Comparison of the Accuracy of Simulation Results

Study Case Comparison of the Accuracy of Simulation Results from Five Electronic Applications in Wheatstone Bridge Circuit Analysis Michael Kurniawan (2018123456) University of Cincinnati, 2600 Clifton Ave, Cincinnati, OH 45221, United States kurniaml@mail.uc.edu Abstract Kirchhoff's laws are the main foundation in the analysis of complex electrical circuits, covering the principles of current conservation (Law I) and voltage conservation (Law II). This study discusses the application of these two laws to Wheatstone bridge circuits using a theoretical approach and digital simulation. Kirchhoff's First Law states that the sum of currents entering a branch point is equal to the sum of currents leaving it, while Kirchhoff's Second Law states that the algebraic sum of voltages in a closed loop is zero. These two principles are important foundations in the analysis of unbalanced electrical circuits, where conventional series-parallel methods cannot be directly applied.This study uses five types of electronic simulators, namely Circuit Simulator Applet, Circuit Lab (C-Lab), Circuit Wizard, PhET, and TinkerCAD, to compare the simulation results with manual (theoretical) calculations. The results show that Wheatstone bridge circuits can be categorized into two main conditions: balanced and unbalanced, which are distinguished by the values of VAB and IAB. The greater the value of VAB, the faster the voltage fluctuations occur and the more unstable the system becomes. This simple experiment confirms the validity of Kirchhoff's Law as the main analytical tool for Wheatstone bridges, while also identifying practical limitations in its application through computer simulation. Keywords: Kirchhoff's Law, Wheatstone Bridge, Circuit Simulator Applet, C-Lab, Circuit Wizard, PhET, TinkerCAD. MICHAEL KURNIAWAN 1 Study Case INTRODUCTION Electrical circuits can have varying degrees of complexity, ranging from simple configurations to systems with multiple branches and components. To analyze complex systems, electrical engineers often apply simplification methods through circuit transformation. This technique allows complex circuits to be converted into simpler forms using a series of mathematical equations without altering their basic characteristics [1]. One example of a branched circuit commonly used in electrical analysis is the Wheatstone bridge (see Figure 1). Analysis of the Wheatstone bridge fundamentally refers to Kirchhoff's laws of current and voltage. A balanced condition is achieved when the cross product of the resistance values on the four arms of the circuit satisfies the following relationship: 𝑅1 𝑅3 = 𝑅2 𝑅𝑥 with R4=R_x. This principle allows the measurement of unknown resistances to be converted into simple mathematical calculations with a high degree of accuracy [2], [3]. Figure 1. Wheatstone bridge circuit. In basic laboratory experiments, a Wheatstone bridge can be constructed using resistors and a DC voltage source (power supply). This circuit is widely used to measure unknown resistance values [4] and is an important component in precision instrumentation systems [5]. Due to its ability to detect very small changes in resistance—down to the milliohm scale—the Wheatstone bridge is widely applied in modern technologies such as structural monitoring using strain gauges, medical diagnostic systems, thermistor-based temperature sensors, and precision calibration of electronic components [6]–[9]. MICHAEL KURNIAWAN 2 Study Case The basic concept of the Wheatstone bridge was first introduced by Samuel Hunter Christie in 1833 to measure electrical resistance, then refined by Sir Charles Wheatstone in 1843 by introducing the formula and circuit design that is known today [10]. Several previous studies have discussed Wheatstone bridge analysis [5], [11], [12]. However, unlike