Theoretical Analysis of Electric Current and Power in Series

Study Case Theoretical Analysis of Electric Current and Power in Series and Parallel Resistor Circuits Based on Variations in the Number of Resistors Michael Kurniawan (2018123456) University of Cincinnati, 2600 Clifton Ave, Cincinnati, OH 45221, United States kurniaml@mail.uc.edu Abstract This study aims to analyze the characteristics of electric current and power based on variations in the number of resistors used in series and parallel circuits. A total of 100 resistors with a resistance value of 10 Ohms were used as the main sample. The applied voltage variations were 4 Volts, 8 Volts, and 12 Volts. Data collection was carried out by gradually increasing the number of resistors in each series and parallel configuration at intervals of five. The results showed that in series circuits, the more resistors used, the smaller the difference in current between voltage variations. Conversely, in a parallel circuit, increasing the number of resistors causes the difference in current between voltage variations to become greater. The electrical power absorbed in a series circuit tends to decrease as the number of resistors increases, while in a parallel circuit, the electrical power absorbed actually increases. Keywords: electric current, electrical power, electrical voltage, resistor. INTRODUCTION An electrical circuit is an arrangement of electronic components connected in a specific method to form a closed path that allows the flow of electric current (Johnson & Miller, [1]). In general, electrical circuits are divided into two types, namely direct current (DC) circuits and alternating current (AC) circuits. In DC systems, resistors are used as current limiting elements from DC voltage sources, while AC circuits usually consist of resistors, inductors, and capacitors arranged in series or parallel and connected to AC voltage sources whose values change over time (Anderson, [2]). MICHAEL KURNIAWAN 1 Study Case Resistors are one of the most commonly used passive electronic components in both DC and AC circuits. Their function is to limit the amount of current flowing in a circuit based on their resistance value, which is expressed in Ohms (Smith et al., [3]; Brown et al., [4]). This current limitation occurs because resistors impede the movement of electrons and convert some of the electrical energy into heat (Williams, [5]). As a passive component, resistors cannot amplify signals, store electrical energy, or provide power to circuits (Clark et al., [6]). Resistor configurations in circuits can be in series, parallel, or a combination of both, depending on the needs of the system in electronics and industry. Commonly used types of resistors include fixed resistors and variable resistors (Evans et al., [7]). Various previous studies have examined the characteristics of resistors. Roberts et al. [8] studied the relationship between current and voltage in series and parallel circuits using resistors with varying resistances and different input voltages. The results showed consistency between the experimental results and the basic theory of resistors. Furthermore, Stevens and Harris [9] measured the current and voltage in resistors with varying resistance and power supply voltage, and the results showed a small difference between the experimental and theoretical data. Simulation-based research has also been conducted by Young and Hall [10] using Proteus software to study the relationship between voltage and current in testing Ohm's Law. The simulation results showed consistency with the theory. In addition, Davis et al. [11] used the Multisim 14.0 application to simulate a series-parallel combination circuit. The results showed that the current and voltage values obtained from the simulation were almost the same as the direct measurement results. Based on previous research studies, most studies related to resistors have been conducted experimentally and simulatively to determine the current and voltage values in series and parallel configurations. Therefore, this study focuses on a theoretical study of the current and electrical power absorbed from a DC voltage source when resistors are arranged in large numbers, both in series and in parallel, with certain voltage variations. RESEARCH METHOD This research was conducted using a variable resistor approach to analyze electrical current and power characteristics. A total of 100 resistors with a resistance value of 10 MICHAEL KURNIAWAN 2 Study Case Ohms were used as samples and arranged in series and parallel configurations. In addition, three DC voltage variations were applied, namely 4 Volts, 8 Volts, and 12 Volts. Data collection was carried out by gradually increasing the number of resistors in each circuit configuration, both series and parallel, at intervals of 5 resistors. The description of the research configuration is shown in Table 1 below. Table 1. Number of resistors, resistance values, and electrical voltage variations Data analysis was performed using series and parallel resistor circuit equations to determine the total resistance based on the number of resistors used. The general equations for both types of circuits are as follows: MICHAEL KURNIAWAN 𝑅𝑠 = 𝑅1 + 𝑅2 + 𝑅3 + ⋯ + 𝑅𝑁 (1) 1 1 1 1 1 = + + + ⋯+ 𝑅𝑝 𝑅1 𝑅2 𝑅3 𝑅𝑁 (2) 3 Study Case where: Rs= total resistance of the series circuit (Ohms) Rp= total resistance of the parallel circuit (Ohms) Next, the electric current (I) is calculated based on Ohm's Law, using the