Electric Circuits Introduction In this lab you will examine how voltage changes in series and parallel circuits. Item Picture Symbol Wires (6) Voltmeter (1) Bulbs (3) (Resistors) Batteries (3) 61
Procedure and Questions Set the digital multimeter dial to 20 V DCV for today s lab. Supplemental Appendix H on the course website illustrates the proper range selector position. When sketching the circuits in Q1 and Q4, use the symbols shown in the Introduction for the various circuit elements: wires, batteries and bulbs. Q1: Wire up a circuit using 2 batteries in series to light 2 bulbs connected in parallel. Sketch the circuit. Q2: (A) Use your voltmeter to measure the voltage across the batteries in Q1, where the wires from the bulbs connect. What is this voltage? (B) Use your voltmeter to measure the voltage across each bulb. What is each voltage? Q3: (A) While both lights are lit, remove one of the light bulbs. What happens to the second light bulb? (B) What is the voltage across the second bulb now? Q4: Wire up a circuit using 2 batteries in parallel to light 2 bulbs connected in series. Sketch the circuit. Q5: (A) Use your voltmeter to measure the voltage across the batteries in Q4, where the wires from the bulbs connect. What is this voltage? (B) Use your voltmeter to measure the voltage across each bulb. What is each voltage? Q6: (A) While both lights are lit, remove one of the light bulbs. What happens to the second light bulb? (B) What is the voltage across the second bulb now? Q7: (A) Which circuit, Q1 or Q4, would cause your batteries to discharge, that is to go dead, the quickest and why? The next 5 questions refer to the circuits shown in the Figures on the last page of the lab. Q8: Build the circuit in Figure 1, using 3 batteries connected in series and 1 bulb. Measure and record the voltage across the batteries and across the bulb. Q9: Build the circuit in Figure 2, using 3 batteries connected in series and 2 bulbs in series. Measure and record the voltage across the batteries and across each bulb. 62
Q10: Build the circuit in Figure 3, using 3 batteries connected in series and 3 bulbs in series. Measure and record the voltage across the batteries and across each bulb. Q11: (A) What trend do you notice in Q8 Q10 with respect to the amount of voltage across each bulb with the addition of bulbs into the circuit? (B) Is the sum of the voltages across the bulbs approximately equal to (within 5%), less than, or more than what is provided by the batteries? Q12: Build the circuit in Figure 4, using 3 batteries connected in series and 2 bulbs in parallel. Measure and record the voltage across the batteries and across each bulb. Q13: Build the circuit in Figure 5, using 3 batteries connected in series and 3 bulbs in parallel. Measure and record the voltage across the batteries and across each bulb. Q14: (A) What trend do you notice in Q8, Q12 and Q13 with respect to the amount of voltage across each bulb with the addition of bulbs into the circuit? (B) Are the voltages across each bulb approximately equal to (within 5%), less than, or more then what is provided by the batteries? Q15: (A) In Figure 6, if the battery voltage is 9.0 V and the voltage across bulb C is 3.0 V, what is the approximate voltage across bulb A? (B) What is the approximate voltage across bulb B? (C) Explain how you came up with your answers. Give the hand-cranked generator at your lab station a few spins with no bulbs connected to it. Pay attention to how easy it is to turn the crank. Next, hook one bulb up to the generator. While your lab partner monitors the voltage across the bulb, crank up the generator so that there is a voltage of approximately 3.0 V. Next, hook 2 bulbs in series up to the generator. While your lab partner monitors the voltage across one bulb (not both), crank up the generator such that you get a voltage of 3.0 V across a single bulb. Q16 (A) Did it require more physical effort to have 2 bulbs burning at the same voltage each as opposed one bulb? (B) What does this imply about the rate electrical energy is converted (i.e., the power) as more resistance is added to a system? Be sure to sign the attendance sheet before you leave class. 63
Figures Needed to Answer Q8 Q15. Figure 1: Q8 Figure 2: Q9 Figure 3: Q10 Figure 4: Q12 Figure 5: Q13 Figure 6: Q15 64
Electric Circuits Data Sheet Q1 s Sketch: Q4 s Sketch: Question # Battery Voltage ( V ) Bulb A Voltage ( V ) Bulb B Voltage ( V ) Bulb C Voltage ( V ) Q8 N/A N/A Q9 N/A Q10 Q12 N/A Q13 65
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Appendix A Extra Credit (5.0 points) Error analysis is one of the most important skills that can be acquired doing lab work. Also note that this extra credit may be turned in at any time throughout the semester. Keep in mind these questions are to help you in recognizing errors in data collection and data analysis. 1) Compare the data you collected in Lab 1, Station 2 to another lab group s or the sample data provided in Appendix I (located on the course website). Under ideal, that is, theoretical conditions, the data would be the same (i.e., 0.32 s for 0.5 m; 0.45 s for 1.0 m and 0.64 s for 2.0 m). List 2 error sources accounting for the timing discrepancies between the data sets. 2) For the timing data for Lab 1, Station 2, assume your 2.0 m height data reads as follows: 0.62 s, 0.54 s, 0.61 s. a. Which data point strikes you as being wrong? b. What would you do as a corrective measure? 