previous studies, this research integrates five electronic simulation platforms that have never been comprehensively compared in the context of Wheatstone bridge analysis: Circuit Simulator Applet, Circuit Lab (C-Lab), Circuit Wizard, PhET, and TinkerCAD. The theoretical calculation results are compared with the simulation output to assess the level of consistency. The following table displays the main characteristics of each simulator used in this study, both those that can be accessed online and those that can be installed locally on a computer [12], [13]. Table I. Comparison of Simulation Platforms RESEARCH METHODOLOGY The Wheatstone bridge circuit is a basic configuration of resistors used to detect very small changes in resistance, so it is widely used in various electronic sensor systems. This circuit is diamond-shaped and consists of five resistors — R1, R2, R3, R4, and R5, one of which (R5) is a resistor with a known resistance value. In general, this research method was carried out using two approaches: 1. Theoretical approach, which involved manual calculations based on Kirchhoff's law and Ohm's law. 2. Simulative approach, which involved using five simulator software programs to test the calculation results digitally. The main parameters observed in the experiment are the total current (I_Total), branch current (IAB), and voltage between points A and B (VAB). MICHAEL KURNIAWAN 3 Study Case This study uses two circuit configuration scenarios, namely: 1. Scenario I: Wheatstone circuit in a balanced condition. 2. Scenario II: Wheatstone circuit in an unbalanced condition. Both scenarios used five resistors and one DC voltage source, with component values shown in Table II and Table III, respectively. Scenario I refers to Figure 1, while scenario II uses the configuration in Figure 2. Figure 2. Wheatstone bridge circuit in a balanced state. If unbalanced, the configuration changes to a Star–Delta (Y–Δ) shape. Table II. Input Voltage (Vin) and Resistor Values for Balanced Circuits Table III. Input Voltage (Vin) and Resistor Values for Unbalanced Circuits The first step in the analysis is to determine whether the circuit is in a balanced or unbalanced state. This is determined by calculating the value of VAB. If VAB=0, then there is no potential difference between points A and B, which means that no current MICHAEL KURNIAWAN 4 Study Case flows through resistor R5 and the circuit is in a balanced state. The balanced condition can be expressed through Equation (1) [14]: 𝑅1 𝑅3 = 𝑅2 𝑅4 (1) By cross-multiplying, a simple relationship is obtained: 𝑅1 × 𝑅4 = 𝑅2 × 𝑅3 If both sides have the same value, the circuit is declared balanced. Conversely, if the results are not the same, the circuit is unbalanced. In a balanced condition, R5 is ignored because VAB=0. As an example of calculation: 𝑅1 × 𝑅4 = 𝑅2 × 𝑅3 = 18 Ω × 36 Ω = 24 Ω × 27 Ω 648 Ω = 648 Ω Since the results on both sides are the same, the circuit is declared balanced. Thus, the voltage between points A and B (VAB) can be calculated as: 𝑉𝐴 = 𝑅2 𝑅4 × 𝑉𝑖𝑛 , 𝑉𝐵 = × 𝑉𝑖𝑛 𝑅1 + 𝑅2 𝑅3 + 𝑅4 𝑉𝐴 = 24 36 × 12 = 6.86 𝑉, 𝑉𝐵 = × 12 = 6.86 𝑉 18 + 24 27 + 36 𝑉𝐴𝐵 = 𝑉𝐴 − 𝑉𝐵 = 0 𝑉 Since VAB=0, no current flows through branch R5. The total current of the circuit in a balanced condition can be calculated using Equation (2): 𝐼𝑇𝑜𝑡𝑎𝑙 = (𝑅1 + 𝑅2 ) × (𝑅3 + 𝑅4 ) × 𝑉𝑖𝑛 𝑅1 𝑅3 + 𝑅1 𝑅4 + 𝑅2 𝑅3 + 𝑅2 𝑅4 (2) Unbalanced Condition In an unbalanced condition, the value of VAB≠0, so additional calculations are needed to determine I_Total, IAB, and VAB. The first step is to find the total resistance (R_Total) using the Delta–Star (Δ–Y) transformation as follows: 1 1 1 = + 𝑅𝑌 𝑅1 + 𝑅2 𝑅3 + 𝑅4 𝑅𝑇𝑜𝑡𝑎𝑙 = 𝑅𝑌 + 𝑅5 𝐼𝑇𝑜𝑡𝑎𝑙 = 𝑉𝑖𝑛 (3) (4) (5) 𝑅𝑇𝑜𝑡𝑎𝑙 To determine the values of IAB and VAB when the circuit is unbalanced, a loop current analysis is performed using the two-loop elimination