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In the following circuit: a) What is the Vrs in this circuit? b) Find the Thevenin Equivalent Resistance from terminals a and b Using a Test Source 50 0 100 FF 250 6.51, 12 f a .b

In the following circuit: a) What is the Vrs in this circuit? b) Find the Thevenin Equivalent Resistance from terminals a and b Using a Test Source 50 0 100 FF 250 6.51, 12 f a .b

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
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THEVENINS theorem( NEED NEAT HANDWRITTEN SOLUTION ONLY OTHERWISE DOWNVOTE).

### Solving a Thevenin Equivalent Circuit Problem #### Problem Statement: In the following circuit: a) What is the \( V_{Th} \) in this circuit? b) Find the Thevenin Equivalent Resistance from terminals a and b using a Test Source. #### Circuit Diagram: The diagram depicts an electrical circuit with the following components and connections: - A 50 Ω resistor is connected in series (leftmost path). - A 10 Ω resistor is connected in parallel with a 5 Ω resistor. - There is a dependent current source \( 6.5 I_x \) where \( I_x \) represents the current through the 5 Ω resistor. - The bottom right branch consists of a 25 Ω resistor. - Terminals labeled "a" and "b" are present (with terminal "a" connected after the 12 Ω resistor in the parallel branch and terminal "b" grounded on the lower end). \[ \begin{array}{c} \text{a} \\ \hspace{-4mm}| \\ \hspace{-4mm}| \\ \hspace{-4mm}\rightleftarrows \, 12 \, \Omega \\ 10 \, \Omega \\ \parallel \\ 5 \, \Omega \\ \hspace{-6mm}\updownarrows \, 6.5 \, I_x \\ 50 \, \Omega \\ \vert \\ \hspace{2mm}\text{b} \end{array} \] #### Steps to Solve: 1. **Determine \( V_{Th} \):** - Calculate the open-circuit voltage across terminals a-b. - Use appropriate circuit analysis techniques to understand how the voltage is distributed across components. 2. **Calculate Thevenin Equivalent Resistance \( R_{Th} \):** - Introduce a test source (voltage or current) across terminals a-b. - Use the electrical response (current or voltage) to determine how resistances combine. - Consider both series and parallel combinations and the effect of the dependent current source. ##### Detailed Diagram Analysis: The circuit analysis would typically involve: - Kirchhoff’s Voltage Law (KVL) - Kirchhoff’s Current Law (KCL) - Ohm's Law - Techniques such as Mesh Analysis or Nodal Analysis may be deployed to simplify and solve complex networks. ### Educational Focus: Understanding and solving Thevenin equivalent circuits is vital for
Transcribed Image Text:### Solving a Thevenin Equivalent Circuit Problem #### Problem Statement: In the following circuit: a) What is the \( V_{Th} \) in this circuit? b) Find the Thevenin Equivalent Resistance from terminals a and b using a Test Source. #### Circuit Diagram: The diagram depicts an electrical circuit with the following components and connections: - A 50 Ω resistor is connected in series (leftmost path). - A 10 Ω resistor is connected in parallel with a 5 Ω resistor. - There is a dependent current source \( 6.5 I_x \) where \( I_x \) represents the current through the 5 Ω resistor. - The bottom right branch consists of a 25 Ω resistor. - Terminals labeled "a" and "b" are present (with terminal "a" connected after the 12 Ω resistor in the parallel branch and terminal "b" grounded on the lower end). \[ \begin{array}{c} \text{a} \\ \hspace{-4mm}| \\ \hspace{-4mm}| \\ \hspace{-4mm}\rightleftarrows \, 12 \, \Omega \\ 10 \, \Omega \\ \parallel \\ 5 \, \Omega \\ \hspace{-6mm}\updownarrows \, 6.5 \, I_x \\ 50 \, \Omega \\ \vert \\ \hspace{2mm}\text{b} \end{array} \] #### Steps to Solve: 1. **Determine \( V_{Th} \):** - Calculate the open-circuit voltage across terminals a-b. - Use appropriate circuit analysis techniques to understand how the voltage is distributed across components. 2. **Calculate Thevenin Equivalent Resistance \( R_{Th} \):** - Introduce a test source (voltage or current) across terminals a-b. - Use the electrical response (current or voltage) to determine how resistances combine. - Consider both series and parallel combinations and the effect of the dependent current source. ##### Detailed Diagram Analysis: The circuit analysis would typically involve: - Kirchhoff’s Voltage Law (KVL) - Kirchhoff’s Current Law (KCL) - Ohm's Law - Techniques such as Mesh Analysis or Nodal Analysis may be deployed to simplify and solve complex networks. ### Educational Focus: Understanding and solving Thevenin equivalent circuits is vital for
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