3) Using the following data, find the timing data average for each height. At 0.25 m, t 1 = 0.31 s, t 2 = 0.25, t 3 = 0.29 s. At 0.75 m, t 1 = 0.35 s, t 2 = 0.43, t 3 = 0.39 s. At 1.25 m, t 1 = 0.50 s, t 2 = 0.58, t 3 = 0.49 s. a. Make a data table showing above the data and averages. b. For each average, what would be the range for a ± 10% margin of error? c. Does any of your data fall outside this margin of error? If so, which data points do? d. The theoretical timing data for 0.25 m equals 0.23 s, for 0.75 m equals 0.39 s, and for 1.25 m equals 0.51s. How could you make your timing averages closer to these numbers? 4) Assume at Lab 1, Station 4, your lab partner makes the following measurements of a non-metallic cube: volume = 1.7 cm 3 and mass = 32.5 g. Your calculations give you an approximate density of 19.1 g/cm 3, indicating the cube is Uranium. a. What should make you doubt the validity of your answer and why? b. Where do you think the error could have occurred? 5) You are timing a cart down an inclined plane. The cart has a tendency to repeatedly rub against the sides of the plane as it travels. How would this change the timing data and speed? 67
6) During the Inclined Plane experiment, you notice your lab partner giving the cart a little push down the plane. How would this push change the timing data and speed? 7) On a web search engine, type in reaction time test and call up one of the online tests available. Take the test a few times. a. List at least 5 of your results. b. How do these times compare to the average human reaction time of 0.20 s - 0.25 s? c. Finally, give the link to the site. 8) Your lab partner brings a new stopwatch to lab, one that records timing data out to a thousandth of a second (0.001 s). Your lab partner claims this will increase your group s accuracy when collecting timing data, thereby decreasing errors. Explain why this claim is wrong. 9) You and your lab partner are timing a swinging pendulum. Your lab partner reports having taken two shots of NyQuil TM (an alcohol-based cold medication known to cause extreme drowsiness) to help with a wicked cold. Who should be responsible for using the stopwatch during the lab and why? Questions 1, 2, 4, 5, 6, 7, 8 and 9 are worth 0.5 points each. Questions 3 is worth 1.0 point. 68
Appendix B Common Write-Up Mistakes Answering the Lab Manual Questions One of the easier ways to avoid answering a question incorrectly is simply to answer what the question asks. o For example, suppose a question asks what happens to speed as you change some variable in your experiment. When answering this question, be sure to mention speed somewhere in your answer. Do not explain what is happening to the timing data. This is not what the question is asking. Timing data and speed results are not o the same thing, though they are related. Also, if the question uses a word or phrase you are unfamiliar with, ask your lab instructor to clarify the question's meaning or look up the meaning yourself. Do not ignore the word or phrase least end up not providing the correct answer. Use full and complete sentences when answering the questions. A "yes" or "no" only answer means you will receive a zero credit. There has to be some kind of supporting information in your answer. A good idea is to use your data to provide support for your answers. Finally, along the same lines, answering a question with I don t know, I don t care, I guessed, or answers in a similar vein will result in zero credit given for the question. Always include units next to number you write when answering questions. For example, if you write the number "7" on your lab report, your lab instructor has no idea what "7" represents. It could mean anything from 7 meters to 7 joules, and there is no way to tell by number "7" by itself. However, if you wrote "7 m", there is no problem determining you meant 7 meters and nothing else. Data Collection Errors No experiment is 100% perfect and you will notice errors creeping into your data collection. o Some errors, such as systematic errors, are unavoidable, though o they can be minimized. Other errors, such as those due to performing the wrong lab procedure or making a calculation error, are correctable and therefore do not count are errors. Often your lab instructor will indicate when your data is too far from the norm. If your instructor screams in fear after looking at your data, you may want to collect new data. When you go to answer the questions, make sure to explain what errors you 69
are taking into account, and where these errors came from. This way you can avoid losing points, even if your lab data is off. Miscellaneous Always sign the attendance sheet before you leave lab. It is policy not to accept labs without your signature on the attendance sheet. You will be given a zero out of 10 points for lab reports turned in without your signature on the sign-in sheet. 70
Appendix C Graphing Throughout the lab course you will be asked to analyze the data you collect. An easy way to do this is via graphing, which allows you to arrange your data in a manner that is both quick and easy to understand. Consider an experiment in which you roll a ball across a horizontal plane with an initial velocity of 2.0 m/s. You measure the distance the ball travels at 1.0 s intervals. The sample data might look something like this (keeping in mind that the numbers are not exact due to various sources of error such as friction and human timing limitations): Time ( s ) Distance ( m ) 1.0 2.0 2.0 3.9 3.0 5.9 4.0 7.9 5.0 10.1 6.0 11.8 You can construct different types of graphs based on the data. For this course, the 2 most common graphs you will use are the line graph and the bar graph. First, we will review the seven steps for creating a line graph, then the six steps for creating a bar graph. A Line Graph In 7 Steps The line graph drawn for the above data is shown at the end of this section. You may refer to this graph to better understand the following steps. 1. Title: It is easy to read and is placed at the top of the graph. It is in the form of A vs. B, where A is the dependent variable and B is the independent variable. In this example, distance is the dependent variable, since it is dependent on the amount of time passed. Time is the independent variable, since the intervals are pre-determined. The title, in this example, is "Distance vs. Time." 2. X-axis: The horizontal axis is clearly labeled, in this example Time. The independent variable is plotted along the x-axis. 71
