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Use the node-voltage method to find the voltages shown, v1, v2, and v3.

Use the node-voltage method to find the voltages shown, v1, v2, and v3.

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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Use the node-voltage method to find the voltages shown, v1, v2, and v3.

**Node-Voltage Method Circuit Analysis** The diagram presented is a circuit schematic for applying the node-voltage method to find the voltages \( v_1 \), \( v_2 \), and \( v_3 \). **Circuit Components and Layout:** 1. **Voltage Source:** - A 40 V voltage source is present on the left side of the circuit. 2. **Resistors:** - A 12 Ω resistor is connected parallel to the 40 V source. - A 25 Ω resistor connects nodes \( v_1 \) and \( v_3 \). - A 20 Ω resistor connects nodes \( v_1 \) and \( v_2 \). - A 40 Ω resistor connects nodes \( v_2 \) and \( v_3 \). 3. **Current Sources:** - A 5 A current source is connected upwards between the nodes \( v_1 \) and \( v_2 \). - A 7.5 A current source is connected downward between node \( v_2 \) and the ground (node \( v_3 \)). 4. **Nodes:** - The circuit has three nodes where voltages need to be calculated: - **Node \( v_1 \):** Connected to the 12 Ω, 25 Ω, and 20 Ω resistors. - **Node \( v_2 \):** Connected to the 20 Ω, 40 Ω resistors and the current sources. - **Node \( v_3 \):** Serves as the reference node (ground) and is connected to the 25 Ω and 40 Ω resistors. **Objective:** To find the node voltages \( v_1 \), \( v_2 \), and \( v_3 \) using the node-voltage method. The problem requires understanding the topology and applying Kirchhoff's Current Law (KCL) at each node.
Transcribed Image Text:**Node-Voltage Method Circuit Analysis** The diagram presented is a circuit schematic for applying the node-voltage method to find the voltages \( v_1 \), \( v_2 \), and \( v_3 \). **Circuit Components and Layout:** 1. **Voltage Source:** - A 40 V voltage source is present on the left side of the circuit. 2. **Resistors:** - A 12 Ω resistor is connected parallel to the 40 V source. - A 25 Ω resistor connects nodes \( v_1 \) and \( v_3 \). - A 20 Ω resistor connects nodes \( v_1 \) and \( v_2 \). - A 40 Ω resistor connects nodes \( v_2 \) and \( v_3 \). 3. **Current Sources:** - A 5 A current source is connected upwards between the nodes \( v_1 \) and \( v_2 \). - A 7.5 A current source is connected downward between node \( v_2 \) and the ground (node \( v_3 \)). 4. **Nodes:** - The circuit has three nodes where voltages need to be calculated: - **Node \( v_1 \):** Connected to the 12 Ω, 25 Ω, and 20 Ω resistors. - **Node \( v_2 \):** Connected to the 20 Ω, 40 Ω resistors and the current sources. - **Node \( v_3 \):** Serves as the reference node (ground) and is connected to the 25 Ω and 40 Ω resistors. **Objective:** To find the node voltages \( v_1 \), \( v_2 \), and \( v_3 \) using the node-voltage method. The problem requires understanding the topology and applying Kirchhoff's Current Law (KCL) at each node.
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