1 - Ohm's Law (updated 3/4/14) Goals The purpose of this laboratory is to observe the relationship between voltage drop across (not through), and current through (not across), certain electrical components. You will gain increased familiarity with connecting circuits and with voltmeters (measuring voltage across a circuit component) and ammeters (measuring current through a circuit component). You will investigate both ohmic (carbon resistor) and non-ohmic components (incandescent flashlight bulb, silicon diode). You can get a pdf version of this manual here. You should make a hardcopy printout of this Lab 4 manual and take it, your laboratory notebook, and your calculator with you to lab. There is no worksheet for this experiment. Record all your data in your laboratory notebook. Boldfaced questions and comments This Lab 4 manual has a number of boldfaced questions. It is expected that each student, working independently, will answer all of the boldfaced questions in the written report. They should not be put in a list at the beginning or end of the report. Rather, they should be inserted where they belong in the narrative of the report. Independently means that the student has not discussed the answer with other student(s). The only exceptions are boldfaced questions that have to do with experimental procedure; we expect student lab partners will do such procedural boldfaced questions together. This Lab manual has NO procedural boldfaced questions. To make it easier for both the students doing the work (and the TAs grading it), the boldfaced questions and comments are numbered. When answering each boldfaced item in the written report, the student should put the number for that item in parentheses immediately before the answer. That will serve to identify easily for both the student and the TA what boldfaced question is being addressed. Remember: Don't put them in a list. Place each answer to a boldfaced question where it belongs in the narrative of the report. Introduction To help you in doing this laboratory, you should review relevant material in a textbook. One choice is Chap. 27, DC Circuits, of G4: D. Giancolli, PHYSICS for Scientists & Engineers, 4th ed. If you don't have a copy, you'll find one bolted to a table in the Help Room, A-129, physics building. Another choice is Chap. 23, Circuits, of KJF2: Knight, Jones, and Field, College Physics: A Strategic Approach, 2nd ed. If you don't have a copy, you'll find one bolted to a table in the (other) Help Room, A-129 physics building. The Math/Physics Library on the C level of the physics building has a few copies of both textbooks on closed reserve. You should also use the active links in the online version of this Lab 4 manual to view certain material on the internet. For V being the voltage drop [units: volt (symbol V) equal to Joule/Coulomb, J/C] across a particular component and I being the current through it [units: ampere (symbol A) equal to Coulomb/second, C/s], Ohm's Law is R = V I. (4.1) Equation (4.1) is often restated as V = IR or I = V/R. The current-voltage (I-V) characteristic (active link here) is the graphical representation of the dependence of I on V. Figure 1 shows how the characteristic curve for a two-terminal device is measured. Fig. 1 is just below here
2 A power supply provides current I at whatever voltage as long as that voltage is within the limits specified specified for that power supply is needed to drive that current through the circuit connected to its two output terminals. An ammeter, always in series never in parallel, is used to measure I. The resistance of the ammeter is small. The current I then passes through the device under test (DUT), which is in series with the power supply and ammeter. A voltmeter, always in parallel with the DUT, never in series, measures the voltage drop V across the DUT. The resistance of the voltmeter is large. Notice that all four devices in Fig. 1 power supply, ammeter, voltmeter, and DUT are two-terminal devices: each device has one input terminal and one output terminal. The whole circuit in Fig. 1 can be called a series-parallel circuit because it has three elements in series and one in parallel. Figure 2 shows I-V characteristic curves for four different devices. Fig. 2 (freely licensed from the Wikimedia Commons) is just below here We can learn much from the four panels in Fig. 2. The first, second, and fourth panel have linear I-V characteristics. Are they all ohmic? No; only the first two are. Though it is sometimes stated that an ohmic component (one that obey's Ohm's Law) has a resistance that is independent of applied voltage, that's a bit simplistic. The fourth panel approximates the behavior of a battery, which is an active device: it is a source of current for which the voltage across it varies with the amount of current it is supplying. As you well know, it is also a perishable device that wears out with use and age (even rechargeable batteries!). If we used a battery as a DUT in a circuit such as Fig. 1, the power supply would have to be able to be a sink of current, i.e., it would have to be able to have current from another source, the battery, flow into it. We will not do that in this lab. The third component, a diode, has a nonlinear I-V characteristic. It is also polar, which means that its I-V characteristic depends on the polarity of the voltage across it, i.e., which of its two terminals is more positive than the other.
