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Use a A-to-Y transformation to find the voltages and v2 in the circuit in Fig. P3.58. με αποτ Figure P3.58 15 Ω Π Το 1Ω 10 Ω + 24 V vΣ 40 Ω + + U2 § 50 Ω απο

Use a A-to-Y transformation to find the voltages and v2 in the circuit in Fig. P3.58. με αποτ Figure P3.58 15 Ω Π Το 1Ω 10 Ω + 24 V vΣ 40 Ω + + U2 § 50 Ω απο

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
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Calculate the value of voltages v 1 and v 2 in the given circuit using without PSIPCE.
 
 
 
### Δ-to-Y Transformation in Circuit Analysis In this lesson, we will use a Δ-to-Y (Delta-to-Wye) transformation to find the voltages \( v_1 \) and \( v_2 \) in the given circuit, as illustrated in Figure P3.58. #### Figure P3.58: Circuit Diagram The circuit consists of: - A 24V voltage source. - A series connection of resistors on the top branch: 1Ω, 15Ω, and 10Ω. - A 40Ω resistor connected in the middle of the circuit. - A 50Ω resistor in the bottom right corner. - Two nodes where voltages \( v_1 \) and \( v_2 \) are to be determined. The resistors and their connections are described as follows: - The 1Ω resistor is connected between the negative terminal of the voltage source and node \( v_1 \). - The 15Ω resistor creates a series connection from the top of the 1Ω resistor. - The 10Ω resistor connects the output of the series at the right node to node \( v_2 \). - The 40Ω resistor is linked between node \( v_1 \) and node \( v_2 \). - A 50Ω resistor is connected in series with node \( v_2 \). To solve for \( v_1 \) and \( v_2 \), follow these steps: 1. Recognize the Δ configuration in the resistor network. 2. Transform the Δ configuration into an equivalent Y configuration. 3. Apply Ohm's Law and Kirchhoff's circuit laws to find the voltages at the required nodes. By understanding these steps and utilizing the Δ-to-Y transformation, complex resistor networks can be simplified, making it easier to analyze the circuit and determine the node voltages \( v_1 \) and \( v_2 \).
Transcribed Image Text:### Δ-to-Y Transformation in Circuit Analysis In this lesson, we will use a Δ-to-Y (Delta-to-Wye) transformation to find the voltages \( v_1 \) and \( v_2 \) in the given circuit, as illustrated in Figure P3.58. #### Figure P3.58: Circuit Diagram The circuit consists of: - A 24V voltage source. - A series connection of resistors on the top branch: 1Ω, 15Ω, and 10Ω. - A 40Ω resistor connected in the middle of the circuit. - A 50Ω resistor in the bottom right corner. - Two nodes where voltages \( v_1 \) and \( v_2 \) are to be determined. The resistors and their connections are described as follows: - The 1Ω resistor is connected between the negative terminal of the voltage source and node \( v_1 \). - The 15Ω resistor creates a series connection from the top of the 1Ω resistor. - The 10Ω resistor connects the output of the series at the right node to node \( v_2 \). - The 40Ω resistor is linked between node \( v_1 \) and node \( v_2 \). - A 50Ω resistor is connected in series with node \( v_2 \). To solve for \( v_1 \) and \( v_2 \), follow these steps: 1. Recognize the Δ configuration in the resistor network. 2. Transform the Δ configuration into an equivalent Y configuration. 3. Apply Ohm's Law and Kirchhoff's circuit laws to find the voltages at the required nodes. By understanding these steps and utilizing the Δ-to-Y transformation, complex resistor networks can be simplified, making it easier to analyze the circuit and determine the node voltages \( v_1 \) and \( v_2 \).
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