Relaxation Method for a real parallel-plate capacitor
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This page first made public: Oct 7, 2016
Students will use this solution to determine the capacitance of a parallel-plate capacitor and compare this result to measurements done on a real system.
Students will learn model development, determining what parameters (grid size, number of iterations, etc) will give the best results. They will also learn to work with dimensionless units in computation, but relate those to SI units when they compare to lab measurements.
Because this is included as part of a laboratory activity, operation of lab equipment will also be emphasized. Finally, technical writing will be required in the writeup for assessment.
Context for Use
We plan one hour for introduction to the numerical tools, one hour for the students to learn the setup of the laboratory and how to take their measurements, and then students complete their measurements and analysis in their lab groups on their own schedule.
If a minimal working program is provided to the students, they need some familiarity with loops, MATLAB's built-in vector derivative functions, and 3D plotting functions.
For efficiency of calculation, it is best if the students are familiar with MATLAB vectorization techniques -- looping over the matrix elements greatly increases runtime. However, for pedagogical purposes, it may be worthwhile to use less-efficient methods that are more intelligible to students.
Description and Teaching Materials
Relaxation Method for Parallel Plates (Matlab File 2kB Sep30 16)
Relaxation Method Handout (Acrobat (PDF) 70kB May9 19)
Measuring Capacitance Lab Handout (Acrobat (PDF) 2.7MB Sep30 16) Measuring Capacitance Lab Handout (Acrobat (PDF) 2.7MB Sep30 16)
Teaching Notes and Tips
A more computationally-focused class could emphasize improvements to this method, such as the Gauss-Seidel method, successive over-relaxation, or multigrid techniques.