PHY 134 Lab 3 - Capacitors

1 PHY 134 Lab 3 - Capacitors (updated 2/13/14) The goal of this experiment is to determine the capacitance of an unknown capacitor by observing the change in potential difference between its plates when, after being initially charged, it is connected in parallel with a known capacitor. You will also study the behavior of capacitors connected in series. Preparation for this Lab If you took PHY 132 in a previous semester, you already covered the topic capacitors in class. If you are taking PHY 132 this semester, you should have already covered it, but because of cancellations of classes this semester on account of weather, you may not have covered capacitors before doing this Lab. To prepare for this Lab 3, then, you should either review or read ahead Sections 24-1 through 24-3 on capacitors in the textbook for PHY 132, D. Giancoli, PHYSICS for Scientists and Engineers, 4th ed. (G4). If you don't have a copy, one is bolted to a table in the Help Room, A-129, physics building. A few copies of this book should be on closed reserve in the Math/Physics Library, C level, physics building. By noon, Friday, 14 February, you will be able to a pdf version of this manual here. Until then prepare yourself with this online version of the Lab 3 manual. You should always start with the online version of a Lab manual. You should make a hardcopy printout of this Lab 3 manual and take it, your laboratory notebook, and your calculator with you to lab. (There is no worksheet for Lab 3. Instead, you will record all your data and observations in your own laboratory notebook.) Numbered boldfaced questions This Lab 3 has numbered, boldfaced questions and instructions. We expect you to answer/follow each of the boldfaced questions/instructions in your report submitted for grading. You SHOULD put each one in the part of the report narrative where it belongs. You should NOT just make of list of them at the beginning or end of your report because then they will be out of context. Learn to craft a good narrative flow in reporting scientific results. The quality of your written responses to the boldfaced questions/instructions will influence the grade you get on the report. Each student, working independently, is expected to answer all the boldfaced questions in the written report. Independently means that the student has not discussed the answer with any other person besides the lab TA. The only exceptions, for some Labs, are boldfaced questions that have to do with experimental procedure, e.g., determining how to measure a particular length or mass or voltage, or some other experimental quantity as precisely as possible. None of the boldfaced questions for Lab 3 is procedural, so you must answer all of them independently.. Equipment Oscilloscope (you should review what you learned about the oscilloscope in Lab 2) Unknown capacitor C 1 Capacitor box to provide C 2 in 1 μf (one microfarad) steps between 0-10 μf Double-pole double-throw (DPDT) switch test leads with banana plugs at each end alligator clips (their tube ends slide over the banana plugs; their teeth grip a terminal) Dry cell with potential difference (voltage) V 0 Figure 1 shows the same closeup picture of an oscilloscope you had for Lab 2. It may be the same model as the one you will use or it may be a slightly different model that looks nearly the same. It doesn't make any difference which oscilloscope you actually use during the lab. What's important is that you use it correctly. Note that the two (vertical) inputs are labeled CH1X. and CH2Y in Fig. 1. Just pay attention to the label CH1, which is the channel you will be using in this experiment. Note in Fig. 1 that the 3-position lever switch to the left of the VOLTS/DIV knob for CH1 is set to AC. This means AC coupling, which is what you do NOT want for this experiment. This places a capacitor (inside the oscilloscope) in series with the signal entering CH1, and this capacitor blocks the DC value, which is what you want to measure. Therefore, move the lever switch for CH1 to DC, the lowest position. Make sure the VERT MODE lever switch is on CH1 (the top-most position), just as it's shown in Fig. 1. Also make sure that the red VAR knob for CH1 (do the same for CH2, also) is full clockwise, the calibrated position as you learned in Lab 1. While you're at it, make sure the VAR SWEEP knob is also full clockwise, and make sure that the white X-Y switch is out so that the oscilloscope is not in the X-Y mode of operation. (You used that mode to see the Lissajous figures in Lab 1.) Rule of thumb for using oscilloscopes: Always use DC coupling unless you have a specific reason not to! Figure 1 is just below here

