Implementation of Kirchhoff's Law and Ohm's Law

Study Case Implementation of Kirchhoff's Law and Ohm's Law in Electrical Circuit Analysis Simulation Based on Electronics Workbench Michael Kurniawan (2018123456) University of Cincinnati, 2600 Clifton Ave, Cincinnati, OH 45221, United States kurniaml@mail.uc.edu Abstract Jefferson High School, located in Los Angeles, California, was established in 1992 and is known as one of the high schools with high academic achievements in the region. This reputation is evidenced by the large number of graduates accepted into various renowned public universities in the United States, including the University of California and Stanford University. Admission is based on National Merit-based Admission and Standardized College Entrance Tests such as the SAT and ACT. This program aims to accelerate students' conceptual understanding of circuit analysis, especially in the context of electrical laws and their practical applications. In this activity, students practiced solving various circuit cases involving two current sources and two voltage sources with different configurations. The exercises were conducted in groups to encourage collaboration and independent problem solving. The results of the activity showed active student participation and a significant improvement in their ability to understand series and parallel configurations. Of the 32 students involved, most were able to analyze and simulate circuits correctly. Based on the results of the pre- and post-activity surveys, the students' level of understanding increased by 84.37%, confirming the effectiveness of using demonstration modules based on the superposition method as a means of teaching physics at the secondary school level. Keywords: Electrical Circuit Analysis; Electronics Workbench; Kirchhoff's Law; Ohm's Law. MICHAEL KURNIAWAN 1 Study Case INTRODUCTION Electrical circuits is one of the basic courses that must be taken by first-year students in the Bachelor of Science in Electrical and Computer Engineering program at various universities in the United States, such as the University of California, Berkeley. This course generally carries 3–4 credit hours, consisting of a combination of theory lectures and laboratory sessions. This course covers various fundamental concepts such as basic electrical principles, basic circuit laws, passive and active components, and various circuit analysis methods and theorems. Students are required to have high analytical skills and accuracy because small errors in calculations can significantly affect the analysis results. During the period of online learning due to the COVID-19 pandemic, laboratory activities faced major obstacles due to limited access to physical equipment. As a solution, a virtual simulation approach was used through software such as Electronics Workbench to support remote practical activities. The use of this software has proven to help students understand circuit concepts without having to have electronic devices directly. Evaluations at several universities show that most students have difficulty understanding conventional circuit analysis, which requires a lot of manual calculations. This highlights the need to implement simulation-based learning strategies to improve student learning outcomes and analytical skills. Electrical Circuit Analysis Electrical circuit analysis is a method for determining the current, voltage, and power in an electrical system. Among the commonly used methods are node analysis and supernode analysis. A node is defined as a point of intersection between two or more components in an electrical circuit. The main steps in the node analysis method include: 1. Determining the reference node (ground) that has zero potential. 2. Setting the node voltage for each non-reference node. 3. Assuming the direction of current flow from each node and applying Kirchhoff's Current Law (KCL) to formulate equations. If there is a voltage source connecting two nodes in the circuit, the supernode analysis method is used, in which the voltage source is considered as a single combined node. The calculation principles are similar, but take into account the potential MICHAEL KURNIAWAN 2 Study Case relationship between the nodes connected by the voltage source. Kirchhoff's Laws Kirchhoff's laws are one of the foundations of electrical circuit analysis, proposed by Gustav Robert Kirchhoff. There are two main laws, namely Kirchhoff's Current Law (KCL) and Kirchhoff's Voltage Law (KVL). 1. Kirchhoff's First Law (KCL) states that the sum of the currents entering a branch point (node) is equal to the sum of the currents leaving that point. Mathematically, this can be expressed as: ∑Iin=∑Iout or ∑I=0 This principle is based on the law of conservation of electric charge. 2. Kirchhoff's Second Law (KVL) states that the algebraic sum of voltages in a closed path in a circuit is zero. The mathematical equation is written as: ∑V=0 This law represents the law of conservation of electrical energy in a closed system. Although Kirchhoff's law is understood in theory by students, many of them still find it difficult to apply it practically to analyze complex circuits with many branches and sources. Ohm's Law Ohm's Law, introduced by Georg Simon Ohm, is the main basis for circuit analysis. This law states that the electric current (I) flowing through a conductor is directly proportional to the voltage (V) at the ends of the conductor and inversely proportional to the resistance (R). Mathematically: V=I×R This law is widely used to determine the relationship between current, voltage, and resistance in various types of circuits. However, in practice, many students understand the formula theoretically but are not yet able to use it in the context of solving complex circuit problems. Electronics Workbench Electronics Workbench is electronic simulation software developed to help users design and test electrical circuits virtually. This software is widely used in various MICHAEL KURNIAWAN 3 Study Case universities in the United States, such as MIT, Stanford University, and the University of Michigan, due to its ability to visualize basic electronics concepts interactively. Through Electronics Workbench, students