Calculation of the (I-V) Characteristics of Corona Discharge with the Configuration Model of Triangular Electrode on a Vertical Plate

INTERNATIONAL JOURNAL OF MULTIDISCIPLINARY RESEARCH AND ANALYSIS ISSN(print): 2643-9840, ISSN(online): 2643-9875 Volume 08 Issue 11 November 2025 DOI: 10.47191/ijmra/v8-i11-05, Impact Factor: 8.266 Page No. 5951-5955 IJMRA, Volume 08 Issue 11 November 2025 www.ijmra.in Page 5951 Calculation of the (I-V) Characteristics of Corona Discharge with the Configuration Model of Triangular Electrode on a Vertical Plate Asep Yoyo Wardaya Department of Physics, Faculty of Science and Mathematics, Diponegoro University, Semarang Indonesia ABSTRACT: This study compares the current-voltage (I-V) characteristics of symmetrical and asymmetrical direct current CCP equipment under corona discharge in air. The electrode configuration model used for the symmetrical CCP case is a coaxial cylinder, and for the asymmetrical CCP case, a Triangular Electrode on a Vertical Plate. Both types of electrodes use a modified capacitance concept in the calculation of the characteristics (I-V). This concept begins with a geometric approach (electrode size), where there is a corona current multiplier factor k (the ratio of corona current to conventional electric current), and the nature of the corona discharge that collects at the sharp tip of the active electrode. KEYWORDS: CCP, (I-V) characteristics, corona discharge, modified capacitance, Triangular Electrode on a Vertical Plate I. INTRODUCTION There is no need to doubt the need for plasma technology to help with daily human activities, especially electronic equipment such as TVs, refrigerators, etc. Plasma technology is also used in the fields of health (Kim, & Kim, 2021), agriculture and biomedicine (Stryczewska, & Boiko, 2022), surface modification of polymer materials (Vidaurre, et al. 2002), area coatings (Anders, 2005), lensshaped electrodes (Schmidt, et al. 2004), and dielectric barrier discharge (Bouremel, et al. 2013), etc. Plasma technology uses equipment similar to a capacitor called capacitively coupled plasma (CCP) (Saikia, et al. 2018). According to Stambouli et al. (2017), CCP equipment is divided into three categories: the electric asymmetric CCP, the direct current CCP, and the dual-frequency CCP. For CCP equipment that uses the direct current (DC) model, the calculation of the plasma discharge's current-voltage (IV) characteristics is very different from that of ordinary conventional electric currents. This can happen because plasma discharge is caused by various physical events, such as electrodynamics (Guan, et al. 2018), electric wind (Robinson, et al. 1961), and so on. Of course, the best solution for the (I-V) characteristics, in this case, is to use a physical properties solution using quantum, electrical, and magnetic properties (usually using the concept of Maxwell's equations); as found by Zheng et al. (2015) & Wardaya et al. (2019), even though the resulting solution is only suitable for the initial corona discharge curve. However, there is a (I-V) characteristic model using a fairly simple formulation through a geometric approach to the dimensions of the electrode. This formulation occurs in the direct current CCP model with a symmetrical arrangement of the active electrode to the passive electrode, namely in the case of a coaxial cylindrical electrode with the inner and outer cylinders, respectively, being the active and passive electrodes, which are radially symmetrical cylinder systems. This characteristic equation is expressed through equation (Robinson, et al. 1967), ( ) 602 4 10 , CC i bC I i V V V l l R  = = − (1) where I is corona current (A), i is corona current/length (A/m), and  is the density of the air relative to standard conditions (250C, 76 cm Hg) in the range of 0.1 <  < 35. The constant b0 is the mobility of air ions (O2) at  = 1. The quantities R and l are the radii of the outer cylinder and the length of the Coaxial Cylinders, respectively. The CCC quantity is a capacitance formulation of a cylindrical coaxial electrode shape (Halliday, et al. 2013) that is, ( ) 2, ln / CC l CRr  = (2) where r is the radii of the inner cylinder (thin wire). The striking thing about characteristic equation (1) is the appearance of the capacitance value of the coaxial cylinder, which is expressed in equation (2), as well as the appearance of an electric current Calculation of the (I-V) Characteristics of Corona Discharge with the Configuration Model of Triangular Electrode on a Vertical Plate IJMRA, Volume 08 Issue 11 November 2025 www.ijmra.in Page 5952 multiplier factor of 106. This multiplier factor is the comparative value of the plasma discharge electric current (which is very large) to that of ordinary conventional electric current. The characteristic equation model (1) can be applied to direct current CCP with the active electrode having a shape that is not symmetrical to the passive electrode, which is referred to as electric asymmetric CCP, but with certain differences in formulation. This difference arises because, according to experimental results by Dobranszky et al. (2008), the plasma discharge will be seen collecting only at the sharper ends of the active electrode compared to the less sharp part of the active electrode, which is the condition of the electric asymmetric CCP model. The correction to equation (1) 's formulation, which is applied to the case of electric asymmetric CCP, appears in the formulation of the concepts of capacitance and electric current multiplier factor. According to research results by Wardaya et al. (2020, 2022, 2022A and 2022B), for the case of electric asymmetric CCP, an electric current multiplier factor of k is inserted in the capacitance calculation from the sharp, active electrode calculation section, which is called the modified capacitance equation. The electrode configuration model used for the electric asymmetric CCP in this study is a Triangular Electrode on a Vertical Plate. II. TRIANGULAR ELECTRODE