method: MICHAEL KURNIAWAN 5 Study Case Loop 1: (𝐼1 × 𝑅2 ) + (𝐼2 × 𝑅5 ) − [(𝐼 − 𝐼1 )𝑅1 ] = 0 18𝐼1 + 39𝐼2 − [0.478 − 𝐼1 ]13 = 0 31𝐼1 + 39𝐼2 = 6.214 Loop 2: (𝐼1 − 𝐼2 )𝑅4 − (𝐼 − 𝐼1 + 𝐼2 )𝑅3 − (𝐼2 × 𝑅5 ) = 0 (30𝐼1 − 30𝐼2 ) − (11.472 − 24𝐼1 + 24𝐼2 ) − (39𝐼2 ) = 0 54𝐼1 − 93𝐼2 = 11.472 From the elimination of the two equations, we obtain: I2=0.00402 A Therefore: IAB=0.00402 A The voltage between points A and B can be calculated as: 𝑉𝐴𝐵 = 𝐼𝐴𝐵 × 𝑅5 = 0.00402 × 39 = 0.15678 𝑉 Thus, this condition is categorized as unbalanced, because VAB≠0. RESULTS AND DISCUSSION The theoretical calculation results for balanced conditions and the verification results through simulation are shown in Table IV, Table V, and Table VI. Based on these results, the values of VAB and IAB are equal to zero (0), indicating that the system is in a balanced state. Meanwhile, the results of the analysis for unbalanced conditions, both theoretically and simulatively, are shown in Table VII, Table VIII, and Table IX, where the values of VAB and IAB are not equal to zero. This indicates a potential imbalance and current at point A–B. Some of the main findings from this experiment can be summarized as follows: 1. Balanced Condition. The circuit is declared balanced when VAB=0 and IAB=0. This occurs due to the equal resistance ratio between the left and right branches of the circuit. Since there is no potential difference between points A and B, no current flows through resistor R5, so the system is in a stable state and the resistor can be ignored. MICHAEL KURNIAWAN 6 Study Case 2. Unbalanced Condition. If VAB≠0 or IAB≠0, then the circuit is in an unbalanced condition. In this situation, current flows through R5, causing uneven current distribution on both branches of the bridge. This can be clearly observed through the simulation results, which show residual current and voltage at points A–B. 3. Relationship between Voltage Values and Stability. The greater the difference between VAB and IAB, the faster the current changes in the A–B path, causing the system to become unstable. Conversely, the smaller the value of VAB, the more stable the system becomes because the rate of current change is lower. 4. The Phenomenon of Static Current in Balanced Conditions. When VAB=0, electrons are in a static state without any charge transfer between points, so the system can be said to be in dynamic equilibrium. 5. Comparison of the Performance of Five Electronic Simulators. • Circuit Simulator Applet: This is a free web-based application with fairly accurate calculation results. However, its display is still limited because decimal values are only shown to one digit after the decimal point (for example, 7.28 V will automatically be rounded to 7.3 V). Nevertheless, the precision values can be seen in the results list at the bottom right of the user interface. • Circuit Lab (C-Lab): Provides high-accuracy simulations and an easy-to-use interface. However, the free version can only be used for a limited time and requires a paid version for long-term use. • TinkerCAD and PhET: Both are web-based, easily accessible without installation, and have intuitive visualizations. Components are easy to find, and the calculation results are very close to theory. • Circuit Wizard: This is offline software that produces simulation results most consistent with theoretical calculations. However, flexibility in arranging component positions is still limited. MICHAEL KURNIAWAN 7 Study Case A comparison of the performance, features, and ease of use of the five simulators is summarized in Table X, which covers aspects of accessibility (free or paid), accuracy of results, ease of use, and feature completeness. This assessment is based on direct experience during testing and therefore contains subjective elements from the user. Simulator Development Recommendations 1. Circuit Simulator Applet has complete features, but its component list does not include visual icons, so users must search manually. 