Capacitors worksheet

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Arizona State University *

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132

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Electrical Engineering

Date

Dec 6, 2023

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pdf

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4

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1 C A P A C I T O R S – W O R K S H E E T Name: Andrew Crist Partners: Nahom, Hunter, Zainab TA: Rekha Joshi DATA & ANALYSIS Part 1 – Distance Dependence Separation (m) Capacitance (unit: pF) 0.02 35 0.03 22.1 0.04 17.3 0.05 14.2 0.06 12.1 Data (20) & Graphs (20): Analysis (30): Post Lab Qs (15): Clean-up/Sign-out (3): Total (88): Calculations SA: 16.5cm x 30cm = .0495m^2 .6835 = E0 x .0495 E0 = 13.81 Slope of ࠵? vs 1/࠵? graph: .6835 pFm Plate area: 495cm^2 ࠵? ! (from slope): 13.81 % error from ࠵? ! = 8.85 ࠵?F/m : 35.916%
2 Part 2 – Area Dependence Area (unit: m^2) Capacitance (unit: nF) .0495 .480 .0462 .456 .04125 .420 Part 3 – Equivalent Capacitance ࠵? " = 101.1 nF ࠵? # = 103.9 nF ࠵? $ = 103 nF Configuration Calculated Capacitance (show your work) Measured Capacitance 1/Cnet = 1/C1 + 1/C2 + 1/C3 = 34.21 nF 34.2 nF 1/Cnet = 1/C1 + 1/(C2 + C3) = 67.91 nF 67.9 nF Cnet = C3 + (1/(1/C1 + 1/C2)) = 154.24 nF 154.2 nF Cnet = C1 + C2 + C3 = 308 nF 308 nF Slope of ࠵? vs ࠵? graph: 7.273 nF/m^2 ࠵? % (from slope): 21.819 Dielectric constant ࠵? &’()*+’,-- : 2.47 % error compared to ࠵? = 3 : 21.457% Calculations SA2: .165m x .28m = .0462 SA3: .165m x .25m = .04125 7.273 = Ed/3 Ed = 21.819 K = Ed/E0 = 21.819/8.85 = 2.47
3 POST LAB QUESTIONS 1) In part 1, was the y-intercept of the graph zero? Why or why not? No. This is because as distance increases, capacitance decreases. Capacitance can never be zero, and so the graph will approach zero without ever actually reaching zero. 2) If the plexiglass was four times as thick, what would be the value of its dielectric constant? Why? K will remain the same because K is a constant depending on the type of material being used. Not on the shape. 3) BONUS (up to 5 pts): Why do we expect the measured value of ࠵? ! to be larger than the real value? Hint: Think about the assumption made in deriving Eq. (2), plus the fringe effects of the parallel plate geometry that you discovered in Lab 1. A small drawing might be helpful. Extra hint: the dielectric constant of air being slightly greater than 1 is not the answer. We expect the measured value of E0 to be larger than the real value because the measured capacitance will be slightly smaller than it’s true value. E0 is found by taking the inverse of the capacitance and graphing it against distance. Therefore when the capacitance is less than expected, the inverse will be greater.
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