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Write the mesh-current equations for this circuit เวV + 212 M=4H THE 38.2 SA O 28H 23 Six $2.2

Write the mesh-current equations for this circuit เวV + 212 M=4H THE 38.2 SA O 28H 23 Six $2.2

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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### Mesh-Current Equations for the Given Circuit The provided circuit diagram consists of several components and connections, including: - **Voltage Source**: A 12V voltage source on the left side. - **Resistors**: - \(2 \, \Omega\) resistor at the top left. - \(5 \, \Omega\) resistor in the middle. - \(2 \, \Omega\) resistor on the far right. - **Inductors**: - \(1 \, H\) inductor and \(8 \, H\) inductor at the middle. - **Coupled Inductors**: The circuit indicates mutual inductance of \(M = 4 \, H\) between the two inductors. - **Current Source**: A \(5 \, A\) current source at the top right. - **Dependent Current Source**: A current source denoted as \(5i_x\), where \(i_x\) is the current through the \(8 \, \Omega\) resistor. #### Mesh Currents: - Loop 1: Mesh current \(I_1\) flows clockwise around the left mesh, including the voltage source and \(2 \, \Omega\) resistor. - Loop 2: Mesh current \(I_2\) flows clockwise around the middle mesh, through the \(1 \, H\) inductor and \(5 \, \Omega\) resistor. - Loop 3: Mesh current \(I_3\) flows clockwise around the right mesh, including the dependent current source \(5i_x\) and the \(2 \, \Omega\) resistor. #### Instructions for Writing Mesh-Current Equations: Follow these steps to form the mesh-current equations: 1. **Apply Kirchhoff’s Voltage Law (KVL)** to each loop: - **Loop 1**: Include the voltage contributions from the \(12 \, V\) source and resistances. - **Loop 2**: Consider the inductor and resistor in series and mutual inductance. - **Loop 3**: Consider the \(5 \, A\) source and dependent source \(5i_x\). 2. **Account for mutual inductance** where the inductors are coupled. 3. **Use controlling variables** (like \(i_x\)) for the dependent source where needed. 4. **Solve for unknown
Transcribed Image Text:### Mesh-Current Equations for the Given Circuit The provided circuit diagram consists of several components and connections, including: - **Voltage Source**: A 12V voltage source on the left side. - **Resistors**: - \(2 \, \Omega\) resistor at the top left. - \(5 \, \Omega\) resistor in the middle. - \(2 \, \Omega\) resistor on the far right. - **Inductors**: - \(1 \, H\) inductor and \(8 \, H\) inductor at the middle. - **Coupled Inductors**: The circuit indicates mutual inductance of \(M = 4 \, H\) between the two inductors. - **Current Source**: A \(5 \, A\) current source at the top right. - **Dependent Current Source**: A current source denoted as \(5i_x\), where \(i_x\) is the current through the \(8 \, \Omega\) resistor. #### Mesh Currents: - Loop 1: Mesh current \(I_1\) flows clockwise around the left mesh, including the voltage source and \(2 \, \Omega\) resistor. - Loop 2: Mesh current \(I_2\) flows clockwise around the middle mesh, through the \(1 \, H\) inductor and \(5 \, \Omega\) resistor. - Loop 3: Mesh current \(I_3\) flows clockwise around the right mesh, including the dependent current source \(5i_x\) and the \(2 \, \Omega\) resistor. #### Instructions for Writing Mesh-Current Equations: Follow these steps to form the mesh-current equations: 1. **Apply Kirchhoff’s Voltage Law (KVL)** to each loop: - **Loop 1**: Include the voltage contributions from the \(12 \, V\) source and resistances. - **Loop 2**: Consider the inductor and resistor in series and mutual inductance. - **Loop 3**: Consider the \(5 \, A\) source and dependent source \(5i_x\). 2. **Account for mutual inductance** where the inductors are coupled. 3. **Use controlling variables** (like \(i_x\)) for the dependent source where needed. 4. **Solve for unknown
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