lecture notes 02

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Chapter 01

Introduction to Instrumentation & Measurements.

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Objectives

At the end of this chapter, the students should be able to:

explain units and quantities in electrical.discuss and calculate various types of

error in measurement.Explain the meaning of some terms in

instrumentation field.

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Outlines

The outline of this chapter is as follow:Principles of instrumentation

and measurementsElectrical UnitsError in measurementSome terms +definitions in

instrumentations.

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Introduction

Why learning DEI 2012?What is the main role/ purpose of

instrumentation?Give Example of applications?

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Introduction

Instrumentations serve three (3) basic functions: -

indicating…

recording…

controlling…

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Fundamental Quantity…

Quantity Symbol Unit Unit Abbre.

Length l meter m

Mass m kilogram kg

Time t second s

Temperature T Kelvin oK

Electric current I Ampere A

Electrical Units

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Derived Quantity…


emf/ voltage V volt V

charge Q coulomb C

resistance R Ohm Ω

capacitance C farad F

inductance L hendry H

Electrical Units

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Measurement Standards

Standards are defined in 4 categories:international standards.primary standards.secondary standards.working standards.

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Measurement Standards

Mass- kg defined the mass of an alloy cyllinder Standards are defined in 4 categories:international standards.primary standards.secondary standards.working standards.

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Error in Measurement

There are various types of error in measurement:

absolute errorgross errorsystematic errorrandom errorlimiting error

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What is the meaning of error?

Please define.

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Error - The deviation of a reading or set of readings from the expected value of the measured variable.

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Absolute error.

Absolute error 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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to express error in percentage

% error =

we also derived relative accuracy, A;

)100(nY

e

n

nn

Y

XYA

1

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Example 1-1.

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) relative accuracy

d) % accuracy

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

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Gross Error generally the fault of the person

using the instrumentssuch as incorrect reading, incorrect

recording, incorrect use etc.

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Systematic Error due to problems with instruments/

environmental effects/ or observational errors.

Example…??? parallax errorwrong estimation reading scale

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Random Errors generally the accumulation of a large

number of small effectsmaybe of real concern only in

measurements requiring a high degree of accuracy.

such errors can only be analyzed statistically.

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Limiting Errors manufacturers of instruments state that

an instrument is accurate within a certain percentage of a full-scale reading.

example is; a voltmeter is accurate within ±2% at full-scale deflection.

this specification is called the limiting errors.

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Limiting Errors However, with reading less than full-

scale, the limiting error will increase.therefore, it is important to obtain

measurements as close as possible to full scale.

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Example 1-2A 300-V voltmeter is specified to be accurate within ±2% at full scale. Calculate the limiting error when the instrument is used to measure a 120-V source?

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Example 1-3A voltmeter and an ammeter are to be used to determine the power dissipated in a resistor. Both instruments are guaranteed to be accurate within ±1% at full scale. If the voltmeter reads 80V on its 150-V range and the ammeter reads 70mA on its 100-mA range, calculate the limiting error for the power calculation.

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Summary

Some terms +definitions are as below: Error – ---??? Accuracy – The degree of exactness of a

measurement compared to the expected value

Precision – A measure of consistency, or repeatability of measurements.

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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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Summary

expected value – the most probable value we should expect to obtain.

deviation – the difference between any piece of data in a set of numbers and the arithmetic mean of the set of numbers.

transducer – a device that converts one form of energy into another form

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Electrical Quantity…


l meter

Capacitance F

Time second

T Kelvin oK

Charge

Evaluation

lecture notes 02

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