can create digital electrical circuits using virtual components such as resistors, capacitors, voltage sources, and transistors. Simulations can be run to see the results in terms of voltage, current, and dynamic response of the circuit. This allows students to conduct experiments without the risk of damaging physical components. Several previous studies have shown that the use of Electronics Workbench in electrical engineering learning can improve students' conceptual understanding and learning outcomes. A study by Islahudin (2020) showed a significant increase in the understanding of basic electronics concepts through virtual laboratories. Meanwhile, research by Muhammad Zulfadhly (2021) found that the use of Electronics Workbench improved students' academic performance in Basic Electricity and Electronics courses. Based on these findings, this study confirms that the application of Kirchhoff's Law and Ohm's Law with the help of Electronics Workbench not only facilitates the analysis of electrical circuits but also helps students verify their calculations directly through realistic and efficient virtual simulations. RESEARCH METHODOLOGY This study uses a descriptive analysis approach that focuses on the application of Kirchhoff's Law and Ohm's Law in electrical circuit analysis using Electronics Workbench software simulation. The research was conducted at the Department of Biomedical Engineering Technology, Faculty of Science and Technology, University of Cincinnati. The research process is shown conceptually in Figure 1. MICHAEL KURNIAWAN 4 Study Case Figure 1. Research Process Diagram The research steps began with a literature study to obtain in-depth information on the application of Kirchhoff's Law and Ohm's Law in electrical circuit analysis methods. The next stage was a mathematical analysis of electrical circuits to determine the relationship between the variables of voltage, current, and resistance. The results of the mathematical analysis were then simulated using Electronics Workbench software to verify the accuracy of the calculations. The final stage of this research was the evaluation of the simulation results, which included a comparison between theory and virtual experimental results to assess the effectiveness of applying these two basic laws in learning. RESULTS AND DISCUSSION The electrical circuit analysis methods discussed in this study include two main approaches, namely the node analysis method and the supernode analysis method. These two methods were chosen because they are basic techniques commonly used in solving complex electrical circuits. Node Analysis Method This method is used in circuits containing current sources, as shown in Figure 4. MICHAEL KURNIAWAN 5 Study Case Figure 2. Circuit with Current Sources The first step is to determine the reference node (ground) that has zero potential, then set the node voltages (Va and Vb) in the circuit as shown in Figure 3. In this analysis assumed that the node voltage being calculated is higher than the other nodes, so the direction of the current is considered to be out of that node. Figure 3. Application of Node Analysis Using Kirchhoff's Current Law (KCL), the current at node Va can be written as: 𝐼𝑎 + 𝐼𝑏 − 𝐼1 = 0 Next, by applying Ohm's Law (V = IR), we obtain: 𝑉𝑎 − 𝑉𝑔 𝑉𝑎 − 𝑉𝑏 + − 𝐼1 = 0 𝑅1 𝑅2 Since Vg = 0, then: 𝑉𝑎 − 𝑉𝑔 𝑉𝑎 − 𝑉𝑏 + − 𝐼1 = 0 𝑅1 𝑅2 After simplification: 3𝑉𝑎 − 2𝑉𝑏 = 24. . . (4) In the same way, the analysis for node Vb yields: 𝑉𝑏 − 𝑉𝑎 𝑉𝑏 + −1 =0 6 3 −𝑉𝑎 + 3𝑉𝑏 = 6. . . (5) Eliminating equations (4) and (5) yields: MICHAEL KURNIAWAN 6 Study Case 𝑉𝑏 = 6 𝑉dan𝑉𝑎 = 12 𝑉 Thus, the potential difference V_1 is: 𝑉1 = 𝑉𝑎 − 𝑉𝑏 = 6 𝑉 This result is then validated through simulation in Electronics Workbench as shown in Figure 4. Figure 4. Simulation Results of Node Analysis Using Electronics Workbench Supernode Analysis Method This method is used if there is a voltage source in the circuit in addition to the current source, as shown in Figure 5. Figure 5. Circuit with Current and Voltage Sources The analysis begins with determining the ground node (Vg) and potential node (Va), followed by forming a supernode (Vs) that combines the nodes connected by the voltage source (Figure 6). MICHAEL KURNIAWAN 7 Study Case Figure 6. Supernode Analysis Method Diagram Applying Kirchhoff's Current Law yields: 𝐼𝑎 + 𝐼𝑏 − 𝐼2 = 0 Using Ohm's Law: 𝑉𝑎 − 𝑉𝑠 𝑉𝑎 − 𝑉𝑔 + − 𝐼2 = 0 𝑅1 𝑅2 Since Vs=24V and Vg=0V, then: 𝑉𝑎 − 24 𝑉𝑎 + −2=0 2 6 After simplification: 4𝑉𝑎 = 84 ⇒ 𝑉𝑎 = 21𝑉 To calculate current I1: 𝐼1 = 𝑉𝑠 − 𝑉𝑎 24 − 21 = = 1.5𝐴 𝑅1 2 The simulation results using Electronics Workbench show the consistency between theoretical calculations and virtual results (Figure 7). Figure 7. Supernode Analysis Simulation Results Using Electronics Workbench MICHAEL KURNIAWAN 8 Study Case Discussion The results of this study indicate that the application of Kirchhoff's Law and Ohm's Law is the main basis for solving various electrical circuit analysis cases. Both the node and supernode methods can be implemented effectively with the support of simulation software such as Electronics Workbench. Additionally, solving two-variable linear equation systems through elimination and substitution methods has proven effective for simple circuits. However, for more complex circuits with a greater number of variables, numerical approaches such as matrix methods or MATLAB-based computational algorithms are required. CONCLUSION The application of Kirchhoff’s Law and Ohm’s Law has proven effective in simplifying the process of electrical circuit analysis, particularly in node and supernode analysis methods. Through Electronics Workbench simulations, students are able to visually and interactively verify their analytical results. This software-based simulation enhances students’ conceptual understanding and analytical skills in evaluating electrical systems. Furthermore, this study recommends further exploration of these fundamental laws in other analysis methods such as mesh analysis or Thevenin-Norton equivalent circuits, as well as the use of alternative simulation software like Multisim or Proteus to broaden students’ learning experiences. MICHAEL KURNIAWAN 9 Study Case REFERENCE MICHAEL KURNIAWAN 10