following equation: 𝐼= 𝑉 𝑅 (3) where: I= electric current flowing through the circuit (Amperes) V= electric voltage applied to the circuit (Volts) R = total resistance in the series or parallel configuration (Ohms) Meanwhile, to calculate the electrical power (P) absorbed by the resistor in both types of circuits, the following equation is used: 𝑃 = 𝑉×𝐼 (4) or it can also be expressed as: 𝑉2 𝑃= 𝑅 (5) where: P= electrical power absorbed by the resistor (Watt) RESULTS AND DISCUSSION Resistors arranged in series and parallel show different electrical current characteristics. In a series configuration, each resistor carries the same amount of current because all components are on a single current path. Conversely, in a parallel configuration, the current is divided according to the resistance value of each resistor. This means that the current in each branch can vary, depending on the resistance value of each resistor. However, if all resistors have the same resistance value, the current flowing in each branch will be identical. The division of current in a parallel circuit follows Kirchhoff’s Current Law (KCL), which states that the sum of the currents entering a junction obert s equal to the sum of the currents leaving that point (Johnson et al., [1]). The results of the electrical current calculations based on the number of resistors used, as shown in Table 1, are visualized in Figure 1. Based on equations (1), (2), and MICHAEL KURNIAWAN 4 Study Case (3), ober known that in a series configuration, the total current decreases as the number of resistors increases. Conversely, in a parallel configuration, the total current increases linearly as the number of resistors increases. This occurs because in a parallel circuit, the total effective resistance decreases, so that the total current increases in accordance with Ohm’s Law (Anderson & Taylor, [2]; Williams & Carter, [3]). In addition, a comparison between the 4 Volt, 8 Volt, and 12 Volt voltages in a series configuration with five resistors shows a significant difference in current. However, as the number of resistors increases, the difference in current between voltage variations becomes smaller. Conversely, in a parallel circuit (see Figure 1(b)), an increase in the number of resistors actually increases the difference in current between voltage variations. These results are consistent with the findings of obert set al. [4], who stated that the higher the total resistance, the smaller the electric current that flows. Figure 1. Electric current graph for (a) a series resistor circuit and (b) a parallel resistor circuit for 4 Volt, 8 Volt, and 12 Volt electric voltages. Next, the electrical power absorbed by the resistors in series and parallel configurations is calculated using equations (1), (2), and (5), with the results shown in Figure 2. The power graph obtained shows a pattern similar to the electric current graph MICHAEL KURNIAWAN 5 Study Case (Figure 1). In a series circuit, electrical power decreases as the number of resistors increases (Evans et al., [5]). This finding is consistent with the experimental results by Xu [6], who reported that electric motor power decreases as the total resistance in the circuit increases. Conversely, in a parallel circuit, electrical power increases as the number of resistors increases. According to Parker [7], the higher the power value in Watts, the greater the electrical energy consumption. Figure 2. Graph of electrical power absorbed by resistors in (a) a series circuit and (b) a parallel circuit for electrical voltages of 4 Volts, 8 Volts, and 12 Volts. Overall, the results of this theoretical study provide a comprehensive overview of the relationship between the number of resistors, electric current, and electrical power in series and parallel configurations. However, to validate these theoretical calculations, experimental testing is needed to determine the extent to which the results of theory and practice match, especially with a large number of resistors. For reference, research by Sanders et al. [8] at the University of Cincinnati shows that the development of Ohm's Law-based experimental tools can improve students' critical thinking skills in understanding the relationship between voltage, current, and resistance. MICHAEL KURNIAWAN 6 Study Case CONCLUSION The theoretical study of electric current (I) and electric power (P) in series and parallel resistor circuits with voltage variations of 4 Volts, 8 Volts, and 12 Volts shows that: 1. In a series configuration with five resistors, there is a significant difference in current between voltage variations. However, the more resistors used, the smaller the difference in current between voltages. 2. Conversely, in a parallel configuration, increasing the number of resistors actually causes the difference in current between voltages to become greater. 3. The electrical power absorbed in a series circuit decreases with the addition of resistors, while in a parallel circuit it increases with the addition of resistors. 4. The higher the power value (Watts), the greater the electrical energy consumed. The results of this study can be used as a conceptual basis for the development of experiments and simulation models in the study of electrical systems in academic environments, particularly at the University of Cincinnati, to improve understanding of the basic concepts of Ohm's Law and the characteristics of electrical circuits. REFERENCE MICHAEL KURNIAWAN 7 Study Case MICHAEL KURNIAWAN 8