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a) RTotal = b) |Total = ON EN R₁ Figure (2) 3) The circuit in Figure (2) has values of, V = 40 Volt, R₁ = 40 2, R₂ = 80 2 and R3 = 80 02. Calculate the following values for the circuit. c) ₁ = , 12 =_ Verify, 11 + 12 + 13 = Total R₂ 13= R3

a) RTotal = b) |Total = ON EN R₁ Figure (2) 3) The circuit in Figure (2) has values of, V = 40 Volt, R₁ = 40 2, R₂ = 80 2 and R3 = 80 02. Calculate the following values for the circuit. c) ₁ = , 12 =_ Verify, 11 + 12 + 13 = Total R₂ 13= R3

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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### Educational Content on Series and Parallel Circuits #### Circuit Diagram Description The diagram, labeled as Figure (2), shows a simple electrical circuit with a voltage source (V) connected to three resistors (R1, R2, and R3). The resistors are connected in a parallel configuration. #### Problem 3 Analyze the circuit in Figure (2) with the given parameters: - **Voltage (V):** 40 Volts - **Resistor R1:** 40 Ω - **Resistor R2:** 80 Ω - **Resistor R3:** 80 Ω **Tasks:** a) Calculate the total resistance (\( R_{\text{Total}} \)) of the circuit. \[ R_{\text{Total}} = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \] b) Determine the total current (\( I_{\text{Total}} \)) flowing through the circuit. \[ I_{\text{Total}} = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \] c) Calculate the current through each resistor (\( I_1 \), \( I_2 \), \( I_3 \)). - \( I_1 = \_\_\_\_\_\_\_\_\_ \) - \( I_2 = \_\_\_\_\_\_\_\_\_ \) - \( I_3 = \_\_\_\_\_\_\_\_\_ \) **Verification:** Ensure that the sum of currents is equal to the total current: \( I_1 + I_2 + I_3 = I_{\text{Total}} \). #### Problem 4 Consider the same circuit in Figure (2) with altered resistor values: - **Voltage (V):** 40 Volts - **Resistor R1:** 40 Ω - **Resistor R2:** 60 Ω - **Resistor R3:** 120 Ω **Objective:** Calculate \( R_{\text{Total}} \) and \( I_{\text{Total}} \) to verify that: \[ I_1 + I_2 + I_3 = I_{\text{Total}} \] This exercise involves understanding how to analyze a parallel circuit, applying Ohm’s Law, and calculating the equivalent resistance. Ensure consistent verification that the sum of the individual currents through each resistor equals the total current.
Transcribed Image Text:### Educational Content on Series and Parallel Circuits #### Circuit Diagram Description The diagram, labeled as Figure (2), shows a simple electrical circuit with a voltage source (V) connected to three resistors (R1, R2, and R3). The resistors are connected in a parallel configuration. #### Problem 3 Analyze the circuit in Figure (2) with the given parameters: - **Voltage (V):** 40 Volts - **Resistor R1:** 40 Ω - **Resistor R2:** 80 Ω - **Resistor R3:** 80 Ω **Tasks:** a) Calculate the total resistance (\( R_{\text{Total}} \)) of the circuit. \[ R_{\text{Total}} = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \] b) Determine the total current (\( I_{\text{Total}} \)) flowing through the circuit. \[ I_{\text{Total}} = \_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ \] c) Calculate the current through each resistor (\( I_1 \), \( I_2 \), \( I_3 \)). - \( I_1 = \_\_\_\_\_\_\_\_\_ \) - \( I_2 = \_\_\_\_\_\_\_\_\_ \) - \( I_3 = \_\_\_\_\_\_\_\_\_ \) **Verification:** Ensure that the sum of currents is equal to the total current: \( I_1 + I_2 + I_3 = I_{\text{Total}} \). #### Problem 4 Consider the same circuit in Figure (2) with altered resistor values: - **Voltage (V):** 40 Volts - **Resistor R1:** 40 Ω - **Resistor R2:** 60 Ω - **Resistor R3:** 120 Ω **Objective:** Calculate \( R_{\text{Total}} \) and \( I_{\text{Total}} \) to verify that: \[ I_1 + I_2 + I_3 = I_{\text{Total}} \] This exercise involves understanding how to analyze a parallel circuit, applying Ohm’s Law, and calculating the equivalent resistance. Ensure consistent verification that the sum of the individual currents through each resistor equals the total current.
Two resistors in parallel: \[ R_{\text{Total}} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2}} = \frac{R_1 \times R_2}{R_1 + R_2} \] Three resistors in parallel: \[ R_{\text{Total}} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}} \] --- 1) The circuit in Figure (1) has \( V_{\text{supply}} = 40 \) Volts, \( R_1 = 30\Omega \) and \( R_2 = 60 \Omega \). a) Calculate the total resistance for this parallel circuit. \[ R_{\text{Total}} = \underline{\quad \quad \quad \quad \quad \quad \quad \quad \quad} \] b) Calculate \( I_1 \) and \( I_2 \), and verify if \( I_{\text{Total}} = I_1 + I_2 \). \[ I_{\text{Total}} = \underline{\quad \quad \quad \quad \quad \quad \quad \quad \quad} \] c) Calculate the total current for this circuit. \[ I_{\text{Total}} = \underline{\quad \quad \quad \quad \quad \quad \quad \quad \quad} \] Figure (1): The diagram shows a parallel circuit with a voltage supply (\( V_{\text{supply}} \)), and two resistors, \( R_1 \) and \( R_2 \), connected in parallel. --- 2) If the values for the circuit in Figure (1) are changed as follows: \( V_{\text{supply}} = 48 \) Volts, \( R_1 = 40 \Omega \) and \( R_2 = 60 \Omega \). Calculate \( R_{\text{Total}} \), \( I_{\text{Total}} \), \( I_1 \), and \( I_2 \) for the new values of the circuit.
Transcribed Image Text:Two resistors in parallel: \[ R_{\text{Total}} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2}} = \frac{R_1 \times R_2}{R_1 + R_2} \] Three resistors in parallel: \[ R_{\text{Total}} = \frac{1}{\frac{1}{R_1} + \frac{1}{R_2} + \frac{1}{R_3}} \] --- 1) The circuit in Figure (1) has \( V_{\text{supply}} = 40 \) Volts, \( R_1 = 30\Omega \) and \( R_2 = 60 \Omega \). a) Calculate the total resistance for this parallel circuit. \[ R_{\text{Total}} = \underline{\quad \quad \quad \quad \quad \quad \quad \quad \quad} \] b) Calculate \( I_1 \) and \( I_2 \), and verify if \( I_{\text{Total}} = I_1 + I_2 \). \[ I_{\text{Total}} = \underline{\quad \quad \quad \quad \quad \quad \quad \quad \quad} \] c) Calculate the total current for this circuit. \[ I_{\text{Total}} = \underline{\quad \quad \quad \quad \quad \quad \quad \quad \quad} \] Figure (1): The diagram shows a parallel circuit with a voltage supply (\( V_{\text{supply}} \)), and two resistors, \( R_1 \) and \( R_2 \), connected in parallel. --- 2) If the values for the circuit in Figure (1) are changed as follows: \( V_{\text{supply}} = 48 \) Volts, \( R_1 = 40 \Omega \) and \( R_2 = 60 \Omega \). Calculate \( R_{\text{Total}} \), \( I_{\text{Total}} \), \( I_1 \), and \( I_2 \) for the new values of the circuit.
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