Download - 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…
Quantity Symbol Unit Unit Abbre.
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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Error in Measurement
What is the meaning of error?
Please define.
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Error in Measurement
Error - The deviation of a reading or set of readings from the expected value of the measured variable.
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Error in Measurement
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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Error in Measurement
to express error in percentage
% error =
we also derived relative accuracy, A;
)100(nY
e
n
nn
Y
XYA
1
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Error in Measurement
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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Error in Measurement
Errors are generally categorized under the following three (3) major headings:Gross ErrorsSystematic ErrorsRandom Errors
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Error in Measurement
Gross Error generally the fault of the person
using the instrumentssuch as incorrect reading, incorrect
recording, incorrect use etc.
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Error in Measurement
Systematic Error due to problems with instruments/
environmental effects/ or observational errors.
Example…??? parallax errorwrong estimation reading scale
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Error in Measurement
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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Error in Measurement
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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Error in Measurement
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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Error in Measurement
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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Error in Measurement
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…
Quantity Symbol Unit Unit Abbre.
l meter
Capacitance F
Time second
T Kelvin oK
Charge
Evaluation