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On the test of novel constitutive relation of capacitor for electrical circuit analysis: a fractal calculus-based approach.

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Title: On the test of novel constitutive relation of capacitor for electrical circuit analysis: a fractal calculus-based approach.
Authors: Banchuin, Rawid1 (AUTHOR) rawid.ban@siam.edu
Source: COMPEL. 2023, Vol. 42 Issue 2, p506-525. 20p.
Subjects: Electric circuits, Fractals, Capacitors, Resistor-inductor-capacitor circuits, Laplace transformation, Fractal analysis, Hamiltonian systems
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. [ABSTRACT FROM AUTHOR]
Copyright of COMPEL is the property of Emerald Publishing Limited and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
An: 161363421
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: On the test of novel constitutive relation of capacitor for electrical circuit analysis: a fractal calculus-based approach.
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  Data: <searchLink fieldCode="AR" term="%22Banchuin%2C+Rawid%22">Banchuin, Rawid</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> rawid.ban@siam.edu</i>
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  Data: <searchLink fieldCode="JN" term="%22COMPEL%22">COMPEL</searchLink>. 2023, Vol. 42 Issue 2, p506-525. 20p.
– Name: Subject
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  Data: <searchLink fieldCode="DE" term="%22Electric+circuits%22">Electric circuits</searchLink><br /><searchLink fieldCode="DE" term="%22Fractals%22">Fractals</searchLink><br /><searchLink fieldCode="DE" term="%22Capacitors%22">Capacitors</searchLink><br /><searchLink fieldCode="DE" term="%22Resistor-inductor-capacitor+circuits%22">Resistor-inductor-capacitor circuits</searchLink><br /><searchLink fieldCode="DE" term="%22Laplace+transformation%22">Laplace transformation</searchLink><br /><searchLink fieldCode="DE" term="%22Fractal+analysis%22">Fractal analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Hamiltonian+systems%22">Hamiltonian systems</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: 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. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of COMPEL is the property of Emerald Publishing Limited and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1108/COMPEL-04-2022-0143
    Languages:
      – Code: eng
        Text: English
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      Pagination:
        PageCount: 20
        StartPage: 506
    Subjects:
      – SubjectFull: Electric circuits
        Type: general
      – SubjectFull: Fractals
        Type: general
      – SubjectFull: Capacitors
        Type: general
      – SubjectFull: Resistor-inductor-capacitor circuits
        Type: general
      – SubjectFull: Laplace transformation
        Type: general
      – SubjectFull: Fractal analysis
        Type: general
      – SubjectFull: Hamiltonian systems
        Type: general
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              M: 03
              Text: 2023
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              Y: 2023
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