On Kirchhoff's equations and variational approaches to electrical network analysis

Abstract

Analysis of electrical networks using variational techniques, while repeatedly mentioned in the literature, is not widely known or utilized. In this short communication, we emphasize the connection between Kirchhoff's network equations, energy conservation, and variational analysis techniques using a brief example.

Conflict between physical analysis and mathematics causing failure: A case on diode circuits

“…Referring to the answer variants (Table 1), all students appear not to conduct analysis but use a "plug and chug" method to solve the problem (Docktor & Mestre, 2014;. Another indicator showing that students do not conduct analysis is that they do not confirm the accuracy of their answers using Kirchhoff's Current Law (Coppens et al, 2017;Ercan, 2016). A common prediction emerges regarding the causes of students' failures in solving question 1.…”

“…Various studies on mastery of basic circuits as well as advanced circuits have been conducted. Studies on mastery of basic circuits show that: 1) students fail to apply Ohm's law and Kirchhoff's law, many students do not consistently and systematically apply basic circuit concepts (Coppens et al, 2017;Ercan, 2016;Liu et al, 2022;Papanikolaou et al, 2015;Ünal, 2022). 2) what happens when circuits are transformed into different circuits remains difficult for students to understand and master.…”

“…This study clearly presents an example of the interconnection between understanding and mastery of basic circuits with success in analyzing advanced electronic circuits, especially diodes. The common causes of students' failures in solving problems are the failure to apply Ohm's law and Kirchhoff's law, as well as the inconsistency and lack of systematic application of basic circuit concepts (Coppens et al, 2017;Ercan, 2016;Liu et al, 2022;Papanikolaou et al, 2015;Ünal, 2022). The researchers found another cause of failure in solving problems, namely the conflict between physical and mathematical analyses.…”

A review of the variational methods for solving DC circuits

“…Then Tellegen's theorem states that the directed sum of voltages and currents over all the branches is zero i.e. (28) Alper Ercan, applying Tellegen's theorem, recently showed that in an electric circuit, "energy conservation, KCL and KVL are strongly interrelated: any two together imply the other" [28]. As an illustrative example, consider the circuit shown in figure 4.…”

“…Ercan, applying Tellegen's theorem, recently showed that in an electric circuit, 'energy conservation, KCL and KVL are strongly interrelated: any two together imply the other' [28]. As an illustrative example, consider the circuit shown in figure 4.…”