3 The first two I-V characterisics are for (ideal) resistors. From Eq. (4.1), the slope of a linear I vs. V plot that passes through the origin, (0,0), is G =1/R, i.e., inverse resistance, which is often called conductance. The unit of resistance is the ohm (symbol Ω, which is an upper-case Greek omega). The unit of conductance is usually called the mho (ohm spelled backwards!) even though the official SI unit for it is the siemens (symbol S), which is sometimes defined as Ω 1. (Tending towards the ridiculous the symbol for the mho is sometimes written as an inverted upper-case Greek omega.) (1) In the first and second panels of Fig. 2, how do you know that the first one is a large resistance and the second one is a small resistance? (2) In the third panel in Fig. 2, for I and V both positive (the first quadrant of the plot), does the resistance increase or decrease as V increases? (3) In the third panel of Fig. 3, for I and V both negative (the third quadrant of the plot), is the resistance large or small? Does it vary appreciably as V goes from small negative values to large negative values? Real, as opposed to ideal, resistors are manufactured in a variety of ways. Each deviates from ideal (ohmic) behavior to some extent. If you want to learn more about real resistors, go to this link. The "color code" on resistors A color code that uses colored bands is used to identify the resistance R and tolerance of most commercial resistors, including the ones you will use in this lab. The colored bands are printed on the outside (usually) cylindrical body of the resistor. Since you will need to decode the color code on each of your resistors, go to this color code link to learn how. Starting at one end of the cylindrical body (you have to know which end to start at!), a few of the bands code the value in ohms of the resistance with a power-of-ten multiplier being one of the bands. Another band after them is used to code the tolerance, which specifies by how many percent the actual resistance of that resistor may deviate from its nominal, color-coded value. Since it's a color code, it makes little sense to embed a figure of it here because most PHY 134 students work from the pdf hardcopy file of the lab manual, and usually they print it out on a black-and-white printer. We assume that when you come to lab you will already be familiar with how to decipher the color code on resistors. Your TA will review it but only very briefly. You will use a circuit like Fig. 1 to perform measurements of I-V characteristics for various ohmic and non-ohmic components. Equipment Power supply, Circuit board Ammeter Voltmeter Red and black test leads (wires with banana plugs) Alligator clips Fig. 3 is just below here
4 Figure 3 shows the Lambda model LL-902-0V power supply you will use. The power switch turns it on and off. The meter switch determines whether the moving-needle meter is reading voltage or current. The left-most black knob is a coarse adjustment for the voltage output, with clockwise (CW) increasing it and counter-clockwise (CCW) decreasing it. The middle black knob is a fine voltage adjustment. The right-most black knob labeled current adj. determines the maximum amount of current the power supply will put out. At full CCW it will (should not) put out any current, which means the power supply will be useless that way. You have to turn that knob CW by some amount to get enough current for your particular measurement. The advantage of using that knob is that you can set it to limit how much current can be supplied, which is useful for protecting a delicate circuit from damage by too much current. An example is the incandescent light bulb invented/developed by Thomas Edison; you will use one in this Lab. You do NOT want to burn out its filament because then it's no longer a light bulb, and, therefore, no longer useful for this Lab! The red, white, and black terminals on the righthand side (banana sockets) are for its output. Red is positive (+) and black is negative (-). White, which you will not use in this lab, is for ground. The maximum specified voltage for this power supply is 20 V; the maximum specified current is 0.65 A. (4) With power P = VI, what is the maximum power that this power supply is specified to be able to supply? Justify your quantitative answer and make sure you include the correct units. Fig. 4 is just below here
