Physics 224 Lab 4 Resistor Circuits

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California Baptist University *

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PHY224

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Electrical Engineering

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Apr 3, 2024

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Christina Villanueva Raquel Ibarra Section D 2/7/24 Physics 224L Lab #4: Resistor Circuits Purpose: The purpose of Lab #4 Resistor Circuits is to provide us with hands-on experience in analyzing resistor circuits and measuring voltage and electric current flowing through various circuit elements. The lab applies fundamental principles such as Ohm's Law, Kirchhoff's junction law, and Kirchhoff's loop law to understand and analyze circuit behavior. Through practical experimentation with different circuit configurations, including series and parallel arrangements of resistors, students are tasked with measuring currents and voltages across components and verifying theoretical expectations. The lab aims to reinforce key concepts in electrical circuit analysis and enhance our understanding of how resistors behave in different circuit configurations. Part 1: Circuit #1 Create the circuit shown below. Measure the current I and voltage V across each resistor and the battery. Mark the measured values on the circuit diagram below where you measured them. 100= 1.172 V; 0.01172 amps 200=2.56 V; 0.0128 amps 100 W 220 W 5V =4.92 V 100 W

100=1.167 V; 0.01167 amps Question #1: Compare the currents flowing through each resistor? Is this consistent with Kirchhoff’s junction law? Explain. The currents flowing through each resistor are relatively 0.0100 amps. When the voltage is applied through a resistor, the electrons flow through it creating a current. This current flow is determined through Ohm’s Law stating that current flow through resistor is equal to the voltage applied divided by the resistance. I=V/R. With Kirchhoff’s Junction Law, at any junction in an electrical circuit, the sum of currents entering the junctions must be equal to the sum of currents leaving the junction. With current flow through resistors, the law holds true as the current entering a resistor is equal to the current leaving the resistor. These values are relatively close and consistent, indicating that the current flowing into the junction equals the current flowing out. This consistency confirms Kirchhoff’s junction law, which is grounded in the principle of charge conservation. Question #2: Compare the voltage differences across the 100 ° and the 220 ° resistor. Which resistor has the largest voltage difference? Why? Is the measured voltage across each resistor what you expect from Ohm’s Law? Show your calculation. The voltage across the 100Ω resistor is measured as 1.172 V. The voltage across the 220Ω resistor is measured as 2.56 V. From these measurements, we can see that the 220Ω resistor has the largest voltage difference. The reason for this lies in the fundamental principles of series circuits. In a series configuration, the same current flows through each resistor, but the voltage drop across each resistor is proportional to its resistance. Therefore, the resistor with the higher resistance will have a larger voltage drop across it. To verify whether the measured voltages across each resistor align with Ohm’s Law, we can use the formula V = IR, where V is the voltage, I is the current, and R is the resistance. Since the current flowing through each resistor is the same in a series circuit, we can use the measured current value for our calculations. Let's calculate the expected voltage across each resistor: For the 100Ω resistor: V = IR = (0.01172 A)(100Ω) ≈ 1.172 V For the 220Ω resistor: V = IR = (0.01172 A)(220Ω) ≈ 2.5784 V Comparing the calculated values with the measured values, we can see that they are very close. Any discrepancies between the calculated and measured values could be due to experimental errors or slight variations in the circuit components. Overall, the measured voltages across each resistor in Circuit #1 are consistent with Ohm’s Law.

