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(a) Find the Thevenin equivalent seen by the load for the circuit shown. 12 V (+ 6Ω wwwww 3Ω www 12 Q2 222 2 A b) Answer question using math symbols, not values from part (a). How to select R₁ to deliver maximum power to the load? What is the load power under this condition? 65 3.2 222 a da

(a) Find the Thevenin equivalent seen by the load for the circuit shown. 12 V (+ 6Ω wwwww 3Ω www 12 Q2 222 2 A b) Answer question using math symbols, not values from part (a). How to select R₁ to deliver maximum power to the load? What is the load power under this condition? 65 3.2 222 a da

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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### Electrical Engineering: Thevenin Equivalent Circuit Analysis #### Exercise: **(a)** _Find the Thevenin equivalent seen by the load for the circuit shown._ The given circuit includes the following components: - A 12V voltage source. - A 2A current source. - Four resistors with resistances of 6Ω, 3Ω, 12Ω, and 2Ω. - A load resistor denoted as \( R_L \). **Diagram Explanation:** The circuit is configured as follows: - The positive terminal of the 12V voltage source is connected to the 6Ω resistor. - The 6Ω resistor is then connected in series with a 3Ω resistor. - The 3Ω resistor is connected to the node labeled 'a'. - From node 'a', there is a parallel connection to both a 12Ω resistor and the 2A current source. - The current source is connected in series with a 2Ω resistor to node 'b'. - The load resistor \( R_L \) spans across nodes 'a' and 'b'. **(b)** _Answer the question using math symbols, not values from part (a). How to select \( R_L \) to deliver maximum power to the load? What is the load power under this condition?_ To deliver maximum power to the load, the value of \( R_L \) is selected such that it is equal to the Thevenin resistance \( R_{th} \) seen from nodes 'a' and ‘b’. This is known as the Maximum Power Transfer Theorem. The maximum power delivered to the load is given by: \[ P_{max} = \frac{V_{th}^2}{4R_{th}} \] where \( V_{th} \) is the Thevenin voltage and \( R_{th} \) is the Thevenin resistance. The detailed process to find the Thevenin equivalent involves: 1. **Removing \(R_L\)** from the circuit. 2. **Calculating \(V_{th}\)**: The open circuit voltage across the terminals 'a' and 'b'. 3. **Calculating \(R_{th}\)**: By turning off independent sources (voltage sources replaced by short circuits and current sources by open circuits) and calculating the equivalent resistance seen from the terminals 'a' and 'b'. By satisfying these conditions, \( R_L = R_{
Transcribed Image Text:### Electrical Engineering: Thevenin Equivalent Circuit Analysis #### Exercise: **(a)** _Find the Thevenin equivalent seen by the load for the circuit shown._ The given circuit includes the following components: - A 12V voltage source. - A 2A current source. - Four resistors with resistances of 6Ω, 3Ω, 12Ω, and 2Ω. - A load resistor denoted as \( R_L \). **Diagram Explanation:** The circuit is configured as follows: - The positive terminal of the 12V voltage source is connected to the 6Ω resistor. - The 6Ω resistor is then connected in series with a 3Ω resistor. - The 3Ω resistor is connected to the node labeled 'a'. - From node 'a', there is a parallel connection to both a 12Ω resistor and the 2A current source. - The current source is connected in series with a 2Ω resistor to node 'b'. - The load resistor \( R_L \) spans across nodes 'a' and 'b'. **(b)** _Answer the question using math symbols, not values from part (a). How to select \( R_L \) to deliver maximum power to the load? What is the load power under this condition?_ To deliver maximum power to the load, the value of \( R_L \) is selected such that it is equal to the Thevenin resistance \( R_{th} \) seen from nodes 'a' and ‘b’. This is known as the Maximum Power Transfer Theorem. The maximum power delivered to the load is given by: \[ P_{max} = \frac{V_{th}^2}{4R_{th}} \] where \( V_{th} \) is the Thevenin voltage and \( R_{th} \) is the Thevenin resistance. The detailed process to find the Thevenin equivalent involves: 1. **Removing \(R_L\)** from the circuit. 2. **Calculating \(V_{th}\)**: The open circuit voltage across the terminals 'a' and 'b'. 3. **Calculating \(R_{th}\)**: By turning off independent sources (voltage sources replaced by short circuits and current sources by open circuits) and calculating the equivalent resistance seen from the terminals 'a' and 'b'. By satisfying these conditions, \( R_L = R_{
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