5 Figure 4 shows two ammeters. The one on the left is set for the 0.2 A range; the one on the right is set for the 2 A range. Note that going from one range to the other moves the decimal point. (5) What is the smallest amount of current that the lefthand meter can show? What is the smallest amount of current that the righthand meter can show? Justify both quantitative answers and make sure you include the correct units. The red banana socket is positive (+), which means current flowing into it will make the reading be positive, which means the LCD display does not show a sign. If current is flowing into the black banana socket (-), which means it's flowing out of the red (+) positive banana socket the LCD display will show a negative sign. If the meter is displaying only 1 or only 1 in the most significant (leftmost) digit, it is overranged. That means the current is larger than the largest value that can be displayed on the range it's on. Fig. 5 is just below here Figure 5 shows a voltmeter. It has four voltage ranges, 0.2 V, 2 V, 20 V, and 200 V. The desired one is chosen by moving the rotary switch to the proper position. In the figure it is on the 2 V range. The red banana socket is positive (+), which means if the voltage there is higher than at the black (-) banana socket, the reading will be positive, which means the LCD display does not show a sign. If the voltage at the red banana socket is more negative than at the black banana socket, the LCD display will show a negative sign. If the meter is displaying only 1 or only 1 in the most significant (leftmost) digit, it is overranged. That means the voltage is larger than the largest value that can be displayed on the range it's on. When there is no voltage being measured, as is the case in the figure, the actual voltage is very close to zero, and the LCD display may indicate a negative zero! (6) What is the smallest voltage V that the voltmeter can read on the 2 V range? Justify your quantitative answer and make sure you include the correct units. Fig. 7 is just below here
6 Figure 7 shows the board with 6 components on it: 4 color-coded resistors, one flashlight bulb (the one on your board may look a bit different from the one in the figure), and one silicon diode. Note that each component is a 2-terminal device with each of its leads captured between two brass nuts on the vertical brass studs. Make your electrical connections to the component of interest by using an alligator clip at the end of a test lead to grab onto the correct brass stud. (7) Resistor R3 (at the top) has color code brown-black-red-silver. What is its nominal, color-coded resistance in ohms? What is its tolerance in percent? Justify your quantitative answers. Method Fig. 7 is just below here
7 Figure 7 shows a completely wired setup doing an I-V measurement on resistor R1. Note that the power supply meter switch is on voltage, and its needle indicates around 7 to 8 V. A red test lead is connected to its red banana socket and the red banana socket (+ input) on the ammeter, which is on the 0.2 A range. It is indicating a current I = 0.035 A. (8) Because of the limited number of digits on the LCD display, what is the minimum uncertainty I in that current? Justify your quantitative answer and include the correct units. Another red test lead goes from the black banana socket on the ammeter to one side of R1. A red test lead is used because we're still on the upstream positive end of the circuit. Two black test leads go from the other terminal of R1, one to the black banana socket on the power supply (to complete that circuit) and the other to the black banana socket (- input) of the voltmeter. The red (+ input) of the voltmeter is connected with a red test lead to the positive, upstream side of R1. Do you see the logic in the way the red and black test leads are being used? The voltmeter, which is on the 20 V range, is indicating a voltage of 7.67 V. (9) Because of the limited number of digits on the LCD display, what is the minimum uncertainty V in that indicated voltage? Justify your quantitative answer and include the correct units. (10) Given the indicated I and V on the two meters, what is the resistance R1? Given the uncertainties from (8) and (9), what is the uncertainty in R1? Justify your quantitative answers and include the correct units. (11) WARNING: What's given next in this boldfaced question is hypothetical; it should not influence the calculations you did for previous boldfaced questions. Suppose that the zero on the ammeter in Fig. 7 is incorrect such that the current value being displayed in the figure is 2 ma higher than its actual, true value. Suppose that the zero on the volmeter in Fig. 7 is incorrect such that the voltage value being displayed in the figure is 20 mv lower than its actual, true value. With this additional knowledge about the displayed current and voltage readings, what will the calculated, actual value of R1 become? (Don't worry about propagating any uncertainties.) Justify your quantitative answer and include the correct units. (12) What name is given to the kind of error caused by the incorrect zero settings of the meters in question (11)? All the measurements you will make will use a setup similar to Fig. 7.
