The chief value of a well-kept measurement record is that
Answer: B
When a component fails in service or a dispute arises, the record is what establishes whether the original acceptance was sound and what instrument and standard stood behind it. Nothing about the record changes the measurement, but a great deal depends on being able to reconstruct it.
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Which of the following most improves the trustworthiness of a measurement?
Answer: C
Traceability is what connects a reading to the definition of the unit, and without it no amount of resolution or repetition establishes correctness. Repetition reduces the random component only, and extra digits may show nothing but noise.
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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 ?
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 :
RSMSSB JE - 2025, RSMSSB - 2025,
Answer: B
The correct matching is (a)-(iv), (b)-(iii), (c)-(ii), (d)-(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 :
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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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 |
MH SET - 2023, SET Exam - 2023,
Answer: C
The correct matching is a-iv, b-iii, c-ii, d-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 :
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 :
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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The error of an instrument is normally given as percentage of :
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.
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For a measurement, indicated value is 225 V while true value is 226 V. What will be the static error of instrument ?
MH SET - 2025, SET Exam - 2025,
Answer: B
The static error is –1 V, option (B).
Static error is the indicated (measured) value minus the true value:
\[ e = 225 - 226 = -1\ \text{V} \]
The negative sign says the instrument reads low. The opposite number, +1 V (option A), is the static correction, the amount that must be added to the reading to get the true value. The values of 0.5 V and –0.5 V do not follow from the given readings.
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