PHYSICSKIRCHHOFFS

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University of Texas, San Antonio *

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1631

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Electrical Engineering

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Dec 6, 2023

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docx

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Analysis of Kirchhoff’s Rules Lab Table 1 (5 points) ΔV__100 V_ _____ R(Ω) i m (A) i t (A) % Error R1 50 0.43 0.4349 1.13 R2 10 2.17 2.176 2.07 R3 30 2.61 2.609 0.05 1. Using Kirchhoff’s Rules, construct enough mathematically independent equations to solve for the current of each resistor. Then calculate the % error between your measured and theoretical values for the current of each resistor. You MUST use Kirchhoff’s Rules and show work to receive any credit . (15 points) 1

Table 2 (5 points) ΔV1____50_____ R(Ω) i m (A) i t (A) % Error R1 20 1.49 1.486 0.27 R2 50 0.41 0.405 1.23 R3 75 0.27 0.27 0.0 R4 25 0.81 0.811 0.12 2. Using Kirchhoff’s Rules, construct enough mathematically independent equations to solve for the current of each resistor. Then calculate the % error between your measured and theoretical values for the current of each resistor. You MUST use Kirchhoff’s Rules and show work to receive any credit . (15 points) 3

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Table 3 (5 points) ΔV1_ 50____ ______ R(Ω) i m (A) i t (A) % Error R1 10 1.63 1.629 0.06 R2 25 0.45 0.4494 0.13 R3 40 0.84 0.8425 0.30 R4 100 0.34 0.3371 0.86 R5 50 0.45 0.4494 0.13 3. Using Kirchhoff’s Rules, construct enough mathematically independent equations to solve for the current of each resistor. Then calculate the % error between your measured and theoretical values for the current of each resistor. You MUST use Kirchhoff’s Rules and show work to receive any credit . (15 points) 5

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Table 4 (5 points) ΔV1__50__ ___ _______ ΔV2___20_____ _____ R(Ω) i m (A) i t (A) % Error R1 10 0.57 0.5714 0.25 R2 25 0.57 0.5714 0.25 R3 50 0.60 0.6 0.0 4. Using Kirchhoff’s Rules, construct enough mathematically independent equations to solve for the current of each resistor. Then calculate the % error between your measured and theoretical values for the current of each resistor. You MUST use Kirchhoff’s Rules and show work to receive any credit . (15 points) 7

5. In the theory section of this worksheet, detailed explanations are given as to how Kirchhoff’s Laws are connected to conservation laws. Briefly, and in your own words, summarize each of these explanations. (10 points) The two principles of conservation are the conservation of energy and the conservation of charge. The conservation of energy law states that in a closed system, total energy is the same. The conservation of charge law states that in a closed system, the net charge is the same. These laws are the basis of Kirchhoff’s Rules, the Loop Rule, and the Junction Rule. The Loop Rule states that the net potential difference (i.e., the voltage of the battery), around a closed system will sum to a value of zero. The charged particles within the circuit never gain nor lose potential energy throughout the circuit, no matter which path the particle takes. The particle also never loses energy throughout the circuit. The Junction Rule states that the current flowing in and out of a junction in the circuit will be equal. The amount of charge in the particles never changes, therefore the amount current entering the junction will be the same amount of current exiting the junction. Both rules show the conservation of energy and charge within a close circuit system because neither the net current nor net potential difference changes throughout the circuit. 6. Did our experiments support the theory? Justify your answer. (10 points) Our experiments did support the theory, because there was little to no percent error between the current measured and the theoretical currents calculated with Kirchhoff’s Rules. The amount of current flowing through all four circuit variations in the experiments each conserved the current flowing in and out of junctions, for example in circuit 4, through resistor 1 (R1), the measured current was 0.57 A. When solving for current using Kirchhoff’s rules, the theoretical current was calculated to be 0.5714 A. To calculate the theoretical current, the derived equations summed to zero, following the Loop Rule. 8