Lab Report #4

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School

Florida International University *

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Course

2048L

Subject

Electrical Engineering

Date

Apr 3, 2024

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pdf

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Uploaded by AdmiralFlowerSardine36

Cynthia Baracaldo 6288719 Isabel Ruiz 6353644 Emily Salgueiros 6286683 Lab Report #4 PRELIMINARY QUESTIONS 1. A good analogy to charging a capacitor would be filling a scuba tank with compressed air. What would be the quantities equivalent to q, V, and C in the relation q = VC? Quantity (q): The total volume of compressed air injected into the tank would be quantity (q) in the example of the scuba tank. Voltage (V): In the analogy of the diving tank, voltage (V) is equivalent to the compressed air pressure inside the tank. Capacitance (C): Using the scuba tank example, capacitance (C) would be comparable to the tank's capacity to hold a specific volume of compressed air at a specific pressure. 2. In simple terms, why would you expect the capacitance of a capacitor to be proportional to the plate area? A larger plate area enables for more electric field lines to be present between the plates, which is why a capacitor's capacitance is proportional to the plate area. The capacity of a capacitor to hold charge for a specific voltage is expressed in terms of capacitance, or C. A greater capacitance is produced by increased surface area on the plate for electric field lines to interact with. In essence, a bigger plate surface gives electric charges more room to build up, which raises the capacitance of the capacitor—its capacity to hold charge. 3. Why would you expect the capacitance of a capacitor to be inversely proportional to the distance between the plates? The distance between the plates of a capacitor determines its capacitance, which is simply inversely proportional to the distance because greater electric field interactions are possible at closer spacings. The distance (d) between the plates and the capacitance (C) are inversely related. The electric field between the plates gets stronger and more concentrated as the distance between them shrinks. Because the capacitor can store more charge for the same voltage when the space between the plates is less, electric charges are subject to a stronger force. This leads to a higher capacitance. Thus, there is an inverse connection between capacitance and distance as the plates get closer together, increasing the capacitor's capacity to store charge. PART 1: BUILD A CAPACITOR

PROCEDURE 1. Take two pieces of aluminum foil approximately the size of your textbook and measure their area. You may want to add small “tabs” for connecting to the multimeter leads. Place them in your textbook separated by 10 pages. They should be carefully aligned with each other. Note that if the areas are slightly different, the area that should be recorded in the data table is the area of overlap. You may want to add small “tabs” for connecting to the multimeter leads. Place a weight on the textbook 2. Attach two leads with alligator clips to the tabs. At your station is a meter that can measure capacitance. Select the capacitance measurement function ( symbol) on the meter. Attach the other ends of the leads to the meter and take a measurement of the capacitance. 3. Fill in the data table with your values. 4. To explore the relationship of capacitance to the separation distance, change the number of pages between the foils. You want to make an additional four (or more) measurements and record them in the table. Make sure to place the weight on the book for each measurement. Decide how to vary the numbers of pages, considering how the capacitance depends on separation distance. 5. To explore the relationship of capacitance to area, reduce the area of both pieces of foil equally, insert them into the book, and record your measurements in the table. You should carry out at least two additional measurements to study the trend. Decide how to vary the size of the foil. Again, consider how to optimize the measurements. 6. Estimate the thickness of the pages by using a Vernier caliper to measure a large number of pages and then determine the average values for the thickness. You may want to make several measurements and average the results. ANALYSIS 1. Open the Logger Pro file "DIY-capacitor" in folder Lab 04, enter your data and plot a graph of the measured capacitance vs. the distance between the plates for the same plate area. - Graph is pasted below. 2. How does the capacitance depend on separation? Does it follow a straight line? Does it follow the trend you expect? Why or why not? - The capacitance depends on the separation because as the separation increases, the capacitance decreases. It does follow a straight line with a negative slope. This follows the trend I expected because the capacitance equation depicts an inverse relationship between the two. 3. What should be plotted on the x and y axes to produce a straight line graph? Plot another graph to check your prediction. (The last column in the data table can be used to enter the appropriate values.) - The x and y-axes should be the inverse of distance and capacitance, respectively, in order to produce a straight line with a positive slope. 4. Plot a graph of the measured capacitance vs. the area of the plates for the same plate separation. - Graph is pasted below.

