Introduction to Electrical Measurement Chapter 1 Introduction to Electrical Measurement ELECTRICAL MEASUREMENTS (BEF 23903) INSTRUMENTATION & MEASUREMENTS (BEE 1313)

ELECTRICAL MEASUREMENTS Objectives At the end of this chapter, you should be able to: explain units and quantities in electrical field discuss and calculate various types of error in measurement ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS Chapter outline The outline of this chapter is as follows: 1.1 Principles of Measurements 1.2 System of Measurement 1.3 SI Systems 1.4 Accuracy of Measurements 1.5 Instruments Accuracy 1.6 Reading Resolution 1.7 Errors in Instruments ELECTRICAL MEASUREMENTS (BEF 23903)

1.1 Principle of Measurements A process to present an observer with a numerical value corresponding to the variable being measured by using appropriate instrument Basically used to monitor a process or operation, or as well as the controlling process Eg: thermometers, multimeter, etc Measurement system Input Output True value of variable Measured value ELECTRICAL MEASUREMENTS (BEF 23903) INSTRUMENTATION & MEASUREMENTS (BEE 1313)

1.1 Principle of Instrumentation & measurements The major problem encountered with any measuring instrument is the error Therefore, it is necessary to select the appropriate measuring instrument & measurement method which minimises error To avoid errors in any experimental work, careful planning, execution & evaluation of the experiment are essential ELECTRICAL MEASUREMENTS (BEF 23903)

1.1 Principle of Instrumentation & Measurements Before measurement process we have to ensure: Methods/procedures of measurement Characteristics of the parameter Quality: time and cost, instrument capabilities, knowledge of measurement, acceptable result What instrument to use ELECTRICAL MEASUREMENTS (BEF 23903)

1.1 Principle of Measurements During the measurements we have to ensure: Quality- best instrument chosen, suitable position when taking the data, etc.. Safety- electric shock, overloaded, instrument limits, read instruction manual Sampling – observe parameter changing, taking enough sample After measurement Analyse the data mathematically/statistically Full result must be reported completely and accurately ELECTRICAL MEASUREMENTS (BEF 23903)

1.1 Principle of Measurements Electrical Units i) Fundamental Quantity… Quantity Symbol Unit Unit Abbre. Length l meter m Mass kilogram kg Time t second s Temperature T Kelvin oK Electric current I Ampere A ELECTRICAL MEASUREMENTS (BEF 23903)

1.1 Principle of Measurements ii) Derived Quantity… Quantity Symbol Unit Unit Abbre. emf/ voltage V volt charge Q coulomb C resistance R Ohm Ω capacitance farad F inductance L hendry H ELECTRICAL MEASUREMENTS (BEF 23903)

1.2 Error in Measurement Error: is defined as the difference between the measured value and the expected value (true value) of the measured parameter Various types of error in measurement: i) absolute error ii) gross error iii) systematic error iv) random error v) limiting error **static error = numerical difference between the true value of a quantity and its value as obtained by measurement (i.e. repeated measurement of the same quantity gives different indications. Static errors

ELECTRICAL MEASUREMENTS 1.2 Error in Measurement i) Absolute error: The difference between the expected value of the variable and the measured value of the variable, or e = Yn – Xn where: e = absolute error Yn = expected value Xn = measured value ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 1.2 Error in Measurement To express error in percentage % error = , e = Yn - Xn We also derived relative accuracy, A; ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 1.2 Error in Measurement Percentage accuracy, a: a = 100% - % error or a = A x 100% ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 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 ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 1.2 Error in Measurement ii) Gross Error Due to human mistakes Example: incorrect reading, incorrect recording, improper use of instruments, etc To minimize: take at least 3 separate reading take proper care in reading & recording ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 1.2 Error in Measurement Instrumental errors iii) Systematic Error due to instrument’s problem or environmental effects or observational errors example…??? defective or worn parts ageing parallax error wrong estimation reading scale Environmental errors Observational errors ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 1.2 Error in Measurement Instrumental errors : due to friction in the bearings of the meter movement, incorrect spring tension, improper calibration, or faulty instruments can be reduced by proper maintenance, use, and handling of instruments Environmental errors : due to external condition of the measuring eg: effects of change in temperature, humidity, barometric pressure, electrostatic fields etc can be avoided by: air conditioning, hermetically sealing certain components in the instrument and using magnetic shields Observational errors : Errors that introduced by the observer The two most common observational errors are probably the parallax error introduced in reading a meter scale and the error of estimation when obtaining a reading from a meter scale ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 1.2 Error in Measurement iv) Random Errors Errors that remain after gross and systematic errors have been substantially reduced Are generally the accumulation of a large number of small effects May be of real concern only in measurements requiring a high degree of accuracy such errors can only be analyzed statistically Due to unknown causes ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 1.2 Error in Measurement v) Limiting Errors Most manufacturers of instruments state that an instrument is accurate within a certain percentage of a full-scale reading Eg: a voltmeter is accurate within ±2% at full-scale deflection (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 ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS Example 1.2 A 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? ELECTRICAL MEASUREMENTS (BEF 23903)

