Help **Problem P2.58: Node Voltage Analysis**Objective: Solve for the node voltages shown in Figure P2.58.**Circuit Description:**The circuit diagram consists of the following elements:- **Current Sources:** - A 1 A current source connected on the left side of the circuit, pointing upwards. - A 2 A current source connected on the right side of the circuit, pointing downwards.- **Resistors:** - A 5 Ω resistor is connected directly to the 1 A current source. - A 15 Ω resistor is connected between nodes \( v_1 \) and the middle node. - A 10 Ω resistor is connected at the top branch, near a dependent voltage source, labeled as \( v_x \). - Another 10 Ω resistor is connected between the middle node and node \( v_2 \). - A 5 Ω resistor is connected directly to the 2 A current source.- **Voltage Sources:** - A dependent voltage source labeled \( 2v_x \).**Node Descriptions:**- **Node \( v_1 \):** - Connections: 1 A current source, 5 Ω resistor, 15 Ω resistor.- **Middle Node:** - Connections: 15 Ω resistor, 10 Ω resistor (top branch), dependent voltage source \( 2v_x \).- **Node \( v_2 \):** - Connections: 10 Ω resistor (bottom branch), 2 A current source, 5 Ω resistor.**Ground Connection:** - The ground is indicated at the bottom center of the circuit. **Task:**- Use node voltage analysis to determine the voltages at nodes \( v_1 \) and \( v_2 \).**Figure P2.58:**The diagram provides a clear depiction of the circuit with all components labeled for reference in solving the problem.

The basic nodal problem is solved below.

Answered: *P2.58. Solve for the node voltages…

*P2.58. Solve for the node voltages shown in Figure P2.58. 1A(1 VI - 1592 www 592 10 92 M- Vx + 10 92 www 20x Figure P2.58 V2 522 12A

Delmar's Standard Textbook Of Electricity

7th Edition

ISBN:9781337900348

Author:Stephen L. Herman

Publisher:Stephen L. Herman

Chapter7: Parallel Circuits

Section: Chapter Questions

Problem 4PP: Using the rules for parallel circuits and Ohmslaw, solve for the missing values....

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Nodal Analysis

In the analysis of any electric circuit, nodal analysis is the method of determining the potential difference or voltage between different nodes in an electric circuit. A node is a point where two or more branches connect each other. In the nodal analysis, the voltages are determined in the terms of branch currents. The nodal analysis is also known as the node voltage method or branch current method. The nodal analysis method is one of the several applications of Kirchhoff's Current Law (KCL).

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**Problem P2.58: Node Voltage Analysis**

Objective: Solve for the node voltages shown in Figure P2.58.

**Circuit Description:**

The circuit diagram consists of the following elements:

- **Current Sources:**
- A 1 A current source connected on the left side of the circuit, pointing upwards.
- A 2 A current source connected on the right side of the circuit, pointing downwards.

- **Resistors:**
- A 5 Ω resistor is connected directly to the 1 A current source.
- A 15 Ω resistor is connected between nodes \( v_1 \) and the middle node.
- A 10 Ω resistor is connected at the top branch, near a dependent voltage source, labeled as \( v_x \).
- Another 10 Ω resistor is connected between the middle node and node \( v_2 \).
- A 5 Ω resistor is connected directly to the 2 A current source.

- **Voltage Sources:**
- A dependent voltage source labeled \( 2v_x \).

**Node Descriptions:**

- **Node \( v_1 \):**
- Connections: 1 A current source, 5 Ω resistor, 15 Ω resistor.

- **Middle Node:**
- Connections: 15 Ω resistor, 10 Ω resistor (top branch), dependent voltage source \( 2v_x \).

- **Node \( v_2 \):**
- Connections: 10 Ω resistor (bottom branch), 2 A current source, 5 Ω resistor.

**Ground Connection:**
- The ground is indicated at the bottom center of the circuit.

**Task:**
- Use node voltage analysis to determine the voltages at nodes \( v_1 \) and \( v_2 \).

**Figure P2.58:**

The diagram provides a clear depiction of the circuit with all components labeled for reference in solving the problem.

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