1 measurement and error

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Chapter 01

Measurement And Error

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Summary

Instrument – a device or mechanism used to determine the present value of a quantity

Measurement – a process of comparing an unknown quantity with an accepted standard quantity.

Standard – an instrument or device having a recognized permanent (stable) value that is used as a reference.

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Error in Measurement

There are various types of error in measurement:

Gross errorsystematic errorrandom error Absolute errorRelative error

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Error - The difference or deviation from the true value of the measurable quantity.

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% Error = true value - measured value × 100% true value

% Accurate = 100% - % Error

Refer to the circuit below, calculate the error percentage and accurate percentage if meter ampiar show the value of 6 mA.

1KΩ

15V

mA

2KΩ


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Errors are generally categorized under the following three (3) major headings:Gross ErrorsSystematic ErrorsRandom Errors

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1.Gross Error generally the fault of the person using the

instruments such as incorrect reading, incorrect recording,

incorrect use etc. They can be avoided only by taking care in

using and reading all instruments.

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2.Systematic Error Devided into two different categories:- i) Instrumental errors are errors inherent in

measuring instrument because of their electrical and mechanical structure.Example : stretching of the spring.

Instrumental error may be avoided by :- 1) selecting a suitable instrument for the particular

measurement application. 2) Calibrating the instrument against a standard.ii) Environmental errors are due to condition external to

the measuring device, including conditions in the area surrounding the instrument.

Example :temperature, humidity and air pressure.

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3.Random Errors These errors are due to unknown causes and occur

even when all systematic errors have been accounted for.

This variation cannot be corrected by any method of calibration or other known method of control.

Random errors may be avoided by increasing the number of reading and using statistical means to obtain the best approximation of the true table of the quantity under measurement.

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ABSOLUTE ERROR AND RELATIVE ERROR

If resistor is known to have a resistance of 500Ω with a possible error of ± 50Ω, the ± 50Ω is an Absolute error.

Relative error – is a percentage or as a fraction of the total resistance .

Example: Measured voltage = 20 V ± 0.1%

(Relative error)

= 20 V ± 0.02V

(Absolute error)

Percentages are usually employed to express errors in resistances and other electrical quantities.

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Absolute errors.

Absolute errors maybe defined as the difference between the expected value of the variable and the measured value of the variable, or

e = Yn – Xnwhere:

e = absolute error.

Yn = expected value.

Xn = measured value

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Example 2

The expected value of the voltage across a resistor is 5.0 V. However, measurement yields a value of 4.9 V. Calculate:

a) absolute error

b) % error

c) % accuracy

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CHARACTERISTIC OF MEASUREMENT

Accuracy – The degree of exactness of a measurement compared to the expected value

Precision – A measure of consistency, or repeatability of measurements

Resolution – The smallest change in measured quantity that can be observed.

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CHARACTERISTIC OF MEASUREMENT

Significant figure – An indication of the measurement is obtained from the number of significant figures in which the result is expressed.Significant figures convey actual information regarding the magnitude and the measurement precision of a quantity.The more significant, the greater the precision of measurement.

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Measurement Standards

Measurement Standards are classified in four

level :-International standards.Primary standards.Secondary standards.Working standards.

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International standards.

Are defined by international agreement , and are maintained at the International Bureau of Weight and Measure in France.

These are as accurate as it is scientifically possible to achieve.

They may be used for comparison with primary standard, but otherwise unavailable for any application.

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Primary Standard

Are maintained at institutions in various countries around the world, such as the National Bureau of Standards in Washington.

These are as accurate as it is scientifically possible to achieve.

They are also constructed for the greatest possible accuracy , and their main function is checking the accuracy of secondry standard.

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Secondary standard

Are periodically checked at the institutions the maintain primary standards.

Are employed in industry as reference for calibrating high accuracy equipment and component and for verify the accuracy of working standards.

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Working Standard

The working standards are the principal tools of a measurement laboratory.They are used to checked and calibrated general laboratory instrument for accuracy and performance or to perform comparison measurement industrial application.

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Summary

Secondary standards are more accurate than working standard and are used throughout industry for checking working standards and for calibrating high accuracy equipment.

Primary standards are more accurate than secondary standards.They are maintained to the highest possible accuracy by national institutions as references for calibrating secondary standards.

International Standards are maintained by international agreement and may be used for checking primary standards.

EXAMPLES 1

A voltmeter, having a sensitivity of 1,000 Ω/V, reads 100 V on its 150 V scale when connected across an unknown resistor in series with a milliammeter. When the milliammeter reads 5 mA, calculate

a) apparent resistance of the unknown resistor,

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b) actual resistance of the unknown resistor

c) error due to the loading effect of the voltmeter.

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EXAMPLE 2

Repeat the above example, if the milliammeter reads 800 mA and the voltmeter reads 40 V on its 150 V scale.

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1 measurement and error

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