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Problem 5-4. Find the value of the load resistance R₁ in figure P5.16 which will dissipate maximum power. Find the power delivered to the load resistance when it is set to this value. 4ΚΩ R₁ ΣΚΩ 1ΚΩ 2ix ↑ 6ΚΩ 2mA 2V 4V 3ΚΩ www

Problem 5-4. Find the value of the load resistance R₁ in figure P5.16 which will dissipate maximum power. Find the power delivered to the load resistance when it is set to this value. 4ΚΩ R₁ ΣΚΩ 1ΚΩ 2ix ↑ 6ΚΩ 2mA 2V 4V 3ΚΩ www

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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**Problem 5-4.** Find the value of the load resistance \( R_L \) in figure P5.16 which will dissipate maximum power. Find the power delivered to the load resistance when it is set to this value. **Diagram Explanation:** The circuit diagram includes: - A load resistor \( R_L \). - Four resistors with resistances: 4kΩ, 2kΩ, 6kΩ, and 3kΩ. - A 1kΩ resistor in series with the load resistor \( R_L \). - Two voltage sources: 2V (positive on the left) and 4V (positive on the bottom). - A current source providing 2mA. - A current-dependent current source positioned vertically, with 2iₓ, where iₓ is the current through the 4kΩ resistor. ### Steps to Solve: 1. **Determine Maximum Power Transfer:** The load resistance \( R_L \) will dissipate maximum power when \( R_L \) equals the Thevenin resistance of the network viewed from the terminals of \( R_L \). 2. **Calculate Thevenin Equivalent:** - Remove \( R_L \) from the circuit. - Calculate the open-circuit voltage and the equivalent resistance seen from \( R_L \)'s terminals. 3. **Power Calculation:** Use \( P = \frac{V_{th}^2}{4R_{th}} \) to find the power delivered to \( R_L \), where \( V_{th} \) is the Thevenin voltage and \( R_{th} \) is the Thevenin resistance. By solving these steps, you can determine both the value for \( R_L \) that maximizes power dissipation, and the amount of power delivered when \( R_L \) is at this value.
Transcribed Image Text:**Problem 5-4.** Find the value of the load resistance \( R_L \) in figure P5.16 which will dissipate maximum power. Find the power delivered to the load resistance when it is set to this value. **Diagram Explanation:** The circuit diagram includes: - A load resistor \( R_L \). - Four resistors with resistances: 4kΩ, 2kΩ, 6kΩ, and 3kΩ. - A 1kΩ resistor in series with the load resistor \( R_L \). - Two voltage sources: 2V (positive on the left) and 4V (positive on the bottom). - A current source providing 2mA. - A current-dependent current source positioned vertically, with 2iₓ, where iₓ is the current through the 4kΩ resistor. ### Steps to Solve: 1. **Determine Maximum Power Transfer:** The load resistance \( R_L \) will dissipate maximum power when \( R_L \) equals the Thevenin resistance of the network viewed from the terminals of \( R_L \). 2. **Calculate Thevenin Equivalent:** - Remove \( R_L \) from the circuit. - Calculate the open-circuit voltage and the equivalent resistance seen from \( R_L \)'s terminals. 3. **Power Calculation:** Use \( P = \frac{V_{th}^2}{4R_{th}} \) to find the power delivered to \( R_L \), where \( V_{th} \) is the Thevenin voltage and \( R_{th} \) is the Thevenin resistance. By solving these steps, you can determine both the value for \( R_L \) that maximizes power dissipation, and the amount of power delivered when \( R_L \) is at this value.
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we need to find the value of the load resistance so that maximum power will transfer to it and finding the maximum power.

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