2. TinkerCAD should add more flexible cable connection options and provide separate voltmeter and ammeter components for more efficient measurement. 3. Circuit Lab (C-Lab) is advised to provide free educational licenses to make it more accessible to students and teachers, given its potential as a medium for learning electrical engineering. 4. PhET needs to add an undo feature to correct errors without having to rebuild the entire circuit. 5. Circuit Wizard has a good interface, but component positioning restrictions make it difficult to precisely form diamond configurations such as Wheatstone bridges. Table IV. Calculation Results for IAB and VAB for Balanced Circuit 1 Vin & Resistor Value Circuit Simulator Applet Circuit Lab (C-Lab) 0A&0V 0A&0V Vin = 12 V R1 = 18Ω R2 = 24Ω R3 = 27Ω R4 = 36Ω R5 = 16Ω 0A&0V MICHAEL KURNIAWAN 8 Study Case Circuit Wizard PhET TinkerCAD 0A&0V 0A&0V 0A&0V Table V. Calculation Results for IAB and VAB for Balanced Circuit 2 Vin & Resistor Value Circuit Simulator Applet Circuit Lab (C-Lab) 0A&0V 0A&0V 0A&0V Circuit Wizard PhET TinkerCAD 0A&0V 0A&0V 0A&0V Vin = 9 V R1 = 33Ω R2 = 24Ω R3 = 22Ω R4 = 16Ω R5 = 15Ω MICHAEL KURNIAWAN 9 Study Case Table VI. Calculation Results for IAB and VAB for Balanced Circuit 3 Vin & Resistor Value Circuit Simulator Applet Circuit Lab (C-Lab) 0A&0V 0A&0V 0A&0V Circuit Wizard PhET TinkerCAD 0A&0V 0A&0V 0A&0V Vin = 6 V R1 = 10Ω R2 = 15Ω R3 = 10Ω R4 = 15Ω R5 = 20Ω Table VII. Calculation Results for IAB and VAB for Unbalanced Circuit 1 Vin & Resistor Value Circuit Simulator Applet Circuit Lab (C-Lab) 4,03 mA & 157,168 mV 4,03 mA & 157,2 mV Vin = 10 V R1 = 13Ω R2 = 18Ω R3 = 24Ω R4 = 30Ω R5 = 39Ω 0,00402 A & 0,15678 V MICHAEL KURNIAWAN 10 Study Case Circuit Wizard PhET TinkerCAD 4,01 mA & 156,41 mV 4 mA & 160 mV 4,03 mA & 157 mV Table VIII. Calculation Results for IAB and VAB of the Second Unbalanced Circuit Vin & Resistor Value Circuit Simulator Applet Circuit Lab (C-Lab) 0,009 A & 0,09 V 9,901 mA & 99,01 mV 9,901 mA & 99,01 mV Circuit Wizard PhET TinkerCAD 9,87 mA & 98,72 mV 10 mA & 100 mV 9,90 mA & 99,0 mV Vin = 10 V R1 = 20Ω R2 = 30Ω R3 = 40Ω R4 = 50Ω R5 = 10Ω MICHAEL KURNIAWAN 11 Study Case Table IX. Calculation Results for IAB and VAB of the Third Unbalanced Circuit Vin & Resistor Value Circuit Simulator Applet Circuit Lab (C-Lab) 0,03 A & 0,7 V 28,239 mA & 677,734 mV 28,24 mA & 677,7 mV Circuit Wizard PhET TinkerCAD 28,16 mA & 675,74 mV 30 mA & 680 mV 28,2 mA & 678mV Vin = 12 V R1 = 43Ω R2 = 33Ω R3 = 27Ω R4 = 36Ω R5 = 24Ω Table X. Comparison and Relevance of Five Simulators MICHAEL KURNIAWAN 12 Study Case CONCLUSION Based on the theoretical calculations and simulations, it can be concluded that the Wheatstone Bridge circuit has two main operational conditions, namely balanced and unbalanced. 1. In a balanced condition, the values of VAB and IAB are equal to zero (VAB=0, IAB=0), so resistor R5 can be ignored. No current flows through the middle branch, and the system is in a stable condition. 2. In an unbalanced condition, the values of VAB and IAB are not equal to zero (VAB≠0, IAB≠0), indicating that current flows through R5. This condition results in potential instability and current fluctuations at point A–B. The greater the value of VAB, the faster the current changes and the more unstable the system becomes. Conversely, the smaller the value of VAB, the more stable the system tends to be. Thus, both theoretical and simulation approaches have proven that Kirchhoff's law can be used effectively to analyze the stability and current distribution in a Wheatstone Bridge circuit, as well as provide strong validation between mathematical models and digital implementations. MICHAEL KURNIAWAN 13 Study Case REFERENCE MICHAEL KURNIAWAN 14