Measurement Errors and Standards Questions and Answers

Answer: D

Correct answer: the corrections found and the uncertainty of the calibration

A certificate is a measurement result, not a verdict. It records what the instrument read against the standard at each point, the correction implied, and the uncertainty of the calibration itself - because a calibration is a measurement and carries an uncertainty like any other. A bare pass or fail conveys none of that.

Answer: A

An instrument that has proved stable over several cycles can have its interval extended, and one whose reading matters greatly is recalibrated more often. Fixing every interval at a year regardless is convention rather than reasoning.

Answer: B

The error was presumably present for some part of the interval, so anything the instrument was used to accept or reject has to be reconsidered. That obligation is why calibration records are kept with the test results.

Answer: C

That is why such an instrument should be used in the upper part of its range: a class 1.0 meter read at a tenth of full scale can be ten per cent wrong on the reading. A digital instrument's specification is usually quoted differently, as a percentage of reading plus a number of counts.

Answer: D

Correct answer: 5 per cent of the reading

A class 1.0 instrument may be in error by 1 per cent of full scale anywhere on the scale, which here is 1 V. At a reading of 20 V that 1 V is \[ \frac{1}{20} = 5\ \mathrm{per\ cent} \] of the reading. This is the reason for the old rule of using the range on which the pointer sits in the upper part of the scale.

Answer: A

Correct answer: 0.0025 V

\[ 0.05\%\ \mathrm{of}\ 1.0000 = 0.0005\ \mathrm{V}, \qquad 2\ \mathrm{counts} = 0.0020\ \mathrm{V}, \] giving 0.0025 V in total. The count term dominates because the reading is at a tenth of the range, which is the digital equivalent of the analogue class problem: both instruments do their best work near full scale.

Answer: B

Correct answer: 1 and 2 only

Statements 1 and 2 are correct and describe the two remedies for the two kinds of error: averaging for random, calibration for systematic. Statement 3 is the error the pairing exists to warn against - a systematic offset is present in every reading and averaging preserves it exactly.

Answer: C

Correct answer: 1 and 2 only

Statements 1 and 2 are correct: accuracy is closeness to truth and precision is repeatability; resolution is the smallest detectable change and sensitivity is the ratio of output change to input change. Statement 3 is the common confusion - an instrument can be highly repeatable and consistently wrong, which is precisely what a calibration is for.

Answer: D

Correct answer: 1-Q, 2-R, 3-P

Each kind of error has its own remedy, and they do not substitute for one another. Random error scatters symmetrically, so averaging reduces it. Systematic error repeats, so only comparison with a standard reveals it. And a gross error is a blunder, which neither statistics nor calibration will catch - only an independent repetition by someone else.

Answer: A

Correct answer: 1-Q, 2-R, 3-P

The three levels form a chain of decreasing accuracy and increasing use. The primary standard realises the unit from its definition; the secondary is checked against it and held in the laboratory; and the working standard, checked in turn against the secondary, does the routine calibration. Each level protects the one above it from wear and handling.