequence is that readings near the bottom of the scale have a much larger relative error, which is why one chooses a range where the reading falls in the upper part of the scale.Quoting error relative to the measured value would make it vary with each reading; mean and RMS values are properties of signals, not the basis of an accuracy specification.

The solution for the unknown resistance for a Wheatstone Bridge is \(R_{4} = \frac{R_{2}R_{3}}{R_{1}}\)

Where, R₁ = 100 ± 0.5% Ω
R₂ = 1000 ± 0.5% Ω
R₃ = 842 ± 0.5% Ω

What will be the limiting error in percent for Resistance R₄ ?

A.0.16%
B.0.50%
C.1.6%
D.1.5%

Exam Year(s)

RSMSSB JE - 2025, RSMSSB - 2025,

Answer: D

The limiting error of \(R_{4}\) is 1.5%.

When a result is a product or quotient of quantities, the limiting (worst-case) relative errors add, whichever side of the fraction each quantity is on.

\[ \begin{aligned} \frac{\delta R_{4}}{R_{4}} &= \frac{\delta R_{1}}{R_{1}} + \frac{\delta R_{2}}{R_{2}} + \frac{\delta R_{3}}{R_{3}} \\ &= 0.5 + 0.5 + 0.5 = 1.5\% \end{aligned} \]

The nominal value is \(R_{4} = 1000 \times 842/100 = 8420\ \Omega\), so it lies within \(8420 \pm 126.3\ \Omega\). 0.50% counts only one resistor. 1.6% and 0.16% do not follow from adding three 0.5% errors.

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Match List I with List II.

List I	List II
(a) Recording Instruments	(i) C.T. and P.T.
(b) Integrating Instruments	(ii) Measurement of current
(c) Galvanometer	(iii) Watt hour Meter
(d) Instrument Transformers	(iv) Magnetic Tape

Choose the most appropriate answer from the options given below :

A.(a)-(iv), (b)-(iii), (c)-(i), (d)-(ii)
B.(a)-(iv), (b)-(iii), (c)-(ii), (d)-(i)
C.(a)-(iii), (b)-(iv), (c)-(i), (d)-(ii)
D.(a)-(iii), (b)-(iv), (c)-(ii), (d)-(i)

Exam Year(s)

RSMSSB JE - 2025, RSMSSB - 2025,

Answer: B

The correct matching is (a)-(iv), (b)-(iii), (c)-(ii), (d)-(i).

Recording instruments keep a continuous record of a quantity over time, on a chart or magnetic tape: (iv).
Integrating instruments add up a quantity over time, like the watt hour meter that totals energy: (iii).
A galvanometer detects and measures small currents: (ii).
Instrument transformers are the C.T. and P.T.: (i).

The option ending (c)-(i), (d)-(ii) swaps the galvanometer and instrument transformers, and the options starting (a)-(iii) confuse recording with integrating instruments.

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In an experiment, the acceleration due to gravity is determined by measuring the time period of a simple pendulum. If there is an error of 1% in the measurement of time period, the error in the value of g is :

A.2%
B.1%
C.0.5%
D.no error

Exam Year(s)

MH SET - 2019, SET Exam - 2019,

Answer: A

The error in g is 2%.

For a simple pendulum \(T = 2\pi\sqrt{L/g}\), so \(g = 4\pi^{2}L/T^{2}\). The relative error in a quantity raised to a power is that power times the relative error:

\[ \begin{aligned} \frac{\Delta g}{g} &= 2\frac{\Delta T}{T} \\ &= 2 \times 1\% = 2\% \end{aligned} \]

The option 1% ignores the square, and 0.5% treats g as depending on the square root of T.

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Direction for [ Question No: 4 To 6 ] :

The static characteristics of an instrument are, in general, considered for instruments which are used to measure an unvarying process condition. All the static performance characteristics are obtained by one form or another of a process called calibration. There are a number of related definitions (or characteristics), which are described below, such as accuracy, precision, repeatability, resolution errors, sensitivity, etc.
(1) Instrument : A device or mechanism used to determine the present value of the quantity under measurement.
(2) Measurement : The process of determining the amount, degree, or capacity by comparison (direct or indirect) with the accepted standards of the system units being used.
(3) Accuracy : The degree of exactness (closeness) of a measurement compared to the expected (desired) value.
(4) Resolution : The smallest change in a measured variable to which an instrument will respond.
(5) Precision : A measure of the consistency or repeatability of measurements i.e., successive reading do not differ. (Precision is the consistency of the instrument output for a given value of input).
(6) Expected value : The design value i.e., the most probable value that calculations indicate one should expect to measure.
(7) Error : The deviation of the true value from the desired value.
(8) Sensitivity : The ratio of the change in output (response) of the instrument to a change of input or measured variable.

Which of the following is not an instrument ?

A.Fuel gauge in motorbike
B.Meter scale
C.PID controller
D.Wrist watch

Exam Year(s)

MH SET - 2019, SET Exam - 2019,

Answer: C

The PID controller is not an instrument.

