Turning Mesh Analysis Inside Out
Elementary linear circuit analysis is a core competency for electrical and many other engineers. Two of the standard approaches to systematic analysis of linear circuits are nodal and mesh analysis, the latter being limited to planar circuits. Nodal and mesh analysis are related by duality and should therefore be fully symmetrical with each other. Here, the usual textbook approach to mesh analysis is argued to be deficient in that it obscures this fundamental duality and symmetry, and may thereby impede the development of intuition and the understanding of the nature of “mesh currents.” In particular, the usual distinction between “inner” and “outer” meshes (if the latter is even recognized) is argued to be meaningless, as can be seen when drawing a planar circuit on the surface of a sphere. A generalized definition of a mesh is proposed that includes both inner and outer meshes on the same footing. Selection of a reference node in nodal analysis should be paralleled by the selection of any mesh to be the reference mesh in mesh analysis, which is always selected to be the outer mesh by default in the usual approach. All branch currents are shown to the difference of two mesh currents, more »
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NSF-PAR ID:
10179929
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American Society for Engineering Education Annual Conference
3. Contribution: A new operational definition of series connections is given based on elements belonging to the same two meshes, which is properly dual to the usual definition of parallel elements being connected to the same two nodes. Furthermore, computer-based exercises have been developed and tested to teach students about such connections in gateway linear circuits courses, using color coding of nodes and meshes as a pedagogical device. Background: Series and parallel connections are a crucial but difficult concept. Existing textbooks give them limited attention, resulting in later difficulties learning circuit analysis. Research Questions: RQ1: Can an improved definition of series elements aid student understanding and student satisfaction? RQ2: Can a computer-based game'' lead to effective mastery and student satisfaction at a wide range of institutions, including minority-serving ones? Methodology: Standard and new definitions were elaborated in a multiple-choice tutorial. A game was developed focusing on identifying series and parallel connections, with color coding of both nodes and meshes. Student learning was assessed over eight years using pretest and posttest in 14 varied institutions. Student opinions were assessed using several types of surveys. Findings: Strong learning gains were observed every semester from built-in pretest and posttest, with average scores of 28%more »