2 Figure 2 shows two capacitor boxes. Your box will be one type or another, but don't worry about which type. They're functionally equivalent so it doesn't make any difference which one you have. Each one has two banana sockets for making connections to its two plates and one knob on a rotary switch that selects the value of C 2. In Fig. 2, each knob is set for 1 μf (one microfarad). Figure 2 is just below here Figure 3 shows the unknown capacitor C 1. You know it's a capacitor, but you don't know its value. That's why you're going to measure it! There are two terminals at the top with each one connected to one of the plates inside. (You can see that each terminal has two metal prongs sticking out; which prong you connect to (with an alligator clip at the end of a test lead ) at a given terminal is not important.) Figure 3 is just below here

3 Method You need to read the sentences in this section carefully. Think about their meanings. Ponder the numbered, boldfaced questions and suggestions because you will need to answer them / comment on them in your written report. In Part I, a capacitor C 1 is charged to potential V 0 by using a double-pole-double-throw (DPDT) switch (learn about electrical switches here) to connect one of its two ends (terminals) to one terminal of a dry cell battery and its other end (terminal) to the other terminal of the battery. Colloquially, but perhaps with some confusion, this is frequently called connecting the capacitor across the battery. (1) Is the part of the circuit in Fig. 5 consisting of just the battery and the capacitor C 1 a series circuit? Or is it a parallel circuit? Could it be both? (2) What makes a circuit a series circuit? (3) What makes a circuit a parallel circuit? (4) What about the oscilloscope in Fig. 5? Is it in a parallel circuit? in a series circuit? with what circuit element(s)? Think carefully about how you will answer these questions. The battery is then disconnected, and an initially uncharged capacitor C 2 is connected (by moving the handle on the DPDT switch to the other position) to C 1 as follows: one of the two ends (terminals) of one capacitor is connected to one of the two ends (terminals) of the other capacitor, and the two other ends (terminals) are connected to each other. Note that this makes the capacitor-capacitor circuit in Fig. 6. (5) Is this capacitor-capacitor circuit a series circuit? a parallel circuit? Could it be both? Charge will flow from C 1 to C 2 until the potential differences across the two capacitors equalize. (6) Why does this happen? You can think of the two capacitors as one equivalent capacitor C eq. (7) How does one determine what C eq is? Express C eq in terms of C 1 and C 2. The voltage V across the two capacitors is given by: V = V 0 C 1 /( C 1 + C 2 ) (1) Derive Eq. (1) in your written report. Rearranging Eq. (1) gives V 0 / V = C 2 / C 1 + 1 (2) C 2 is an adjustable capacitor. As C 2 is changed, the final voltage V will vary according to Eqs. (1) and (2). In Part II, a similar procedure using the double-pole-double-throw (DPDT) switch changes the circuit the two capacitors are in. (8) With the DPDT switch in position 1, Fig. 8., can there be a non-zero voltage across C 2? You must explain your answer. (9) In Fig. 8 can there be a non-zero voltage across C 1? You must explain your answer. When the DPDT switch is moved to position 2, Fig. 9, (10) how is the circuit changed from that in Fig. 8? You may intitially find the questions asked above to be puzzling. We expect that. In thinking about them, make sure you're aware that in all figures below, there is more than just capacitors and just capacitors and a battery and a DPDT switch in the electrical circuits. There is also a measuring instrument the oscilloscope! that must become part of the circuit for you to be able to measure the voltage differences that show you what's going on. Don't forget that some of the figures do NOT show the DPDT switch. Instead one figure shows you the circuit that's created for one position of the DPDT switch handle; a second figure shows you the circuit that's created for the other position of the DPDT switch handle. Procedure

4 I. Capacitors in Parallel Figure 4 is just below here C 1 is a fixed capacitor whose capacitance is to be measured. C 2 is a capacitance box with capacitance variable from 0 to 10 microfarads ( μf ) in 1 μf steps. With the DPDT switch in position (1), C 2 is discharged and out of the circuit and C 1 is charged to the voltage of the battery V 0 and in the circuit. This voltage can be read on the oscilloscope, in the same way as the battery voltage was measured in Lab 2. Figure 5 is just below here With the DPDT switch in position (2), the battery is disconnected, C 1 and C 2 are connected in parallel, and the voltage across the parallel combination can be read on the oscilloscope. Figure 6 is just below here

