Lab-in-a-Box
Experiment 2: Component Tolerances
Name: ______
Pledge: ______
ID: ______
Date: ______
Procedure (Resistors):
1. Gather fifteen 10 kΩ resistors. What is the color pattern of the bands? Five of these resistors are in the resistor kit and ten more are found in the plastic bag of course-dependent parts. If possible, keep the resistors from the two sources identifiably separate.
2. Read the instruction manual for your multimeter and record the specified accuracy for resistance measurements on the scale that includes 10 kΩ.
3. Select one of the resistors obtained in step 1. Following the procedures outlined in Section 2.5, measure its resistance at least 10 times. Be sure to take notes on your measurement procedure.
4. Calculate the mean and standard deviation of the measurements made in step 3 using Eqs (1) through (3). If you do the calculations manually, show your intermediate results. If you use a spread sheet, a calculator with statistical functions, or some other scientific program such as MATLAB, provide data to verify that you are calculating the unbiased variance.[‡]
5. Compare the results of step 4 with the accuracy of the meter as found in step 2. What conclusions can you draw from these measurements?
6. Is the sample mean found in step 4 within the specified 5% tolerance of the resistor? If not, re-read Section 2.5 carefully for reasons that may explain this observation. If you find a reason, record it here and repeat the experiment starting at step 3.
7. Using Eq (9), calculate the 95% confidence interval for your measure-ment technique. Does this interval include the nominal value of 10 kΩ?
8. Following the procedures outlined in Section 2.5, measure the resistance of each of the resistors. If possible, record the data for the resistors from each source separately.
9. Are any of the measured values outside the specified 5% tolerance of the resistors ? If so, re-read Section 2.5 and if you are unable to find a logical explanation, see your instructor.
10. Calculate the mean, the variance (s2), and the standard deviation (s) of the measured values for the combined sample of all 15 resistors.
11. Calculate the value of t for the combined sample using Eq (10). Find the value of t for a sample size of 15 and 95% probability from the table in Appendix C. Are the measured values of your resistors statistically significantly different from the nominal value of 10 kΩ? Explain.
12. If you have data for the resistors from each source separately, perform the following steps. Otherwise, proceed to step 16.
13. Using Eqs (1) through (3), calculate the mean, the variance (s2), and the standard deviation (s) of the measured values for each group of samples.
14. Calculate the value of t for each sample using Eq (10). Find the value of t for the correct degrees of freedom for each sample and 95% confidence from the table in Appendix C. Are the measured values of your resistors statistically significantly different from the nominal value of 10 kΩ? Explain.
15. Compare the two sources of supply of resistors using Eqs (12) and (13). Are they statistically significantly different? Explain.
Procedure (Capacitors):
16. Gather fourteen 0.1 μF Mylar capacitors. Determine the tolerance of these devices fro their markings.
17. Read the instruction manual for your multimeter and record the specified accuracy for capacitance measurements on the scale that includes 0.1 μF.
18. Following the procedure outlined in Section 2.5, measure the capacitance of the same device at least 10 times. Be sure to remove the capacitor from the DMM and remount it between each measurement.
19. Calculate the mean, the variance, and the standard deviation of the data acquired in step 18. Pay attention to the cautions in step 4.
20. Compare the results of step 19 with the accuracy of the meter as found in step 17. What conclusions can you draw from these measurements?
21. Is the sample mean found in step 19 within the specified tolerance of the capacitor? Explain.
22. Using Eq (9), calculate the 95% confidence interval for your measure-ment technique. Does this interval include the nominal value of 0.1 μF?
23. Following the procedure outlined in Section 2.5, measure the capacitance of each device with the multimeter.
24. Calculate the mean, the variance (s2), and the standard deviation (s) of the measured values. If you do the calculations manually, show your intermediate results. If you use a spread sheet, a calculator with statistical functions, or some other scientific program such as MATLAB, provide data to verify that you are calculating the unbiased variance as described in Step 4 above.
25. Calculate the value of t for these data at the 95% confidence level from the table in Appendix C. Are the measured values of your capacitors statistically significantly different from the nominal value of 0.1 μF? Explain.
26. Using Eq (9), calculate the 95% confidence limits for your measurements of the capacitors. Does this confidence band include the nominal value of 0.1 μF?
27. What may you conclude about the sample of capacitors in your lab kit?
Last Revision: Rev 4.0: 11/21/2006
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[‡] You may easily verify which calculation your calculator or program performs (Excel can do both, depending on the function you select!) by calculating the variance of the three numbers 1, 2 and 3. If the variance is 1.000 you are calculating the (correct) unbiased variance; if it is 0.667, you are calculating the (incorrect) biased variance.