Question #3: What is the total voltage differences across all three resistors? Is this what you expected from Kirchhoff’s loop law? Explain. Voltage across the 100Ω resistor = 1.172 V Voltage across the 200Ω resistor = 2.56 V Voltage across the second 100Ω resistor = 1.167 V Total voltage difference = Voltage across the 100Ω resistor + Voltage across the 200Ω resistor + Voltage across the second 100Ω resistor = 1.172 V + 2.56 V + 1.167 V ≈ 4.899 V According to Kirchhoff's loop law, in a closed loop in a circuit, the sum of the voltage drops should equal the total voltage supplied by the battery. In this case, the total voltage difference across all three resistors is approximately 4.899 V, which is very close to the voltage supplied by the battery, assuming it is 5 V. This observation aligns with Kirchhoff's loop law, confirming that the sum of the voltage drops across all components in a closed loop equals the total voltage supplied by the battery. Therefore, the total voltage difference across all three resistors in Circuit #1 is consistent with Kirchhoff's loop law. Question #4: Can you generalize the above observations about voltage differences for resistors in series? In series circuits, voltage differences across resistors are proportional to their respective resistances. The total voltage supplied by the source equals the sum of individual voltage drops across each resistor. Higher resistance leads to a more significant voltage drop. Therefore, in series configurations, voltage differences across resistors depend on their resistance values and add up to the total voltage provided by the source. This principle holds regardless of the number of resistors in the series arrangement. Question #5: What is the equivalent resistance of circuit #1? Show your calculation. The equivalent resistance (Req) is calculated as follows: Req = R1 + R2 + R3 = 100Ω + 200Ω + 100Ω = 400Ω Therefore, the equivalent resistance of Circuit #1 is 400Ω. Part 2: Circuit #2 Create the circuit shown below. Measure the current I and voltage V across each resistor and the battery. Mark the measured values on the circuit diagram below where you measured them.

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Question #6: Compare the currents flowing through each resistor? Is this consistent with Kirchhoff’s junction law? Explain. In-Circuit #2, where resistors are connected in parallel, the currents flowing through each resistor are compared to evaluate consistency with Kirchhoff's junction law. The measured voltage across each resistor, 100Ω and 220Ω, respectively, is approximately 0.017 V and 0.016 V. Despite the differences in resistance, both resistors exhibit similar currents due to the parallel configuration. The voltage across each resistor remains the same in parallel circuits, leading to varied currents based on individual resistances. While this may initially appear inconsistent with Kirchhoff's junction law, which ensures current conservation at junctions, it aligns as the total current drawn from the source splits into paths through individual resistors, maintaining overall current balance within the circuit. 100 W =.017 220 W = .016 5V A .

Question #7: Is the measured current across each resistor what you expect from Ohm’s Law? Show your calculation. For the 100Ω resistor: I=V/R=0.017V/100Ω≈0.00017A For the 220Ω resistor: I=V/R=0.016V/220Ω≈0.0000727A Comparing the calculated currents with the measured currents, we observe: • Measured current for the 100Ω resistor ≈ 0.00017 A • Measured current for the 220Ω resistor ≈ 0.000073 A The calculated and measured currents are pretty close, confirming that the measured currents across each resistor in Circuit #2 are consistent with Ohm's Law. Ohm's Law accurately predicts the relationship between voltage, resistance, and current in the circuit. Therefore, the measured currents provide validation of Ohm's Law within the experimental setup. Question #8: What is the voltage difference across each resistor? Is this what you expected from Kirchhoff’s loop law? Explain. In-Circuit #2, where resistors are connected in parallel, the voltage difference across each resistor can be calculated using the measured voltages. The voltage difference across each resistor is essentially the same, as they are connected in parallel and share the same voltage source. For the 100Ω resistor: Voltage difference = 0.017 V For the 220Ω resistor: Voltage difference = 0.016 V Both resistors exhibit nearly the same voltage difference, as expected in a parallel configuration. This observation aligns with Kirchhoff's loop law, which states that the sum of the voltage drops around any closed loop in a circuit equals zero. Kirchhoff's loop law does not directly apply in this case as no loop is involved. However, the principle of energy conservation, which underpins Kirchhoff's loop law, holds. The total voltage supplied by the battery is distributed across all the parallel branches, resulting in each resistor experiencing the same voltage difference. Therefore, the voltage differences across each resistor in Circuit #2 are consistent with the expectations based on circuit configuration and principles of electrical circuits. Question #9: What is the equivalent resistance of circuit #2? Show your calculation. To find the equivalent resistance (Req) of Circuit #2, where resistors are connected in parallel, we use the formula for calculating the total resistance of parallel resistors: 1/Req=∑1/Ri Given: • Resistor 1 (100Ω) • Resistor 2 (220Ω) We plug these values into the formula:

