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# HARVARD PHYS 15b - Lab 2

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Phys 15b: Lab 2, Spring 20071REV 0; February 21, 2007Phys 15b: Lab 2: I-V Curves; Voltage DividersDue Friday, March 161, before 12 noon in front of Science Center 301Note that this lab, like Lab 1, is to be done in SC305, at your assigned section times (Thursday, Mar.1 or Mar. 15). There is no lab work to be done in the week of March 5 (and there will be no helplabs), because of the hour exam scheduled for that week.Attachments: LED data sheet; meter schematic.Note: In this experiment, and others, there are questions, set off by the boldface label “Question:”,to be answered in the write-up. Please answer them in your notebook as you go along, with all workshown. Remember that you should include circuit diagrams, discussions, etc in your lab notebookso that someone who had never seen this handout would be able to understand exactly what youdid in the lab. Please present your data in tables that include the units of the measurement, and theuncertainty or error. Also, please make your graphs large (at least half a page), with labeled axesand both horizontal and vertical error bars on your plots.1 Purpose1. To understand the voltage divider2. To understand “bridge” circuits3. To study the I-V characteristic of a light emitting diode4. To study the I-V characteristic of an AA dry cell5. To get some insight into the operation of your VOM as current meter and as voltmeter1Yes, this is a long way off. It’s a two-week lab, and we lose one week to an hour exam, as well.Phys 15b: Lab 2, Spring 200722 Background2.1 The Voltage DividerThe single most important d.c. (“direct current”) circuit configuration is called a voltage divider.It is used to produce a variety of desired voltages from one single source. This is important sincethe obvious alternative way to get a variety of voltages is clumsy and expensive: a “power sup-ply” is required to convert the AC “line” voltage that comes from the wall plug into the DC levelrequired by virtually every instrument. You don’t want to buy many heavy, expensive power sup-plies. Instead, you want to buy a handful of resistors to do the job. Here’s a voltage divider:R2R1VoutVinIFigure 1: A Voltage DividerGiven an input voltage Vin, the output voltage Voutcan be any fraction of Vin, depending upon thevalues of R1and R2. It is easy to find a formula for Voutbeginning with two truths from Purcell, p.151:• the “condition” (no. 3 on p. 151) that the sum of the potential differences around a closed loopmust be zero;• the “condition” (no. 2, often called “Kirchoff’s current law”) that the currents into and out of anode add to zero, so top and bottom currents are equal. It follows thatVin= IR1+ IR2and... I =VinR1+R2, (solving for 1)Finally,Vout= IR2= Vin{R2R1+R2}Depending upon the values of R1and R2, the ratio in curly brackets can vary from 0 to 1 and thevalue of Voutcan vary from 0 to Vin. You will use the circuit twice in this experiment, and manytimes in others. Notice that the ratio of the voltages across the two resistors is simply:V2V1=I∗R2I∗R1=R2R1That is, it is equal to the ratio of the resistors, a straightforward easy-to-remember result that youcan use to design your voltage dividers.Question 1: If you have batteries which give Vin≈ 6V and you want to make a voltage dividerwith Vout≈ 4V , which of your resistors, or combinations of resistors, can you use, and hooked upin what circuit?Phys 15b: Lab 2, Spring 200732.2 The PotentiometerVery often, a device known as a potentiometer, or pot is used to make a voltage dividerwhose outputvoltage can be continuously varied:PotentiometerVoutVinIFigure 2: A “Potentiometer”The pot is made of a length of resistive material (called “cermet,” in our case) with leads connectedto its ends and with a third lead connected to a slider that can move along the resistor.As the slider is moved from one end to the other, all ratios of R2/R1are accessible, and all values ofoutput voltage from 0 to Vin. Thus a pot can be used with a fixed voltage source (e.g. a battery) toprovide a continuouslyvariable voltage source (although a low quality one, as we shall: low qualityin the sense that the output voltage will vary with the “load” that it drives). We will use the 100 Ωpot in this way many times throughout the course. Most knobs on electronic equipment turn pots.Question 2: (How to burn out a pot) Consider what can happen if you connect a “short circuit”(e.g. a clip lead, or a stray wire) across the Voutterminals of the pot. Suppose Vin=3V , and thepot resistance is 100 ohms, with a maximum allowable power dissipation of 0.5 watts (you will usesuch a pot in this experiment). Now let’s look at two cases: one safe, the other not. Suppose the potis initially set for Vout/Vin=0.5, and then you short circuit Vout. Calculate the current that willflow in the circuit. You can use this current to calculate the power that will be dissipated by the pot.Or you can calculate the power dissipation using, instead the alternative power formula, P =V2R,where R is the segment of the pot that is carrying current. You can see how to get into trouble if youchange your assumption about the pot setting: suppose the pot was set to Vout/Vin=0.9. Now, ifyou repeat your calculations, you can see that your pot is not short-circuit proof.2.3 A “bridge” circuitThe “bridge” circuit can be used to make very sensitive measurements given relatively crude mea-suring tools. You may recall that it was hard to use your meter to measure resistors with large values.A bridge circuit would have allowed you to make a much more accurate measurement. Bridge cir-cuits are widely used in measuring devices, like thermometers. The basic idea is that you can geta much more accurate measurement by comparing the difference between an unknown thing anda known thing of nearly the same size, than by simply trying to measure the unknown thing itself.The circuit below is an example of a bridge circuit. It is designed to measure very small changes inR2It compares the voltage at A to the voltage at B by measuring the voltage difference betweenpoints A and B.Phys 15b: Lab 2, Spring 20074R2R1Vout1VinVVout2ABpotFigure 3: A differential measurement can improve resolutionYou can adjust the pot to make this difference, Vout1− Vout2, small, so that you can then measureit on the voltmeter’s most sensitive scale. Now, if the resistance R2changes, the correspondingchange in Vout1will be measured very accurately.

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