5. How does the capacitance depend on area? Does it follow a straight line? Does it follow the trend you expect? Why or why not? - The capacitance depends on the area because as the area increases, the capacitance increases. It does follow a straight line with a positive slope. This follows the trend I expected because the capacitance equation depicts a direct relationship between the two. 6. Using the slope of this graph, together with the distance between the plates, determine the dielectric constant of paper. Find a value for the dielectric constant of paper on the Web or elsewhere and compare it to your measured value. (Note that different types of paper could have different dielectric constants.) - Write equation in word. The literature value of the dielectric constant is 2 - 4, which differs greatly from the calculated value. So, the obtained values for capacitance due to area are likely inaccurate, thus explaingint the incorrect calculate dielectric constant of paper. PART 2: CAPACITORS IN SERIES AND IN PARALLEL 1. Use the multimeter to measure the capacitances of three capacitors 2. Connect the capacitors in series and measure the capacitance of the combination. 3. Connect the capacitors in parallel and measure the capacitance of the combination. ANALYSIS 1. Calculate the capacitance of the series combination of capacitors and compare it with what you measured. 2. Calculate the capacitance of the parallel combination of capacitors and compare it with what you measured.

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PART 3: INVESTIGATE DISCHARGING OF A CAPACITOR PROCEDURE 1. Connect a series circuit of the resistor, capacitor, current probe and battery as shown in Fig. 2. Make sure the capacitor and current probe terminals labeled + and – are as shown in Fig. 2, and that the battery pack's red and black terminals are as shown. One end of the connecting wire, labeled A, from the resistor is shown disconnected. If the end A is connected to the battery's positive terminal, B, the battery will charge the capacitor through the resistor. If, subsequently, the end A is connected to the terminal C, the battery pack is eliminated from the circuit, and the capacitor will discharge through the resistor. 2. We now want to obtain a graph of the rate of flow of charge (current) as the capacitor discharges. Plug the third current probe lead into the Labquest unit, and plug the Labquest into a USB port on the computer. 3. Open the Logger Pro file "Capacitor" in folder Lab 04. A graph will be displayed. The vertical current axis of the graph should be rescaled, if necessary, from 0 to 0.1 amps. The horizontal axis has time scaled from 0 to 10 s. With end A still disconnected, zero the current probe by clicking the "Set zero point" button ± on the toolbar. 4. Connect the end A of the connecting wire to the battery's positive terminal, B. The capacitor will become fully charged after about 10 seconds. 5. With A still connected to B, use the multimeter to measure the voltage between the plates. To do so, set the multimeter to DC volts, and then touch the multimeter probes to the terminals of the capacitor. Calculate the charge on the capacitor from the relation q = VC. 6. Disconnect the end A of the connecting wire from B (the capacitor will retain its charge), click to begin data collection, and immediately connect the end A to terminal C. 7. You should obtain a curve similar to Fig. 1a, but with a zero current portion for the period before A was connected to C. Repeat steps 4 to 6 if necessary to obtain a good graph. The curve should have reached baseline. If necessary, rescale the horizontal time axis.

ANALYSIS 1. Using only the portion of the graph from the peak out to baseline (~ 10 seconds), determine the area under the curve using the integration button. Record it as the total charge that has flowed.. - The area under the curve is 0.1518 A*s 2. Print a copy of the graph of current flowing as a function of time. - Graph is pasted below. 3. How did the initial charge on the capacitor compare with the total charge that flowed? - The initial charge we measured was 0.075525 C and the total charge measured was 0.1518 C. The total charge was more than double the initial charge on the capacitor. 4. How quickly the capacitor discharges depends, as you will learn later, on the "time constant" of the RC circuit. It is defined as the time taken for the current to decrease to 1/e of the initial value. (e = 2.718 is the base of natural logarithms.) From your graph, determine the time constant and enter the value in the table. - The time constant we determined from the graph is 1.477 s. 5. Theoretically, the time constant, t, can be shown to be equal to R times C (t = RC). If R is in ohms and C is in farads, t will be in seconds. Calculate the time constant, enter the value in the table, and compare it with the value from your graph. - Using the formula t=RC, the time constant we calculated is 1.25 s. The time constant we determined from examining the graph is greater than the measured time constant. GRAPHS

DATA TABLES

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