The passage defines an instrument as "a device or mechanism used to determine the present value of the quantity under measurement". A fuel gauge shows the fuel level, a meter scale determines length, and a wrist watch determines the time, so all three fit that definition.

A PID controller does not determine the present value of a quantity. It takes a measured value from an instrument, compares it with a set point and computes a control action, so it is a controller acting on measurements and not itself a measuring device.

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Which of the following is most accurate device for length measurement ?

A.Odometer
B.Calorimeter
C.Micrometer
D.Vernier calipers

Exam Year(s)

MH SET - 2019, SET Exam - 2019,

Answer: C

The most accurate device for length measurement is the micrometer.

The passage defines accuracy as closeness of a measurement to the expected value. A micrometer screw gauge normally reads to 0.01 mm, and 0.001 mm with a vernier thimble, while vernier calipers usually read to 0.02 mm or 0.05 mm, so the micrometer can resolve and report a length more closely.

An odometer measures distance travelled only roughly, in tenths of a kilometre or so, and is affected by tyre wear. A calorimeter is not a length instrument at all; it measures heat. So the choice is between the two hand tools, and the micrometer wins on accuracy.

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Which of the following instruments has highest resolution ?

A.Electrometer
B.Micro-ammeter
C.6½ digit multimeter
D.Galvanometer

Exam Year(s)

MH SET - 2019, SET Exam - 2019,

Answer: A

The key gives the electrometer as having the highest resolution.

The passage defines resolution as the smallest change in the measured variable to which an instrument will respond. An electrometer is built to measure extremely small charges and currents, down to femtoamps, with input resistances of teraohms, so it responds to the smallest changes of the four.

A galvanometer and a micro-ammeter respond to currents around a microamp or at best nanoamps, and a 6½ digit multimeter, although it has many digits, resolves about 100 nV or 1 nA on its most sensitive ranges. I did not find a published table comparing all four, so this ranking rests on the typical resolutions of each class of instrument.

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Match the pair :

SET I	SET II
(a) Output power measurement	(i) Q meter
(b) High resistance measurement	(ii) Calomel electrode
(c) pH measurement	(iii) Megger
(d) Electrical properties of coil and capacitors	(iv) Wattmeter

A.a-iv, b-i, c-ii, d-iii
B.a-iv, b-ii, c-iii, d-i
C.a-iv, b-iii, c-ii, d-i
D.a-i, b-ii, c-iii, d-iv

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

Answer: C

The correct matching is a-iv, b-iii, c-ii, d-i.

Output power is measured with a wattmeter (iv).
High resistance, such as insulation resistance, is measured with a megger (iii).
pH is measured with a glass electrode against a calomel reference electrode (ii).
The electrical properties of coils and capacitors, such as Q, inductance and self-capacitance, are measured with a Q meter (i).

The other codes give the Q meter to power measurement or the megger to pH, which do not match the instruments' uses.

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The difference between the indicated value and true value of a quantity is known as :

A.Gross error
B.Absolute error
C.Dynamic error
D.Relative error

Exam Year(s)

MH SET - 2023, SET Exam - 2023,

Answer: B

The difference between the indicated and true value is the absolute error.

\[ \delta A = A_{m} - A_{t} \]

where \(A_{m}\) is the measured (indicated) value and \(A_{t}\) the true value. The relative error is this difference divided by the true value, \(\delta A/A_{t}\), often expressed as a percentage.

Gross errors are human blunders, such as misreading a scale or recording the wrong figure. Dynamic error is the difference between the true and indicated value of a quantity that is changing with time, caused by the instrument's slow response, rather than the general definition asked for here.

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A digital to analogue converter has 5.0 V full scale output voltage and an accuracy of ±0.2. The maximum error for any output voltage will be :

A.5.0 mV
B.10.0 mV
C.20.0 mV
D.100 mV

Exam Year(s)

MH SET - 2024, SET Exam - 2024,

Answer: B

The maximum error is 10.0 mV.

A DAC's accuracy is quoted as a percentage of full scale, so ±0.2 means ±0.2% of 5.0 V:

\[ \begin{aligned} \Delta V &= 0.002 \times 5.0\ \text{V} \\ &= 0.010\ \text{V} \\ &= 10\ \text{mV} \end{aligned} \]

Because the error is based on full scale, it is the same 10 mV whatever the output voltage. 5.0 mV and 20.0 mV halve or double it, and 100 mV takes 2% instead of 0.2%.

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10.

The error of an instrument is normally given as percentage of :

A.Measured value
B.Full scale value
C.Mean value
D.RMS value

Exam Year(s)

MH SET - 2024, SET Exam - 2024,

Answer: B

Instrument error is normally given as a percentage of Full scale value.

Manufacturers specify accuracy as a percentage of full-scale deflection, because the absolute error of a meter is roughly constant over its range. A consequence is that readings near the bottom of the scale have a much larger relative error, which is why one chooses a range where the reading falls in the upper part of the scale.

Quoting error relative to the measured value would make it vary with each reading; mean and RMS values are properties of signals, not the basis of an accuracy specification.

Discuss in Forum

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Measurement Errors and Standards Questions and Answers

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