8 Procedure Part 1 (If you are working with a partner, each one of you MUST choose a DIFFERENT resistor and do all work independently) Using the setup in Fig. 7, for one of the resistors on your board measure the current for at least 5 values of voltage. Make a sketch of your setup in your laboratory notebook and record your data (these and all subsequent data) in properly labeled, neat table(s) in your laboratory notebook. For the chosen resistor, decode its color code and write in your laboratory notebook what the colored bands are, what the nominal resistance is based on them, and what the specified tolerance is. Make a plot of I vs. V from your data. Make sure you have error bars on each data point. Use the graphical max-min method to find the conductance G and its uncertainty G, both with the proper units. From those results find the resistance R and its uncertainty R, both with the proper units. (13) Is your measured value of R consistent with the nominal value you got from decoding the colored bands? Part 2 (If you are working with a partner, do ONLY the measurements together) Repeat the measurement procedure from Part 1 only now with the flashlight bulb in place of the resistor. Also increase the number of data points to 10. Make most of your measurements below the voltage and current needed to make the bulb glow brightly, but for half of them the bulb should be visibly glowing. Make a plot of I vs. V from your data. Make sure you have error bars on each data point. (14) How does the I-V characteristic of the flashlight bulb differ from that of the resistor? Explain the reason for any differences you describe. Part 3 (If you are working with a partner, do ONLY the measurements together) Repeat Part 2 only now with the silicon diode. Since, as was noted early on in this Lab 4 manual, the diode is a polar device, you must take data for both polarities. This means that you must take a series of data for one end of the diode positive, and you must take another series of data for the other end of the diode positive. Do at least 5 measurements for each polarity. Make a plot of I vs. V from your data. Make sure you have error bars on each data point. (15) Is the I-V characteristic of your diode similar/different from that shown for a diode in Fig. 2? Don't just say it's the same or it's different. Describe carefully what you see. Grading of this lab, Lab 4 - Ohm's Law, in PHY 134 You will write and submit a report for this lab that will be graded by your lab TA on a scale of 0 to 100. Though you should not turn in your laboratory notebook, you should base your written report on what was recorded there during your in-lab work and subsequent after-lab (further) analysis and thinking about your results. You will find it helpful to use the (clickable-link) document that is the new, revised version 2.01: How to Construct and Present a Good Lab Report - Do's and Do Not's ver. 2.01.pdf (23 Feb 2014) You must 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 7. Boldface Questions (25), which carries a weight of 25 points, includes these: a. Answer all boldface questions and requests for comments to be made in the lab manual. b. Must be distributed throughout the `narrative' of the report (a serial list of answers is NOT allowed)
9 Though these boldface questions are important, section items 1 through 6 carry 3/4 of the point total for the report. Make sure your report addresses all 7 items in the document! Your report must include 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 are instructed to (or just want to) submit something that's in your laboratory notebook, you must make a high-quality photocopy of it and include that in your report. Please pay special attention to the final entry in the Do/Not Do document: 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 4 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 4 - Ohm's Law 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 4 and did the in-lab work for Lab 4. 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 4 - Ohm's Law (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 and SINGLE, ABSOLUTE deadline Submit your package to the proper mailbox bin in room A-129 of the physics building by the special deadline given below. The proper bin is the one for your PHY 134.L## lab section. See the active link on the homepage of the PHY 134 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! Because of Spring Break during 17-21 March, there will be ONE, absolute deadline for all PHY 134 lab sections:
10 noon, Monday, 24 March. AFTER THAT TIME, IT WILL NOT BE ACCEPTED, WHICH MEANS IT WILL EARN YOU ZERO POINTS.