Experiment 32_ Kirchoff's Rules

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Texas A&M University, Kingsville *

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1102

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Electrical Engineering

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Dec 6, 2023

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Experiment 32: Kirchhoff's Rules Giovanna Garza Group Members: Alexandra Salas, Gabriela Cruz, Kaytelyn Malacara, Marilyn Camacho Texas A&M International University PHYS 1102 4L1 SU23 - General Physics II Lab Dr. Cesar Contreras July 24, 2023

I. Objective: The purpose of this experiment is to analyze a two-loop circuit using Kirchhoff's Rules for circuits in order to identify the circuit's currents and the electric potential differences around each loop. After the experiment, you should be able to examine and recognize junctions and branches in circuits. You can better understand Kirchhoff's Rules for charge and energy conservation by carrying out the experiment. II. Theory: Gustav Kirchhoff created methods for the two loop system analysis. Numerous resistance networks that could not be directly evaluated using Ohm's law or simplified to series-parallel combinations could now be analyzed. The first rule of Kirchhoff is that any junction's algebraic sum of currents is zero (I = 0). The second rule of Kirchhoff is that a closed loop's voltage changes have an algebraic total of zero (V = 0). Kirchhoff's Junction Rule states that the sum of the currents entering a junction must be zero. The conservation of electric charge is the foundation of the junction rule. Kirchhoff's Loop Rule states that the sum of the potential differences (voltages) in any given loop (including electromotive forces and resistive electrical components) must be zero. In other words, the total charges entering a junction must equal the total charges leaving the junction. The conservation of energy within a circuit serves as the foundation for the loop rule. The total amount of potential increases and drops equals each other when a charge revolves a loop. III. Equipment: The equipment necessary to do this experiment include:

● Ammeter (0 to 10/100/1000 mA) ● Voltmeter (0 to 5/25 V) ● Two batteries or voltage supplies (6 V and 12 V) ● Two single-pole, single-throw (SPST) switches ● Composition resistors, 2-W rating (100, 150, 220, 330, 470, 680, 1000 ohms) ● Connecting wires IV. Procedure: 1. Install the two loop circuit by setting it up as shown by the instructor. Adjust each power supply as closely as possible to the values. 2. Let the professor check the circuits before beginning the procedure and make sure to leave the switches open. 3. Once the circuits have been checked, measure and record the operating value (V1 and V2) in data table 1. 4. Open the switches only temporarily. Connect one of the branches to the ammeter in series. After measuring and recording the branch current, close the switches before opening them. 5. Repeat procedure 4 for each of the branches. 6. Calculate the theoretical values for the circuit's branch currents. Use the measured values for the batteries V1 and V2 and the provided values for the resistors in the analysis (procedure 1). 7. Find the percent error between the measured branch current values and the calculated theoretical values.

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V. Results and Discussion: For our results, we estimated the theoretical value using a matrix approach. After determining the theoretical value of the currents using the matrix findings, we calculated the percent error by comparing our observed value to the theoretical value. It was discovered that the calculated percent error had large percent values. This might have occurred because the connecting wires were not put properly, there were connection problems, or the ammeter was malfunctioning in this experiment. The resistances and voltages we used to conduct this experiment may have had an impact on the outcomes. VI. Conclusion: After the experiment, it is simpler to comprehend how to apply either of Kirchhoff's principles to multiloop circuits, understand how Kirchhoff's rules relate to the conservation of charge and energy, and explain how circuit branches and junctions differ from one another. It is also simpler to understand Kirchhoff's laws and how they apply to various circuits after setting up the multiloop circuit. It is also clear to figure out how the resistances and voltages in these kinds of circuits are affected after calculating theoretical values and comparing them to those we had gathered from the experiment.

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