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MEASUREMENT AND
INSTRUMENTATION:
Theory and Application
ALAN S. MORRIS
REZA LANGARI 1 / 4
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SOLUTIONS MANUAL
GENERAL GUIDANCE ON MARKING
(a) Concept-type questions The expectation from students answering concept-type questions depends on the mode of examination.
Where such questions are set as part of time-limited, invigilated examinations, recall of all relevant information from the book is sufficient for many courses to justify a mark of 100% for the question. However, especially at higher course levels, where lecturers expect students to do additional reading beyond just studying the set course text, it would be appropriate to reflect this in the marking scheme, with perhaps 20% of the available mark being dependent on the extent of further reading that a student demonstrates in his/her answer.
Where such questions are set as part of coursework, homework or non-invigilated examinations, evidence of further reading beyond study of the course text is required in most courses. The lecturer concerned will obviously set their own marking scheme, but we have found ourselves that a fair marking scheme is where 80% of the available mark depends on the extent to which students summarize information provided in the set course textbook and 20% is dependent on the amount of further reading that they demonstrate.
(b) Numerical questions Full solutions to all numerical questions set at the end of each chapter are provided in the following pages. Where questions are sub-divided, the proportion of the total marks that should be awarded to each sub-component is indicated by a percentage number in square brackets at the end of each section.
Practice amongst lecturers varies according to the size of mark penalty applied if a student demonstrates application of the correct method to a problem but makes arithmetic errors in working out a numerical solution. Our own approach is to give students some credit for knowing the correct method to apply to a problem, but to apply a mark penalty according to the magnitude of any arithmetic errors.
In penalizing arithmetic errors in numerical questions, we also vary the size of penalty according to whether the question is set as part of an invigilated examination or as non- invigilated homework etc. Since invigilated examinations are time-limited, students have less opportunity to check numerical calculations and our own practice is to be more lenient towards arithmetic errors (i.e. to apply a smaller penalty). However, in the case of non- invigilated coursework etc, students have ample time to properly check their arithmetic. In this case, any arithmetic errors are due to their laziness in not taking time to check for errors and we apply a greater penalty than is applied for invigilated examinations. 2 / 4
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CONTENTS Page Number Student problems and solution for chapter 1 Student problems and solution for chapter 2 Student problems and solution for chapter 3 Student problems and solution for chapter 4 Student problems and solution for chapter 5 Student problems and solution for chapter 6 Student problems and solution for chapter 7 Student problems and solution for chapter 8 Student problems and solution for chapter 9 Student problems and solution for chapter 10 Student problems and solution for chapter 11 Student problems and solution for chapter 12 Student problems and solution for chapter 13 Student problems and solution for chapter 14 Student problems and solution for chapter 15 Student problems and solution for chapter 16 Student problems and solution for chapter 17 Student problems and solution for chapter 18 Student problems and solution for chapter 19 Student problems and solution for chapter 20 Student problems and solution for chapter 21 3 / 4
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SOLUTIONS FOR QUESTIONS AT END OF CHAPTER 1
1.1 Discussion expected to start with units used in barter trade (explain barter trade, example units – e.g. the hand, the foot and the cubit, and limitations due to variation in size of hands etc). Moving on to standard units and improvements in these over time – e.g. platinum bar for length initially, then wavelengths of radiation, then distance travelled by light in an interval of 1/299792458 seconds. Give examples of standard units for other physical quantities. Mention Imperial, metric and SI units.
1.2 Discussion should cover primary sensor, secondary sensors, conversion elements, signal processing elements, signal transmission element, signal presentation units and signal recording units.
Sample answer: Discussion should cover the primary sensor, explaining its function and giving examples of primary sensors. Mention that some primary sensors like a liquid-in-glass thermometer are a complete measurement system in themselves. Intelligent instruments also have one or more secondary sensors. These measure the environmental conditions, particularly temperature and pressure, surrounding a measurement system in order to correct the output of primary sensors affected by the environment conditions.Conversion elements are needed in a measurement system where the output variable of a primary transducer is in an inconvenient form and has to be converted to a more convenient form. For instance, the displacement-measuring strain gauge has an output in the form of a varying resistance. The resistance change cannot be easily measured and so it is converted to a change in voltage by a bridge circuit, which is a typical example of a conversion element. In some cases, the primary sensor and variable conversion element are combined, and the combination is known as a transducer. Signal processing elements exist to improve the quality of the output of a measurement system in some way. A very common type of signal processing element is the electronic amplifier, which amplifies the output of the primary transducer or variable conversion element, thus improving the sensitivity and resolution of measurement. This element of a measuring system is particularly important where the primary transducer has a low output.For example, thermocouples have a typical output of only a few millivolts. Other types of signal processing element are those that filter out induced noise and remove mean levels etc. In some devices, signal processing is incorporated into a transducer, which is then known as a transmitter. In addition to a primary sensor, variable conversion element and signal processing element, some measurement systems have one or two other components, firstly to transmit the signal to some remote point and secondly to display or record the signal if it is not fed automatically into a feedback control system. Signal transmission is needed when the observation or application point of the output of a measurement system
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