INSTRUMENTATION &ELECTRICAL MEASUREMENTS Example 1.2 Solution The magnitude of the limiting error is: 2/100 x 300 = 6V Therefore, the limiting error at 120 V is: 6/120 x 100 = 5% (reading < full scale, limiting error increased) INSTRUMENTATION &ELECTRICAL MEASUREMENTS (BEF 23903)

INSTRUMENTATION &ELECTRICAL MEASUREMENTS Example 1.3 A 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. ** The limiting error for the power calculation is the sum of individual limiting errors involved INSTRUMENTATION &ELECTRICAL MEASUREMENTS (BEF 23903)

INSTRUMENTATION &ELECTRICAL MEASUREMENTS 1.2 Error in Measurement Precision of measurement A measure of the consistency or repeatability of measurements where Xn = the value of the nth measurement Xn = the average of the set of n measurements = sum of the nth measurement values / nth INSTRUMENTATION &ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS Example 1.4 Table below gives the set of 10 measurement that were recorded in the laboratory. Calculate the precision of the 6th measurement. = ?? Precision = ?? Measurement number Measurement value Xn 1 98 2 101 3 102 4 97 5 6 100 7 103 8 9 106 10 99 ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 1.2 Error in Measurement STATISTICAL ANALYSIS OF MEASUREMENT DATA Important because it allows an analytical determination of the uncertainty of the final result A large number of measurements is usually required can be divided into 4: Arithmetic mean / average deviation average deviation standard deviation ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 1.2 Error in Measurement Arithmetic mean/average: - the most probable value of measured variable n = total number of reading xn = nth reading taken xi = set of number ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 1.2 Error in Measurement ii) Deviation: - The difference between each piece of data and arithmetic mean - Algebraic sum of deviation, ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 1.2 Error in Measurement iii) Average deviation (D): - precision of a measuring instrument - high D low precision - low D  high precision ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 1.2 Error in Measurement iv) Standard deviation: - also known as root mean square deviation - the most important factor in statistical analysis - reduction means improvement in measurement ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS Example 1.5 For the following data compute (a) The arithmetic mean (49.9) (b) The deviation of each value (0.2,-0.2,-0.3,0.3) (c) The algebraic sum of the deviation (0) (d) The average deviation (0.25) (e) The standard deviation (0.294) x1= 50.1 x2= 49.7 x3= 49.6 x4= 50.2 ELECTRICAL MEASUREMENTS (BEF 23903)

1.3 Measurement Standards Standards are defined in 4 categories: i) international standards ii) primary standards iii) secondary standards iv) working standards ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 1.3 Measurement Standard i) International Standards Defined by international agreements These standards are maintained at the International Bureau of Weight and Measures in Paris, Frances They are periodically evaluated and checked by absolute measurements in term of the fundamental units of physics They represent certain units of measurement to the closest possible accuracy attained by the science and technology of measurement and used for comparison with primary standards ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 1.3 Measurement Standard ii) Primary Standard Are maintained at institution in various countries around the world, such as the National Bureau of Standard In Washington D.C, SIRIM in Malaysia The primary standards are not available for use outside the national laboratories Their principle function is to calibrate and verify the secondary standards Also known as National Standard ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 1.3 Measurement Standard iii) Secondary Standard Use as the basic reference standards used by measurement & calibration laboratories in industry Each industrial laboratory is completely responsible for its own secondary standards Each laboratory sends its secondary standards to the national standards ( primary standards) laboratory for calibration After calibration, the secondary standards are returned to the industrial users with the certification Needs to check periodically (e.g. once in six months ..) ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 1.3 Measurement Standard iv) Working Standard Working standard is the principle tools of a measurement laboratory and the lowest level of standards Used to check and calibrate the instruments used in the laboratory or to make comparison measurement in industrial application Example: the standard resistor, capacitors, inductor which usually found in an electronics laboratory are classified as working standards. ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 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. ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 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. ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS 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 ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS Evaluation Electrical Quantity… Quantity Symbol Unit Unit Abbre. l meter Capacitance F Time second T Kelvin oK Charge ELECTRICAL MEASUREMENTS (BEF 23903)

ELECTRICAL MEASUREMENTS ANY QUESTIONS? ELECTRICAL MEASUREMENTS (BEF 23903)