ON A VERTICAL PLATE CONFIGURATION MODEL. We present an example of the modified capacitance model for the Triangular Electrode on a Vertical Plate configuration to illustrate the capacitance calculation for the electric asymmetric CCP model in air. The capacitance model is illustrated in Fig. 1. Figure 1. Sketch of the Triangular Electrode on a Vertical Plate configuration model. To calculate the capacitance of the Triangular Electrode on a Vertical Plate configuration model shown in Fig. 1, we can create a calculation sketch as shown in Fig. 2 below. Figure 2. Calculation of half-section capacitance of Triangular Electrode Configuration Model on a Vertical Plate. Calculation of the (I-V) Characteristics of Corona Discharge with the Configuration Model of Triangular Electrode on a Vertical Plate IJMRA, Volume 08 Issue 11 November 2025 www.ijmra.in Page 5953 Figure 2 shows the calculation of half the capacitance of the Triangular Electrode Configuration Model on a Vertical Plate. Now consider an area element with width du and height s. The capacitance of this area element can be written as 00 . A du dC h b d s    == +− (3) Through triangle comparison 1 , su bu = (4) then the capacitance of the Triangular Electrode on a Vertical Plate Configuration Model in Fig. 1 can be written as 1 1 1 1 11 00 1 22 c u c u u c u c du du Cb d s u b d b u     ++ == == +−  +−    ( ) ( ) ( ) ( )   1 0 1 1 1 1 2 ln ln ucb u d cb u b d b    = − − − − +   (5) where factor 2 indicates the symmetry of Fig. 1, which has a capacitance value 2 times that of figure 2. However, equation (5) is only suitable for the case of ordinary electrical circuits. For the case of corona discharge, the capacitance equation (5) needs to be added with a sharpness factor in the form of k, so that the modified form of the capacitance equation (by adding the factor k to the sharp surface), will be ( ) ( ) ( ) ( )   1 0 1 1 1 1 2 ln ln . plasma u C k c b u b d c b u d b    = − + − −   (6) Furthermore, the characteristic equation (1) needs to be revised because the form of equation (1) only applies to the symmetrical electrode shape between the active electrode and the passive electrode. At the same time, the Triangular Electrode on a Vertical Plate is an asymmetrical electrode configuration between the active and passive electrodes. We can try the form of the (I-V) characteristic equation through the following equation. ( ) 0 2 4. plasma i bC I V V V d  =− (7) Equation (7) is a form of the characteristic equation that is tried for the case of an electric asymmetric CCP, namely for the position of the active electrode, which is asymmetric to the position of the passive electrode. The difference that arises between the calculation of characteristics (I-V) from equation (1) for the CCP symmetric case and equation (5) for the CCP asymmetric case is a. The method of symmetrical multiplication of the electric current multiplier factor in the symmetric CCP case cannot be applied to the asymmetric CCP case because the corona electric current does not spread evenly to all parts of the active electrode tip but is only focused on the active electrode tip which has a sharp surface only. b. In the case of asymmetric CCP, the electric current multiplier factor k is inserted on the sharp part of the capacitance formulation's sharp electrode surface, referred to as the modified capacitance. c. The value of the multiplier factor k cannot be calculated using geometric concepts because it involves complex physical effects such as electrodynamic effects, electron winds, etc. The k value can only be calculated by a (I-V) characteristic graph program as a curve fitting effect, which physically shows the size of the corona discharge that occurs, or the large/small value of the discharge is determined by the considerable/small value of the k value. d. The radius of the outer cylinder R of the passive electrode in the symmetric CCP case in equation (1) can be replaced as the distance between the two electrodes in the asymmetric CCP case. III. DISCUSSION The current-voltage (I-V) characteristics equation of corona discharge cases in symmetric and asymmetric CCP equipment can be calculated using physical methods (via Maxwell's equations) or geometric methods (electrode dimensions and modified capacitance). This study touches on the geometric approach to calculating the current-voltage (I-V) characteristics of the DC corona plasma discharge case in air. It adopts the geometric method used in the CCP symmetric case and applies it to the CCP asymmetry case with a plane-serrated knife electrode configuration model. The position of the active electrode is vertical, and the position of the passive electrode is horizontally below the active electrode. Calculation of the (I-V) Characteristics of Corona Discharge with the Configuration Model of Triangular Electrode on a Vertical Plate IJMRA, Volume 08 Issue 11 November 2025 www.ijmra.in Page 5954 IV. CONCLUSIONS This research uses a plane-serrated knife configuration model to calculate plasma corona discharges' (I-V) characteristics. This calculation also uses a modified capacitance concept through a geometric approach. The physical or geometric approach method only calculates the approximate initial discharge curve from the (I-V) characteristic graph because the continuation curve of the (I-V) characteristic is quite difficult to predict due to the too complex physical problems in corona discharge events, which involve physical effects such as electrodynamics, electron wind, quantum, etc. The use of a modified capacitance model by generating an electric current multiplier k as a fitting curve is a relatively simple approach to calculating the (I-V) characteristics of a corona discharge, compared to a solution approach based on physical effects, which requires the use of Maxwell's equations or quantum solutions. REFERENCES 1) Kim, S., & Kim, C. 2021 Applications of Plasma-Activated Liquid in the Medical Field. 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