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4 Pages

### Lab 2

Course: PHYS 2Cl, Winter 2012
School: UCSD
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Word Count: 839

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Werry Partners: Christopher Lexi Baker, Alex Mara, Michael Kreisman 1/30/12 Lab 2 Wed 9AM Data Variable Capacitor: # of pages Distance (mm) 25 0.725 50 1.45 100 2.9 150 4.35 200 5.8 250 7.25 Capacitance (nF) 0.18 Area (m2) 0.0302 0.163 0.12 0.092 0.07 0.066 RC Circuit (qualitative): Graph for charge and discharge of a lightbulb in an RC circuit RC Circuit (quantitative): Capacitance Resistance run # (F) ()...

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Werry Partners: Christopher Lexi Baker, Alex Mara, Michael Kreisman 1/30/12 Lab 2 Wed 9AM Data Variable Capacitor: # of pages Distance (mm) 25 0.725 50 1.45 100 2.9 150 4.35 200 5.8 250 7.25 Capacitance (nF) 0.18 Area (m2) 0.0302 0.163 0.12 0.092 0.07 0.066 RC Circuit (qualitative): Graph for charge and discharge of a lightbulb in an RC circuit RC Circuit (quantitative): Capacitance Resistance run # (F) () expected meas amplitude (Vo) % error for 1 93.8 100.5 0.009427 0.01 2.993 6.079411047 2 93.8 561.7 0.052687 0.06 2.994 13.87909001 3 93.8 1001 0.093894 0.09 2.992 4.147025682 4 93.8 10030 0.940814 0.93 2.936 1.149430174 5 325 100.5 0.032663 0.009 2.997 72.44546498 6 325 561.7 0.182553 0.19 2.991 4.07964832 7 325 1001 0.325325 0.32 2.963 1.636824714 8 325 10030 3.25975 3.2 2.919 1.832962651 Methods Variable Capacitor: Page widths were of what was in the lab instructions. RC Circuit (qualitative): 4F capacitor instead of a 10F capacitor used resistor board instead of individual resistors used a light bulb of resistance 1.7 0.1 ohms Instead of a 10 ohm resistor used a resistor board of 1 ohms, and then 2 ohms Start voltage was 3V Analysis Capacitor Basics: Yes, it would still be a capacitor It was 0.9 pF, this is smaller than what I would expect Yes, the capacitance is additive because the wires have a capacitance that isnt negligible, and the wires are in series with the capacitor plates The crackling is caused by the aluminum foil crunching together. They are attracted to each other because of equal and opposite charge being distributed to each piece of foil. Thus, charging the capacitor creates an attraction between the plates. The amount of energy required to move one charge from one plate to the other is zero, because the plates have equal and opposite charge. The energy stored in a capacitor is: CV2, in this case with C = 0.9 pF and V = 5 kV, the stored energy is 11 micro Joules. The strength of the electric field is F = qE, where q = 2E/V = 5nC. So F = 5x10-14N Construction of Capacitor: The capacitance of the dielectric capacitor is larger. This is to be expected; assuming the dielectric constant of acrylic is above 1. A potential difference is created between the plates as well as an electric field. Fringing of the fields occurs when like charges gathered on a plate of a capacitor repel each other, causing the charge density to be greater on the edges of the plate. The standard equations for capacitance are an approximation because fringing effects significantly increase the capacitance. If a semiconductor was placed in-between capacitor plates, the capacitance would probably drop. The semiconductor would have charge separation due to attraction to the plates, this would create more a neutral electric field. Variable Capacitor: How do you expect the slope of this line relates to physical characteristics of the capacitor? The slope of the plot of Capacitance vs. 1/d would be directly proportional. This is because of the relationship between C and d for parallel plates: Our value is not what Id expect due to the following experimental error. Reason for discrepancy: We measured our pages as page numbers, not actual pages. So all of our values for page width were one half of the suggest width. This allowed for extra noise caused by the measuring equipment. Calculating permittivity of paper: A is area of the capacitor plates, D is the distance between the plates, is the permittivity of free space, and is the permittivity of the paper. RC Circuit (qualitative): The time to dim the bulb decreases as the resistance increases. The current is greatest when it first starts flowing at the light bulb is brightest. The current is lowest when the bulb is completely out. The current is zero because of the resistors present. The current slowly drops to zero as the capacitor charges. When the capacitor discharges, the current flows immediately again at the same original magnitude and in the same direction. RC Circuit (quantitative): For % errors for tao, see data If a larger DC voltage had been used, our measurements of would have decreased. Plot is in data. The slope of tao vs resistance for the 93uF capacitor is 10810, for the 325uF capacitor the slope is 3128.5. The voltage across a capacitor AND its capacitance increases the amount of charge it can store. Q(t) could be determined by multiplying V(t) by the capacitance I(t) is the derivative of Q(t) with respect to time The energy stored in a fully charged capacitor with C = 325uF: E= CV2 = 0.00146 J. Discussion/Conclusion In section 4, the demonstration was faulty in that the charges between the foil wasnt enough to attract them together and cause a crinkling noise. This was most likely the fault of the charge generator. In section 6 we measured the page numbers wrong and used half of the width values. This led to more noticeable noise caused by the measuring devices, which caused the graph of C vs 1/d to be off. This could have been solved by using the correct page widths. T-values could not be determined because there was no value for measurement uncertainty of the devices used. Instead, percent error was used to evaluate the correctness of the values of tao. The permittivity of paper was found to be 1.5, when this value should have been higher (Wikipedia estimates 3.4). Once again the page widths may have thrown off this result. In addition, the glossy pages of the textbook may have a lower permittivity than regular printer paper.
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