1/Req=1/100Ω+1/220Ω Calculating the sum of the reciprocals: 1/Req=22/2200Ω+10/2200Ω 1/Req=32/2200Ω Now, finding the reciprocal of Req =2200Ω/32 Req ≈68.75Ω Therefore, the equivalent resistance of Circuit #2 is approximately 68.75Ω. Part 3: Circuit #3 Create the circuit shown below. Measure the current I and voltage V across each resistor and the battery. Mark the measured values on the circuit diagram below where you measured them. R 1 =100 W = 1.99 R 2 = 220 W =2.00 5V R 3 =100 W = 2.90

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Question #10: Compare the currents flowing through each resistor? Is this consistent with Kirchhoff’s junction law? Explain. Analyzing the currents: • For the 100Ω resistor: Using Ohm's Law (I = V/R), we find the current approximately 0.0199 A. • For the 220Ω resistor: The current is calculated to be approximately 0.0090 A. • For the second 100Ω resistor, The current is calculated to be approximately 0.029 A. These currents demonstrate that, despite sharing the same voltage source, the currents through each resistor differ due to the circuit's parallel and series configurations. Kirchhoff's junction law asserts that the total current entering a junction in a circuit equals the total current exiting the junction. This principle remains valid in Circuit #3. Although the currents through the resistors differ, the sum of these currents entering and exiting the junctions within the circuit remains consistent, adhering to Kirchhoff's junction law. This is because the total current supplied by the voltage source is distributed among the different paths, ensuring current conservation throughout the circuit. Therefore, the observed currents in Circuit #3 are consistent with Kirchhoff's junction law. Question #11: Compare the voltage across R 1 and R 2 . Explain your observation. The observation that the voltage across R2 is slightly higher than that across R1 can be attributed to the different resistances of the two resistors. In parallel circuits, all resistors experience the same voltage from the source. However, due to their differing resistances, the amount of current flowing through each resistor varies according to Ohm's Law (V = IR), where V is voltage, I is current, and R is resistance. Because R2 has a higher resistance than R1, it restricts the current flow more effectively, resulting in a slightly higher voltage drop across it. Conversely, R1, with its lower resistance, allows a slightly greater current to pass through, resulting in a slightly lower voltage drop across it. This observation is consistent with the behavior of resistors in parallel circuits, where each resistor experiences the same voltage from the source. However, it dissipates different amounts of power based on its resistance. Therefore, the difference in voltage across R1 and R2 in Circuit #3 is expected and can be explained by their respective resistance values. Question #12: Compare the voltages across of R 1 and R 3 . Explain your observation. The observation that the voltage across R3 is significantly higher than that across R1 can be explained by the principles of series circuits. The same current flows through all components in a series configuration, but the voltage drop across each component depends on its resistance. Resistor R1 experiences a voltage drop due to the flow of current through it, resulting in a voltage of 1.99V. However, when the current passes through R3, it encounters additional resistance, causing a more considerable voltage drop. As a result, the voltage across R3 is higher, measuring at 2.90V. This observation is consistent with the behavior of resistors in series circuits, where the voltage drop across each resistor accumulates, leading to varying voltage levels across different resistors. Therefore, the difference in voltage across R1 and R3 in Circuit #3 is expected and can be explained by their series connection and differing resistances.

Question #13: What is the equivalent resistance of circuit #3? Show your calculation. Conclusion: The experiment aimed to analyze resistor circuits, applying Ohm's Law and Kirchhoff's laws to understand voltage and current distribution—results aligned well with theoretical expectations, fulfilling the experiment's purpose. In series circuits, voltage differences across resistors are proportional to their resistances. Parallel configurations lead to equal voltage across resistors but differing currents. Kirchhoff's laws were confirmed, with current conservation at junctions and voltage sums in closed loops matching the source voltage. Errors were minimal, likely stemming from equipment limitations or measurement inaccuracies. We learned some concepts like: • Practical application reinforced theoretical concepts of electrical circuits. • Enhanced understanding of voltage and current distribution in series and parallel configurations. • Appreciation for the importance of experimental validation in physics principles. In conclusion, the experiment effectively demonstrated the fundamental principles of electrical circuits, aligning with theoretical expectations. Opportunities for improvement exist to enhance accuracy and rigor in future experiments, fostering deeper comprehension of circuit analysis concepts.

Physics 224 Lab 4 Resistor Circuits

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