Measurement Errors and Standards Questions and Answers

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: Accuracy of an instrument describes

Correct answer: how close its reading is to the true valueAccuracy is a statement about correctness, and it requires a reference - the true value, or the best available approximation to it from a standard. An instrument reading consistently 2 per cent high is inaccurate however repeatable its readings are, which is the distinction from precision.

Q: Resolution of an instrument is

Correct answer: the smallest change in input it can detectResolution is the fineness of discrimination: on a digital instrument, one count of the least significant digit; on an analogue one, the smallest scale division that can be judged. It is often confused with accuracy, but adding digits to a display improves only the resolution.

Q: Static error of a measurement is defined as

Correct answer: the indicated value less the true value\[ e = A_m - A_t. \] The sign convention matters: an instrument reading high has a positive error, and the correction to be applied is therefore negative. Reversing the order gives the correction rather than the error, which is why calibration certificates state explicitly which they are quoting.

Q: A gross error in a measurement arises from

Correct answer: human mistakes in reading or recordingGross errors are blunders - misreading a scale, transposing digits, recording against the wrong entry, using the wrong range. They are not amenable to statistical treatment, since they are not small and not random, and the only defence is care and independent repetition by another observer.

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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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Accuracy of an instrument describes

A.how close its reading is to the true value
B.how closely repeated readings of the same quantity agree
C.the smallest change in input it can detect
D.the ratio of its output change to its input change

Answer: A

Correct answer: how close its reading is to the true value

Accuracy is a statement about correctness, and it requires a reference - the true value, or the best available approximation to it from a standard. An instrument reading consistently 2 per cent high is inaccurate however repeatable its readings are, which is the distinction from precision.

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Precision of an instrument describes

A.the range of input over which it can be used
B.how closely repeated readings of the same quantity agree
C.how close its reading is to the true value of the quantity
D.the smallest change in input it is able to detect

Answer: B

Correct answer: how closely repeated readings of the same quantity agree

Precision is about scatter alone and says nothing about correctness. An instrument can be very precise and quite wrong - a systematic offset repeats faithfully in every reading. Precision is what averaging improves; accuracy is what calibration establishes.

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Resolution of an instrument is

A.how close its reading is to the true value
B.the ratio of its output to its input
C.the smallest change in input it can detect
D.the largest input it is able to indicate

Answer: C

Correct answer: the smallest change in input it can detect

Resolution is the fineness of discrimination: on a digital instrument, one count of the least significant digit; on an analogue one, the smallest scale division that can be judged. It is often confused with accuracy, but adding digits to a display improves only the resolution.

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Sensitivity of an instrument is

A.the smallest input change that produces a detectable output
B.how close its reading lies to the true value
C.the range of input over which it may be used
D.the ratio of the change in output to the change in input

Answer: D

A sensitive instrument gives a large deflection for a small input, which is a different property from being able to resolve a small change. The two are often confused because a sensitive instrument is usually well resolved.

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The true value of a measured quantity is

A.never known exactly, only estimated
B.the value the instrument indicates on the day
C.the average of a large number of readings taken
D.the value stamped on the instrument's calibration certificate

Answer: A

Every measurement carries an uncertainty, so the best that can be offered is an estimate with a stated interval around it. Treating the mean of many readings as the truth ignores any systematic error present in all of them.

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Static error of a measurement is defined as

A.the smallest change the instrument can detect
B.the indicated value less the true value
C.the true value less the indicated value
D.the ratio of the indicated value to the true value

Answer: B

Correct answer: the indicated value less the true value

\[ e = A_m - A_t. \] The sign convention matters: an instrument reading high has a positive error, and the correction to be applied is therefore negative. Reversing the order gives the correction rather than the error, which is why calibration certificates state explicitly which they are quoting.

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10.

A gross error in a measurement arises from

A.unpredictable variations in the quantity or the environment
B.the instrument drawing power from the circuit it measures
C.human mistakes in reading or recording
D.a fault in the design or calibration of the instrument

Answer: C

Correct answer: human mistakes in reading or recording

Gross errors are blunders - misreading a scale, transposing digits, recording against the wrong entry, using the wrong range. They are not amenable to statistical treatment, since they are not small and not random, and the only defence is care and independent repetition by another observer.

Discuss in Forum

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Measurement Errors and Standards Questions and Answers

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