You will set up the following circuits with two \\(1.5\\:\\rm{V}\\) batteries connected in series to produce an approximate \\(3.0\\:\\rm{V}\\) source.\u00a0\u00a0 Use the smaller light bulb that came in your In Lab Kit.\u00a0 This exercise we will not be measuring voltage nor current and thus not calculating the power dissipated by the bulb.\u00a0 Instead you will give qualitative comparisons of how bulb brightness differs between configurations. Think about how you want to qualify the brightness.\u00a0 You may use terms like brightest, very bright, dim, etc.\u00a0 How you qualify the brightness is up to you.\u00a0 Then try to explain why<\/em> you think the bulb is bright or dim in terms of the relative amount of voltage drop across and<\/em> the relative amount of current through each of the elements in each circuit.\u00a0 Record your observations and explanations in the table below (this table is reproduced in the “Write-Up Template”).\u00a0 WARNING: The carbon resistors and light bulb may get very hot when the circuit is energized.\u00a0 Do not touch them.\u00a0 Use their leads to connect and disconnect them.<\/strong><\/span><\/p>\n Ohm’s Law, \\(V=IR\\), (\\(V\\propto I\\), where the proportionality constant is a constant resistance \\(R\\)), holds for devices whose resistance is independent of current. Such a device is said to be “ohmic”.\u00a0 It is also said to be “linear” since the voltage across it is linearly related to the current flowing through it by its resistance value. You will examine this relationship for the \\(10\\:\\Omega\\) ceramic\u00a0 resistor by creating \\(four\\) different circuits.\u00a0 The first circuit will consist of a single battery and the resistor wired in series.\u00a0 For each additional circuit, add another battery in series to the previous circuit.\u00a0 For each circuit use the BK PRECISION DMM<\/a> (Digital Multi-Meter) to measure the voltage drop across the resistor.\u00a0 Then use the BK PRECISION DMM<\/a> (Digital Multi-Meter) to measure the current flowing through the resistor for each circuit.\u00a0 Make sure that you record which range setting you are using for each of your measurements.\u00a0\u00a0 WARNING: The ceramic resistor may get very hot when the circuit is energized.\u00a0 Do not touch it.\u00a0 Use its leads to connect and disconnect it.<\/strong><\/span><\/p>\n The uncertainty of the meters for each range is given by the manufacturer’s “specs” in the operator’s manual<\/a>. Look up the appropriate uncertainty formulas and record them. You will be using them to find \\(\\delta V\\) and \\(\\delta I\\) for each measurement you take!<\/p>\n Record your data a table set up similarly to the one below:<\/p>\n <\/p>\n One Battery\u00a0\u00a0\u00a0 Two Batteries\u00a0 etc.<\/p>\n Plot<\/a> \\(V\\) vs. \\(I\\). You may use EXCEL to make your plot, or you may plot by hand.\u00a0 If your uncertainties are too small to plot as error bars, make a note on the plot stating so.<\/p>\n Calculate the resistor’s value with uncertainty by using Straight Line Analysis.\u00a0 Compare the equation of your line to the expected relationship \\(V=IR\\) (Key Equation).\u00a0 It should be apparent that you should force your best fit line through 0,0 because if there is no voltage, there can be no current.\u00a0 Make sure you show how the equation of your line relates to the Key equation.\u00a0 Now calculate the uncertainty of the resistor’s value using worst fit lines.\u00a0 Note: If your uncertainties were too small to plot as error bars, you will have to calculate the slopes of the upper worst and lower worst fit lines using the mathematical method.<\/p>\n Measure the \\(10\\:\\Omega\\) resistor’s resistance using your multimeter (note that the resistor must be removed from the circuit in order to measure its resistance with the meter). Calculate this measurement’s uncertainty using the manufacturer’s uncertainty specification (multimeter manual<\/a>).\u00a0 Compare your calculated resistance from above to the measured resistance.\u00a0 Are they equal within uncertainty?<\/p>\n In this section we will measure the resistance of the tungsten filament in the larger light bulb that came in your Lab Kit. This device is non-ohmic<\/em> since R is not constant.\u00a0 The resistance in non-ohmic devices changes as a function of current \u2013 in this case due to the increase in temperature with increasing current.<\/p>\n Use the same procedure that you followed in Part 2, except this time use the larger light bulb in the circuit instead of the resistor.\u00a0 Just as you did with the resistor in Part 2,\u00a0 build\u00a0 the four different circuits and use the BK PRECISION DMM<\/a> (Digital Multi-Meter) to measure the voltage drop across the light bulb and the current through the light bulb for each circuit.\u00a0\u00a0 Make sure that you record which range setting you are using for each of your measurements.\u00a0 WARNING: The light bulb may get very hot when the circuit is energized.\u00a0 Do not touch it.\u00a0 Use its leads to connect and disconnect it.<\/strong><\/span><\/p>\n Create a table similar to the one you used in Part 2, but this time add columns for Resistance (calculated by V\/I) and its uncertainty (refer to the error propagation rules sheet available on Blackboard or refer to the error propagation rules in the manual if necessary).\u00a0 You will then make two plots:\u00a0 one of voltage versus current to obtain the \u201ccharacteristic curve\u201d* of the light bulb, and another of resistance versus current to see how resistance changes with current.\u00a0 You do not need to put error bars on these two plots.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 *Note: You are not doing straight line analysis for this Lab because your plots are not linear.<\/p>\n Extrapolate the light bulb resistance at room temperature (when current is zero) from your graph .\u00a0 Compare<\/u> the extrapolated light bulb resistance to that read using the DMM on its ohm scale.\u00a0 Comment on the agreement of your two values.<\/p>\n <\/p>\n Background<\/a> Equipment<\/a> Summary Questions<\/a><\/p>\n <\/p>\n![\"\"](\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2019\/09\/circuits-jpeg.jpg\")
<\/p>\nPart 2: Quantitative Verification of Ohm’s Law<\/h2>\n
![\"\"](\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2019\/09\/data-table.jpg\")
<\/p>\nPart 3: Quantitative Study of Non-Ohmic Behavior of a Light Bulb<\/h2>\n
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<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"![BK PRECISION DMM<\/a> (Digital Multi-Meter) to measure the voltage drop across the resistor.\u00a0 Then use the](\"https:\/\/courses.bowdoin.edu\/physics-1140-lab-manual\/wp-content\/uploads\/sites\/105\/2018\/02\/bk-meter.jpg\"){kind=link}