5 1. Connect the circuit as shown in Figure 4. 2. Move the DPDT switch to position (1) to discharge C 2 and charge C 1. Then move the DPDT switch to position (2) and record the voltage V immediately appearing on the oscilloscope. This voltage will decay to zero as time passes; its value immediately after the DPDT switch is thrown is what you must record. Repeat the measurements several times so that you can estimate the uncertainty in this voltage. (11) Why does the voltage decay? 3. Repeat the above procedure using at least 5 other values of C 2. For each value of C 2 you should have a value of V and an estimate of the uncertainty V in its value. 4. In-lab work: Make a plot of V 0 /V vs. C 2 by hand in your laboratory notebook. Determine C 1 (by hand), the unknown capacitance, from this byhand plot by referring to Eq. (2). Estimate the uncertainty C 1 (by hand) in your value of C 1 (by hand). (12) What must you get from a plot of V 0 /V vs. C 2, which should be linear, to determine C 1 (by hand)? A high-quality photocopy of your by-hand plot must be included in your written report. The original by-hand plot must remain in your laboratory notebook. 5. After-lab work: Make a plot of V 0 /V vs. C 2 using this active link to a handy plotting tool that is in the PHY 134 Navigation area of the PHY 134 lab course wiki. Determine C 1 (plotting tool), the unknown capacitance, from this plotting-tool plot by referring to Eq. (2). Estimate the uncertainty C 1 (plotting tool) in your value of C 1 (plotting tool). (13) What must you get from a plot of V 0 /V vs. C 2, which should be linear, to determine C 1 (plotting tool)? A printout of your plotting-tool plot must be included in your written report. The plotting tool contains a feature that allows you to email the plot to yourself. Make a second printout of the plotting-tool plot and staple or tape that permanently into your laboratory notebook. (14) Are the two values C 1 (by hand) and C 1 (plotting tool) consistent? You must justify your answer. How do you determine if two values are consistent? II. Capacitors in Series Figure 7 is just below here

6 In this arrangement, DPDT switch in position 1, two capacitors connected in series are initially uncharged. This makes the circuit like that in Fig. 8. Figure 8 is just below here When the DPDT switch is thrown to position (2), the series combination is connected to a potential difference V 0 and the oscilloscope measures the voltage across C 1. The circuit, therefore, is as shown in Fig. 9. Figure 9 is just below here 1. Connect the circuit as shown in Fig. 7. 2. Set C 2 to 5 μf, flip the DPDT switch from position (1) to position (2), and record the voltage V 1 appearing across C 1 immediately after switching.

