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Use ix + superposition to find ix. 4~ ww 20V 13 A 2.2 www +I 1ix

Use ix + superposition to find ix. 4~ ww 20V 13 A 2.2 www +I 1ix

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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**Using Superposition to Find \( i_x \)** The circuit diagram above requires the use of the superposition principle to find the current \( i_x \). In this circuit, there are three sources: 1. A 20V voltage source on the left side of the circuit. 2. A 3A current source in the middle of the circuit. 3. A dependent voltage source \( 1i_x \) on the right side. The resistors in the circuit are labeled as follows: - A 4Ω resistor is connected next to the 20V voltage source. - A 2Ω resistor is placed in the branch with the dependent voltage source. **Explanation:** - **Superposition Principle**: This principle involves solving the circuit multiple times, each time with only one source active (all others replaced by their internal impedances). The final current \( i_x \) is the algebraic sum of the currents produced by each source acting independently. - **Steps for Analysis**: 1. **Deactivate all but one source:** - For the voltage source, short circuit it. - For the current source, open circuit it. 2. **Calculate the resulting \( i_x \) for each scenario.** 3. **Sum the contributions from each scenario to determine the total \( i_x \).** This approach helps in understanding the individual contribution of each source and the interplay between different circuit elements.
Transcribed Image Text:**Using Superposition to Find \( i_x \)** The circuit diagram above requires the use of the superposition principle to find the current \( i_x \). In this circuit, there are three sources: 1. A 20V voltage source on the left side of the circuit. 2. A 3A current source in the middle of the circuit. 3. A dependent voltage source \( 1i_x \) on the right side. The resistors in the circuit are labeled as follows: - A 4Ω resistor is connected next to the 20V voltage source. - A 2Ω resistor is placed in the branch with the dependent voltage source. **Explanation:** - **Superposition Principle**: This principle involves solving the circuit multiple times, each time with only one source active (all others replaced by their internal impedances). The final current \( i_x \) is the algebraic sum of the currents produced by each source acting independently. - **Steps for Analysis**: 1. **Deactivate all but one source:** - For the voltage source, short circuit it. - For the current source, open circuit it. 2. **Calculate the resulting \( i_x \) for each scenario.** 3. **Sum the contributions from each scenario to determine the total \( i_x \).** This approach helps in understanding the individual contribution of each source and the interplay between different circuit elements.
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