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the values of v1 and v2

the values of v1 and v2

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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On this question, I used the node voltage method to formulate two equations to solve for v1 and v2.

I then used Cramer's rule to solve for the values of v1 and v2. My issue is with v2. I checked the back of my book, and v1 is correct, it should be 48V. v2, however, should be 64V. I got 39V.

Where did I go wrong?

**Educational Content: Node-Voltage Method in Circuit Analysis** **Circuit Description and Problem Statement:** A circuit diagram is presented in the problem statement, accompanied by the following tasks: 1. Find the voltage, \( V_1 \). 2. Determine how much power is delivered to the circuit by the 80V source. 3. Calculate the power absorbed by the 5A source. **Node Analysis:** 1. **Node \( V_1 \):** - Equations: - \( (V_1 - V_2) / 4 + 5 = 0 \) - Rearranging gives: - \( V_1 / 4 = V_2 / 4 + 5 \) - \( V_1 = V_2 + 20 \) 2. **Node \( V_2 \):** - Equations: - \( V_2 / 20 + V_2 / 80 + (V_2 - V_1) / 4 = 0 \) - Simplifying: - \( V_2 / 10 + (V_2 - V_1) / 4 = 0 \) - Multiply through to eliminate fractions: - \( 2V_2 + 5V_2 - 5V_1 = 0 \) - Rearranging gives: - \( 7V_2 - 5V_1 = 0 \) 3. **System of Equations:** - \( V_1 - V_2 = 20 \) - \( 4V_2 - V_1 / 2 = 12 \) - Rearranged: - \( 8V_2 - V_1 = 24 \) (Equation 1) - \( V_1 - V_2 = 20 \) (Equation 2) 4. **Matrix Representation:** \[ \begin{bmatrix} 1 & -1 \\ -1 & 8 \end{bmatrix} \begin{bmatrix} V_1 \\ V_2 \end{bmatrix} = \begin{bmatrix} 20 \\ 24 \end{bmatrix} \] 5. **Solving the Matrix:** - Determinant \( \Delta = (1)(8) - (-1
Transcribed Image Text:**Educational Content: Node-Voltage Method in Circuit Analysis** **Circuit Description and Problem Statement:** A circuit diagram is presented in the problem statement, accompanied by the following tasks: 1. Find the voltage, \( V_1 \). 2. Determine how much power is delivered to the circuit by the 80V source. 3. Calculate the power absorbed by the 5A source. **Node Analysis:** 1. **Node \( V_1 \):** - Equations: - \( (V_1 - V_2) / 4 + 5 = 0 \) - Rearranging gives: - \( V_1 / 4 = V_2 / 4 + 5 \) - \( V_1 = V_2 + 20 \) 2. **Node \( V_2 \):** - Equations: - \( V_2 / 20 + V_2 / 80 + (V_2 - V_1) / 4 = 0 \) - Simplifying: - \( V_2 / 10 + (V_2 - V_1) / 4 = 0 \) - Multiply through to eliminate fractions: - \( 2V_2 + 5V_2 - 5V_1 = 0 \) - Rearranging gives: - \( 7V_2 - 5V_1 = 0 \) 3. **System of Equations:** - \( V_1 - V_2 = 20 \) - \( 4V_2 - V_1 / 2 = 12 \) - Rearranged: - \( 8V_2 - V_1 = 24 \) (Equation 1) - \( V_1 - V_2 = 20 \) (Equation 2) 4. **Matrix Representation:** \[ \begin{bmatrix} 1 & -1 \\ -1 & 8 \end{bmatrix} \begin{bmatrix} V_1 \\ V_2 \end{bmatrix} = \begin{bmatrix} 20 \\ 24 \end{bmatrix} \] 5. **Solving the Matrix:** - Determinant \( \Delta = (1)(8) - (-1
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