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R4-92, Vs1-22V, VS2=11V, 40. wwww R3 1 + Usl R₁ 4 Vs2 R₁ www Va + wwwww R₂ se nodal analysis to calculate the node voltages. Give the voltage va in

R4-92, Vs1-22V, VS2=11V, 40. wwww R3 1 + Usl R₁ 4 Vs2 R₁ www Va + wwwww R₂ se nodal analysis to calculate the node voltages. Give the voltage va in

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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For the circuit below with the given reference node and  R1=10 Ω , R2=8 Ω , R3=9 Ω , R4=9 Ω , vs1=22V, vs2=11V, Use nodal analysis to calculate the node voltages.  Give the voltage va in Volts.

 

**Title: Nodal Analysis of a Electrical Circuit** **Introduction:** This section provides an analysis of an electrical circuit using nodal analysis, a systematic method for determining the voltage at each node in a circuit. Below is the description and schematic representation of the given circuit. **Circuit Description:** - **Resistors:** - \( R_1 = 10 \Omega \) - \( R_2 = 8 \Omega \) - \( R_3 = 9 \Omega \) - \( R_4 = 9 \Omega \) - **Voltage Sources:** - \( v_{s1} = 22V \) - \( v_{s2} = 11V \) **Schematic Diagram:** - The schematic features a circuit with two voltage sources and four resistors. - \( v_{s1} \) is connected in series with resistor \( R_3 \). - \( v_{s2} \) is connected parallel to resistors \( R_4 \) and \( R_2 \), with the negative terminal grounded. - A controlled voltage source, \( 4v_a \), depends on the voltage across \( R_1 \). - \( R_4 \) and \( R_1 \) are in series, and their junction is the node of interest where \( v_a \) is measured. - The circuit features a diamond-shaped dependent source \( 4v_a \) in the branch with the described resistors and voltage sources. **Analysis Task:** - Use nodal analysis to determine the voltage \( v_a \) at the given node. - Calculate all node voltages by applying Kirchhoff's current laws (KCL) and the relationships defined by Ohm's law. **Instructions:** 1. **Define Nodes:** - Analyze the circuit by identifying all nodes. Choose the reference node (ground) and set it at 0V. 2. **Apply KCL:** - At each non-reference node, apply Kirchhoff’s Current Law (KCL) to set up equations based on current entering and leaving a node. 3. **Solving Equations:** - Use the relationships \( V = IR \) and solve the nodal equations to find \( v_a \). This analysis will provide insight into voltage distribution across circuit components based on the configuration and component values.
Transcribed Image Text:**Title: Nodal Analysis of a Electrical Circuit** **Introduction:** This section provides an analysis of an electrical circuit using nodal analysis, a systematic method for determining the voltage at each node in a circuit. Below is the description and schematic representation of the given circuit. **Circuit Description:** - **Resistors:** - \( R_1 = 10 \Omega \) - \( R_2 = 8 \Omega \) - \( R_3 = 9 \Omega \) - \( R_4 = 9 \Omega \) - **Voltage Sources:** - \( v_{s1} = 22V \) - \( v_{s2} = 11V \) **Schematic Diagram:** - The schematic features a circuit with two voltage sources and four resistors. - \( v_{s1} \) is connected in series with resistor \( R_3 \). - \( v_{s2} \) is connected parallel to resistors \( R_4 \) and \( R_2 \), with the negative terminal grounded. - A controlled voltage source, \( 4v_a \), depends on the voltage across \( R_1 \). - \( R_4 \) and \( R_1 \) are in series, and their junction is the node of interest where \( v_a \) is measured. - The circuit features a diamond-shaped dependent source \( 4v_a \) in the branch with the described resistors and voltage sources. **Analysis Task:** - Use nodal analysis to determine the voltage \( v_a \) at the given node. - Calculate all node voltages by applying Kirchhoff's current laws (KCL) and the relationships defined by Ohm's law. **Instructions:** 1. **Define Nodes:** - Analyze the circuit by identifying all nodes. Choose the reference node (ground) and set it at 0V. 2. **Apply KCL:** - At each non-reference node, apply Kirchhoff’s Current Law (KCL) to set up equations based on current entering and leaving a node. 3. **Solving Equations:** - Use the relationships \( V = IR \) and solve the nodal equations to find \( v_a \). This analysis will provide insight into voltage distribution across circuit components based on the configuration and component values.
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