| Title: | On the test of novel constitutive relation of capacitor for electrical circuit analysis: A fractal calculus based approach |
| Researcher: | Rawid Banchuin |
| Degree: | M.Sc. (Information Technology) |
| Major: | Master of Science Program in Information Technology |
| Faculty of study: | Graduate School |
| Academic year: | 2568 (2025) |
| Published: | COMPEL-The international journal for computation and mathematics in electrical and electronic engineering, Volume 42, Issue 2, pp. 506-525) Click |
Abstract
Purpose: The purpose of this paper is to test the capability to properly analyze the electrical circuits of a novel constitutive relation of capacitor.
Design/methodology/approach: For ceteris paribus, the constitutive relations of the resistor and inductor have been reformulated by following the novel constitutive relation of capacitor. The responses of RL, RC, LC and RLC circuits defined on the fractal set described by these definitions have been derived by means of the fractal calculus and fractal Laplace transformation. A comparative Hamiltonian formalism-based analysis has been performed where the circuits described by the conventional and the formerly proposed revisited constitutive relations have also been considered.
Findings: This study has found that the novel constitutive relations give unreasonable results unlike the conventional ones. Like such previous revisited constitutive relations, an odd Hamiltonian has been obtained. On the other hand, the conventional constitutive relations give a reasonable Hamiltonian.
Originality/value: To the best of the author’s knowledge, for the first time, the analysis of fractal set defined electrical circuits by means of unconventional constitutive relations has been performed where the deficiency of the tested capacitive constitutive relation has been pointed out.
Keywords: Capacitor, Conventional constitutive relation, Fractal calculus, Hamiltonian, Novel constitutive relation, Revisited constitutive relation, Circuit analysis, Integral equations
รศ. ดร.รวิศวร์ บานชื่น – Assoc. Prof. Dr. Rawid Banchuin. 2568 (2025). On the test of novel constitutive relation of capacitor for electrical circuit analysis: A fractal calculus based approach. บทความ (Paper). ปริญญาโท (Master’s Degree). บัณฑิตวิทยาลัย (Graduate School). วิทยาศาสตรมหาบัณฑิต สาขาวิชาเทคโนโลยีสารสนเทศ – Master of Science Program in Information Technology. วท.ม. (เทคโนโลยีสารสนเทศ) – M.Sc. (Information Technology). Bangkok: Siam University