3. Y-axis: The vertical axis is clearly labeled, in this example Distance. The dependent variable is plotted along the y-axis. 4. Axis Labels: The names of the dependent and independent variables are written next to each axis. Units in which the dependent and independent variables are given are written in parenthesis under or next to each axis label. 5. Legend: It is a list of the scale factors used in determining the graph axes. It states the relation between the units of the collected data and the squares on the graph paper. It is written off to the side of the graph. The scale factors are determined so the collected data can conveniently fit on the graph paper and the graph takes up the majority of graph paper space. In the example, the scale factor for the x-axis was chosen so every 4 squares = 1 s. For the y-axis, every 1 square = 1 m. 6. Data Points: All data points are plotted on the graph. To plot the first data point, first you move to where 1.0 s is located on the Time axis, then you move up until you meet the line where 2.0 m is located on the Distance axis, placing a mark at that spot. You follow the same procedure for the rest of the data points. 7. Best-Fit Straight Line: This is the line that best represents the average of all your data points. Approximately half of all your data points should lie above the line and half should lie below. Keep in mind when drawing any best-fit line to make sure your data points are distributed equally to either side of it. While some of your data points will lie directly on your best-fit line, not all of them will or even should, for that matter. The points that lie to either side of your best-fit line represent errors that have crept into your experiment. These are expected, so try not to cover them by "fudging" your best-fit line such that all data points lie on the line. You can always explain why your data points do not lie along a perfectly straight line in the lab write-up. A common graphing mistakes is "connecting the dots." Never connect the "dots" on your graph. If you do so, you will lose points on your lab report. 72
Figure 1: An example of a hand-drawn line graph A Bar Graph In 6 Steps The bar graph drawn for the above data is shown at the end of this section. You may refer to this graph to better understand the following steps. 1. Title: It is easy to read and is placed at the top of the graph. It is in the form of A vs. B. The title, in this example, is "Distance vs. Time." 2. X-axis: The horizontal axis is clearly labeled, in this example Time. Your lab manual will tell you what should be placed on the x-axis. 3. Y-axis: The vertical axis is clearly labeled, in this example Distance. Your lab manual will tell you what should be placed on the y-axis. 4. Axis Labels: The names of the variables are written next to each axis. Units in which variables are given are written in parenthesis under or next to each axis label. 73
5. Legend: It is a listing of the scale factors used in determining the graph's axes. It states the relation between the units of the collected data and the squares on the graph paper. It is written on the graph so as not to interfere with any of the bars. The scale factors are determined so the collected data can conveniently fit on the graph paper and the graph takes up the majority of graph paper space. In the example, the scale factor for the x-axis was chosen so every 4 squares = 1 s. For the y-axis, every 1 square = 1 m. 6. Data Points: All data points are plotted on the graph. To plot the first data point, first you move to where 1.0 s is located on the Time axis, then you move up until you meet the line where 2.0 m is located on the Distance axis, making a bar from the x-axis to that spot. Follow the same procedure for the rest of the data points. Figure 2: An example of a hand-drawn bar graph Blank graph paper is available at the back of the lab manual. 74
Appendix D Grade Sheet for Recording Lab Scores This page is to assist you in keeping track of your lab scores. You need a 60% (66 points out of 110 points) in order to pass lab. If you do not pass lab, you will fail the course. Your lecture syllabus will tell you how your lab score is used in determining your final course score. Experiment Points Maximum Possible Points Experiment 1 [1] 10 Experiment 2 10 Experiment 3 10 Experiment 4 10 Experiment 5 [2] 10 Experiment 6 10 Experiment 7 10 Experiment 8 Presentation 15 points max. Paper 15 points max. 30 Experiment 9 10 Make-Up Lab [3] 10 Appendix A: Extra Credit [4] 5 Total 110 Notes [1] 2.0 extra credit points are possible. [2] 3.0 extra credit points are possible. [3] Available only to those who have missed a lab. It cannot be used to replace a low score. [4] Due when the Make-Up Lab Report is due. 75
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