Physics Lab: Capacitors and RC Decay PDF

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Summary

Second lab of the Physics 2 course....

Description

Konstantin A. Vostrikov! PHYS 1440! Section 804 ! Razvan Stanescu! 6 March 2018! Billy Zhang! Capacitors & RC Decay!

Objective:! To measure Rm through a comparative analysis of series and parallel RC circuits. In the second part of the lab the objective was to calculate the capacitance of the experimental capacitor 3 different ways.

Introduction/Theory:! Q = C•V#

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Vc = Vo e-t / RC!

Rm = ( t’ - t’’ )Rx / ( t’’ ) #

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ln(Vc) = ln(Vo) - t / (Rm • C1)!

C in Series: C = C1 + C2#

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C in Parallel: (1/C) = (1/C1 ) + (1/ C2) !

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With the equations above, we are able to see the relationships of Capacitance, Voltage, and Resistance. Using these equations, we were Abel to calculate the internal resistance of our experimental voltmeter. !

Experimental Procedure:! Starting out, we obtained the time for variously set-up capacitors to discharge to RC1, or 3.7V. With the discharging time intervals for the large and small capacitor set up individual, series, or parallel we were then able to obtain Rm, the internal resistance of our experimental voltmeter. In this section of the experiment we also examined the difference in capacitance between the experimental capacitors being set up in parallel or series.! In the subsequent section of the lab, we analyzed and measured the exponential RC decay of the first capacitor. With the help of a stopwatch, we patiently recorded the voltage through the capacitor for 10 second intervals.! To better understand the data we proceeded to graph our data from the later portion of the lab. ! The materials used in carrying out this experiment are as follows:! (2)#Different Capacitors#

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Stopwatch!

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Digital Voltmeter, with Probes#

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Power Supply Unit!

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Electrical Cables & Wire Clips#

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Resistor!

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Circuit Switch!

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Results & Analysis:! #

Table 1: [Attached]!

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Pt 1: Timed the duration it took for the various capacitor set-ups to decay

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to RC1. Here, we tested C1, C1 & Resistor, C2, C1 & C2 in series, and C1 & #

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C 2 in parallel. Knowing that C1 > C2 we see that the average time interval #

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decay to RC1 for C2 was greater than half that of C1. Using the equations #

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presented in the Introduction/Theory, we can see that the capacitors in #

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parallel should have the greatest capacitance. Glancing at the top table, #

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this holds true as we see that the average time interval decay is the #

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greatest. !

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Moving down the sheet, we come down to our data for the full RC decay #

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of C1. For our time interval we recorded the voltage across the capacitor #

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every 10 seconds. Looking at the data, we see the voltage decrease by #

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nearly 1 full volt initially. Traveling down the columns, we see the voltage #

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decrease becoming smaller every 10 seconds. After 2 minutes of # #

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discharging, we see the voltage decreasing at a rate of 0.25V/10s. After 4 #

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minutes of discharging, we see the voltage decreasing at a rate of 0.10V/#

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10s.!

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Graph 1: [Attached]!

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Plotting the exponential RC decay of C1, we are presented with an ##

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exponential decay graph.# Labeling the RC constants on the graph, we #

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see RC is at 106s, 2RC is at 224s, and 3RC is at 355s. This left us with an

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average RC of about 112.3 seconds. !

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Graph 2: [Attached]!

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Linearizing Graph 1 with the help of logarithms, we are presented with a #

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decreasing linear plot with positive x and y intercepts!

Discussion:! #

After graphically displaying our data, allowed us to calculate the the capacitance

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of C1 in a two extra ways. Looking at the first graph, figuring out the value of RC,

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we were able to use the equation: RC = R•C, to calculate the C because R was a

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value we obtained from the first section of the table. Moving onto the second #

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graph that was plotted through the equation: ln(Vc) = ln(Vo) - t / (Rm • C1), the #

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slope of the line would be: m = 1 / Rm C1. Figuring out the slope of the line #

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allowed us to calculate C1 another way. Comparing our two values for the #

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calculated capacitance, we see a large variation to the first one that was # #

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calculated through the equation: C1 = t’ / Rm. Examining potential sources of #

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error, we se that all of our data is reliant on our accuracy in measuring Rm. Such #

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errors in measurements can also be attributed to the lack of research-grade #

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laboratory equipment which would have allowed us to measure and obtain #

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precise measurements.!

Conclusion:! #

In conclusion, though our obtained C1 values were not equal, we were still able #

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to obtain the capacitance of our experimental capacitor three different ways. #

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With the help of the RC time constant, we were able to find the internal # #

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resistance of our experimental voltmeter that was used in obtaining the # #

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capacitance of our capacitor.#

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Questions:! 1.#

An RC circuit has a resistance of 20 MOhms and a time constant of 100 sec. If #

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the capacitor is charged to a voltage of 10v, what is the charge in coulombs on #

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its plates?!

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C = t / R = 100 s / 20•106 Ohms = 5•10-6 F!

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q = C•V = 5•10-6 F • 10 V = 5•10-5 C!

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A charged 1uF capacitor is connected in parallel with a 1 MOhm resistor. How #

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long after the connection is made will the capacitor voltage drop to a) 50% b) #

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10% c) 2% of its initial value?!

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T = R • C = 1•106 Ohms • 1•10-6 F = 1!

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a) (0.7)T!

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How many 1uF capacitors would need to be connected in parallel in order to #

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store a charge of 1 coulomb with a potential of 200 volts across the capacitors?!

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Q = (x)C•V = 1!

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x = 1 / (1•10-6 • 200V) = 5000!

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5000 1 uF Capacitors!...