7 Repeat the measurement a few times to get a good estimate of its uncertainty. Now change the position of the oscilloscope leads so that they measure the voltage V 2 appearing across C 2 immediately after switching. (We don't show you a figure for this, but by now you shouldn't need another one!) Follow the same procedure as with C 1. 3. (14) Derive an equation giving V 1 as a function of C 1, C 2, and V 0 and an equation giving V 2 as a function of C 1, C 2, and V 0. 4. (15) Using the value for C 1 obtained in Part I, does your equation correctly predict the observed voltages? You must justify your answer. 5. (16) In this circuit, what is the relationship between V 1, V 2, and V 0? Grading of this lab, Lab 3 - Capacitors, in PHY 134 You will write and submit a report for that will be graded by your lab TA on a scale of 0 to 100. You will find it helpful to use the (clickable-link) document Writing a Laboratory Report in PHY 133 and PHY 134: What to Do and What Not to Do. We strongly urge you to read this document carefully, do what is says to do, and do not do what it says not do do. Pay special attention to the suggestions for point values for the various sections of your report. You obviously want to think hard about the ones that carry the most weight. Note that the section that carries a weight of [35] includes this: answer all boldface questions and requests for comments to be made in the lab manual. Make sure your report includes whatever graphs, derivations, and other items or tasks you've been instructed to make or do. Unless a Lab manual explicitly says otherwise, during the semester the originals of all by hand graphs must be done on the graph paper side of a page in your permanent laboratory notebook. All laboratory notebook pages must remain there; they are NOT to be ripped out and submitted. If you need to submit something that's in your laboratory notebook, make a high-quality photocopy of it and include that in your report. In the Do/Not Do document referenced three paragraphs above, please pay special attention to its final entry: Do NOT plagiarize! All work presented in your written report should be your own work. Assuming you had an in-lab partner (but no more than one: no triples!), you and your partner did the in-lab work together, and you should have shared equally in it. The written report, however, will have your name as its author, and you must do it alone. This means that you made the graphs, did the calculations, did the derivations, answered/responded to the relevant boldface areas of the Lab 3 manual, and did the rest of the work that's in the report with your name on it. If you seek help from anyone beside your TA on analyzing your data or writing your report, or if you give such help to another student asking you for it, when this is discovered, you should expect to be reported to the Academic Judiciary. Please do NOT let this happen to you. It has happened in previous semesters. Your grade of up to 100 points is subject to the late-to-lab penalty and/or the late-submittal penalty: both are specified on the PHY 134 lab course wiki and are in effect. Please make sure you do not cause yourself be penalized. The "package" you submit for Lab 3 - Capacitors You must submit all your written work as a package by the deadline (see the next section) that applies to your PHY 134.L## lab section. It's a package because you must staple together all the submitted materials. If you need a heavy duty stapler to keep your package together, make sure you know where to find one before the deadline! The package will be worth 100 points. Expect your TA to take into account how diligently and well you prepared for Lab 3 and did the in-lab work for Lab 3. All that, of course, will affect the quality of your written report and the rest of the package. You will need a cover page for your package. This must include your full name, your ID number, the course and section number PHY 134.L## (where you fill in your section number in place of the ##), the full name of your TA, the full name of your lab partner (if you had one), the title of the Lab, viz., PHY 134 Lab 3 - Capacitors (Spring 2014), AND the date and exact time at which you put your package into the proper bin. Write that date and time by hand on your cover page just before you put the package in the bin. Do NOT even think of writing a date and time earlier than the actual date and time of submittal into the bin. Anyone caught doing this will be reported to the Academic Judiciary. This information on your package will identify it as YOUR PACKAGE in case something goes wrong when/after you submit it. Make a photocopy of everything in your package BEFORE you submit it. This will protect you in case something really DOES go wrong. Each Lab TA has been instructed by Prof. Koch to monitor carefully which packages are submitted before the full-creditworthy deadline and before the < 24 hour late deadline and after then. As you know, if you attempt to submit your work > 24 hours after the deadline, it will not be accepted. At that point it will get you zero credit. The only exception to this is if you worked out BEFORE the deadline with your TA a special exception to the policy. You will have to have a good, documentable reason for requesting such an exception. I need more time. is not such a reason. Submittal details, deadlines, and late-submittal penalties Make sure your full name, ID number, PHY 133.L## lab section (put in the correct numbers in place of the ## symbols), and the name of your TA is on the front cover of your written report package. Submit your package to the proper mailbox bin in room A-129 of the physics building by the following deadlines below. The proper bin is the one for your PHY 133.L## lab section. See the active link on the homepage of the PHY 133 lab course wiki for how to find your proper bin. If you submit your package to the wrong bin, you may well receive a late-submittal penalty. Don't let this happen to you!

8 for all lab sections meeting on Monday: by noon, Thursday, 20 February. After that it is late until noon Friday, 21 February, and your point score will be reduced by 50%. AFTER THAT TIME, IT WILL NOT BE ACCEPTED, WHICH MEANS IT WILL EARN YOU ZERO POINTS. for all lab sections meeting on Tuesday: by noon, Friday, 21 February. After that it is late until noon, Monday, 24 February, and your point score will be reduced by 50%. AFTER THAT TIME, IT WILL NOT BE ACCEPTED, WHICH MEANS IT WILL EARN YOU ZERO POINTS. for all lab sections meeting on Wednesday: by noon, Monday, 24 February. After that it is late until noon, Tuesday, 25 February, and your point score will be reduced by 50%. AFTER THAT TIME, IT WILL NOT BE ACCEPTED, WHICH MEANS IT WILL EARN YOU ZERO POINTS. for all lab sections meeting on Thursday: by noon, Monday, 24 February. After that it is late until noon, Tuesday, 25 February, and your point score will be reduced by 50%. AFTER THAT TIME, IT WILL NOT BE ACCEPTED, WHICH MEANS IT WILL EARN YOU ZERO POINTS. lab3.txt Last modified: 2014/02/13 13:35 by pmkoch