Appendix A Laboratory Experiments A.1 Introduction In this appendix, we illustrate nine experiments that we have used extensively in our laboratory classes. They are designed as the necessary complement to the matters dealt with in the main text and they allow for the practical implementation of the many concepts that we deem students should internalize when attending the lecture classes. The sequence and the content of these experiments have been designed keeping in mind a series of considerations. First, we required that in each laboratory session students should produce quantitative information about the relevant physical quanti- ties, a fundamental requirement for a course aimed at teaching the principles of the measurement science. Second, we devised a learning path whereby students begin by using simple instru- ments and by performing basic data analysis and conclude their laboratory experience exploiting advanced instrumentation and devising rather complex procedures of data handling. In this perspective, we started by using simple analog devices in order to introduce later in the sequence the use of the most modern digital instrumentation and to allow data transfer to a computer for further specialized elaboration. The third consideration is perhaps the most important. We thought that it is impor- tant that students understand that it is never easy to obtain accurate results in exper- imental science. We wanted to make them aware that the measurement process can have by itself an important impact on the measured quantity, and the analog instru- mentation, when still available, can be extremely useful to exemplify this concept in practice. Similarly, we wanted to make them able to minimize the impact of parasitic elements related to cables connecting the measured circuit to the measuring instru- mentation. Finally, we wanted that students learn that there are always variables of influence that can have an important effect on the quantity of interest and that critical thinking is the most effective approach to gain control of this important aspect of experimental science. © Springer International Publishing Switzerland 2016 251 R. Bartiromo and M. De Vincenzi, Electrical Measurements in the Laboratory Practice, Undergraduate Lecture Notes in Physics, DOI 10.1007/978-3-319-31102-9 252 Appendix A: Laboratory Experiments In the following sections, we illustrate the aim of each of these experiments, followed by a list of the necessary equipment. Then we give a plan of action that students should adopt to fulfill the requirement of each experimental session. Students should be required to write a report on each experiment adopting the proper style of a scientific publication. Finally, we give for each experiment a note that can be useful to tutors in the preparation of the experiment and in its illustration to students. We remark that these notes are written for experienced teachers and, therefore, they can turn out to be of little use for most undergraduate students without appropriate help from their tutor. A.2 Experiment: Laboratory Instrumentation and the Measure of Resistance Aim of the experiment: to gain confidence with electrical instrumentation and to learn how to evaluate correctly the effects of averaging on uncertainties. Material available for the experiment: • Analog multimeter • Digital multimeter • 100 resistors with identical nominal value • Cables and connectors Plan of the Experiment Measure the resistance of 100 resistors with identical nominal value. For each resistor, measure the resistance value with both the analog and the digital ohmmeter. For the analog instrument, it is required to interpolate its reading between the divisions of its ruler. Collect the values and their uncertainty in a spreadsheet. Use the data to perform the following tasks. 1. Compare the two averages obtained from data collected with the digital instrument and data collected with the analog meter. 2. Verify the compatibility of these two values taking into account the uncertainties provided by the user manuals of the instruments. 3. Build a histogram of the resistance values measured with the digital instrument. Check compatibility with the nominal value of resistors taking into account its uncertainty as stated by the color code. 4. Build a histogram of the difference between each analog value and the corre- sponding digital measurement. Calculate the estimated standard deviation of the distribution. Discuss the origin of the dispersion. 5. In this experimental session, your colleagues are measuring the same resistors with different instruments. Collect the average values obtained by them and use these data to Appendix A: Laboratory Experiments 253 • obtain a more accurate estimate of the average value of the 100 measured resistances and • verify the compatibility of your analog result with the class of the instrument to assess if a new calibration is needed. Notes to the Tutor In this first experimental session, students must gain confidence with instrumentation and learn how to evaluate the effects of averaging on uncertainties. The tutor will introduce them to the electrical laboratory instrumentation: resistors, and the color code to read their resistance value, solder-less breadboards to mount circuits and cables to connect them to power supplies and measuring instruments. Then he will illustrate the use of measuring instruments, namely an analog and a digital multimeter. For the analog instrument, he will illustrate the use of the mirror for compensation of parallax error and will discuss the need to interpolate the reading between the divisions of the graduated scale. For the digital instrument, he will discuss the two contributions to the uncertainty, namely the calibration factor and the quantization error, and the different nature of their correlations. The tutor should explain that in digital instruments in general, uncertainties of type B due to calibration are different from those due to quantization. These two contributions are not correlated with each other and should be added in quadrature. Students must learn to consult the user manual of each instrument to evaluate features and capabilities, identifying formulas and parameters needed to assess the uncertainty of measurement. They will configure them for use as ohmmeter and control that the instrumental zero is properly set by measuring a short circuit. In the preparation of this experiment, the tutor must choose a nominal value of the resistance such that the nonlinear scale of the analog instrument is used in the low resistance end so that the distance of its divisions is sufficiently wide to allow for a visive interpolation between them. For the execution of the measures, resistors can be mounted in groups of ten on breadboards with ten resistors each. Rotating them among students, one can obtain multiple measurements of the same resistances with different ohmmeters. Each student will measure with both the analog and the digital instrument. By making sure that each student measures at least a hundred resistors, after data collection each student should perform the following analysis: • Calculate and compare the two mean values using digital or analog data. Evaluate the uncertainty on these averages taking into account the correlation between the different components of the uncertainties of the individual measures. After completing this task, students should have understood that, since the experimental uncertainty is strongly correlated, in first approximation the relative uncertainty of the average is equal to the relative uncertainty of the single measurements. • Verify the compatibility of the average values obtained with the two instruments, taking into account the uncertainties supplied by the manufacturers of the instru- ments (type B uncertainties). 254 Appendix A: Laboratory Experiments • Build a histogram of the values of the resistances measured with the digital instru- ment, which usually present a smaller uncertainty. Assess their compatibility with the accuracy of the nominal value of the resistance provided by their manufac- turer, typically 5%. Discussing the shape of the histogram obtained, explain that the resistance of a resistor depends on the setting of the machine that produced it. If care is taken to avoid choosing all resistors from the same batch, the histogram has more than one peak. • Build a histogram of the difference between digital and analog measurement of each resistor and calculate the mean and standard deviation of the estimate. Discuss the shape of the histogram (if well done, it will be a bell curve that resembles a Gaussian) and the origin of the dispersion (reading error manly of the analog instrument, which are random and not correlated, and generally better half of the difference between the divisions on the graduated scale). Students should realize that by visual inspection they could interpolate much better than half the division spacing. In absolute terms, a skilled eye can distinguish a thickness with an uncertainty better than 0.1mm. • Compare the average values obtained by different students to verify that none of the instruments used requires a calibration check. Usually digital instruments maintain calibration over time and the distribution of the observed values falls within the manufacturer’s specifications. Therefore, from these measurements one can get a more accurate estimate of the average resistance using all available values since now they are not correlated. An analysis of the difference in analog measurements