Lab 205 w_ MATLAB EC

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Montclair State University *

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111

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Electrical Engineering

Date

Apr 3, 2024

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pdf

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Uploaded by HighnessScorpion14087

Physics Laboratory Report Title: Parallel Plate Capacitor Lab number and Title: Lab 205: Parallel Plate Capacitor Name: Sami Choudhury Group ID: Group 7 Date of Experiment: _3__/_3_/_23____ Date of Report Submission: _3__/_10__/__23___ Course & Section Number: 102A Instructor’s Name: Dolores Termini Partners’ Names: Kyle, Michael, Fidel 1. INTRODUCTION (10 points) 1.1 Objectives To understand the principle of a parallel plate capacitor, to investigate how the capacitance of a parallel plate capacitor varies as the plate separation changes and to measure the dielectric constant of a material. 1.2 Theoretical background The capacitance C of a parallel plate capacitor is with the variables 𝐶 = ε𝐴 𝑑 ?𝑟 𝐶 = 𝑘ε ? 𝐴 𝑑 representing the permittivity of the material between plates, a dielectric constant, and permittivity of free space. Additionally, in a series circuit, if two capacitances C1 and C2 are connected, the total capacitance is calculated through 1 𝐶𝑡 = 1 𝐶1 + 1 𝐶2

2 3 Experimental Procedure (10 points)

2.1 Experimental Variables k → dielectric constant → 8.85e-12 permittivity of free space ε ? d → Distance (m) of plate separation. A → Area of the plane 2.2 Experimental Procedure To start the experiment, we first set up the apparatus which consisted of the parallel plate capacitor, rotary motion sensor, and the capacitance meter. We first adjusted the rotary motion sensor onto the parallel plate capacitor and made sure that the wheel was aligned with the track since that is how we get our measurements. Then we attached the Test leads to the apparatus and the capacitance meter to measure at each varying distance. Then for part II we added the dielectric plate in between the two petal plates to observe the capacitance increase. 4 Results (30 points in total) 4.1 Experimental Data (15 points) Capacitance(pF) vs. Separation(mm)

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Capacitance vs. inverse of separation Inverse of total capacitance vs. distance of air gap in Part II

4.2 Calculation (15 points) Data Analysis using MATLAB part 1: Equation: 𝐶(𝑑) = (ε 0 𝐴) * ( 1 𝑑 ) Theoretical capacitance v. separation Data Analysis using MATLAB part 2: Theoretical Ct and experimental Ctexp

Part 1 Calculations (1) 𝐶 = ϵ 0 𝐴 𝑑 ϵ 0 = 𝐶𝑑 𝐴 From Figure 4, the value of C*d is 278 pF*mm ϵ 0 = 278?𝐹·𝑚𝑚 (100𝑚𝑚) 2 π ε 0 = 8.84901*10 -12 F/m %error = |8.84901*10 -12 F/m - 8.85419*10 -12 F/m| / 8.85419*10 -12 F/m %error = 0.00518% Part 2 Calculations (2) 1 𝐶 = 𝑑 ϵ 0 𝐴 + ∆ 𝑘ϵ 0 𝐴 Slope = , y-intercept = 1 ϵ 0 𝐴 ∆ 𝑘ϵ 0 𝐴 ϵ 0 = 1 𝑚𝐴 From Figure 6, the slope is 0.00336 1/pF*mm ϵ 0 = 1 0.00336 1/?𝐹*𝑚𝑚 · (100𝑚𝑚) 2 π ε 0 = 9.47350*10 -12 F/m %error = |9.47350*10 -12 F/m - 8.85419*10 -12 F/m| / 8.85419*10 -12 F/m %error = 7.05% ϵ 0 = ∆ 𝑘𝑦 0 𝐴 From Figure 6, the y-intercept is 0.00781 1/pF ϵ 0 = 6.4𝑚𝑚 3·0.00781 1/?𝐹·(100𝑚𝑚) 2 π ε 0 = 8.69476*10 -12 F/m %error = |8.69476*10 -12 F/m - 8.85419*10 -12 F/m| / 8.85419*10 -12 F/m %error = 1.74%

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3.3 ANALYSIS and DISCUSSION (20 points) 3.3.1 Our objectives were met during the experiment and we were able to observe the varying capacitance as the plate capacitor changes its distance. Our percent errors were also relatively small implying that we did go about the experiment properly with human error possibly taking place in a few instances resulting in the percent error. However, we were able to confirm that as the distance between the plates increased, the capacitance decreased respectively. 3.3.2 Discussion Questions Why is the electric field inside the dielectric smaller than the electric field in the air between the plates? Some electrostatic energy is lost to polarize the dielectric, resulting in a field inside the dielectric that is smaller than the one outside, where k is the material's relative dielectric constant. What is the direction of the electric field inside the dielectric when the dielectric is implemented inside the charged parallel plate capacitor? The direction of the electric field inside of the dielectric is opposite to the electric field on the outside in the electric field in the air that is between the plates. 5 CONCLUSIONS (10 points) In conclusion this lab has provided a base understanding on the formulas mentioned earlier in the theoretical, and it has helped us understand the principles of a parallel plate capacitor. We learned that as the distance between the plates increased, the capacitance decreased and how a dielectric influences the capacitor when inserted between both plates, and we learned that it in fact increases the capacitance. We were able to quantify our capacitance which further allowed us to visualize how the capacitance varied given certain measurements. Overall this lab has definitely provided more understanding towards the concept of capacitance in general and the only question that arose during this experiment was whether there are different dielectric materials that increase capacitance differently, for instance, is there a dielectric material that shows the biggest increase in capacitance or a weaker material that shows the smallest increase in capacitance? 6 Attachment of Raw Data (5 points)