Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
For the circuit below, find Ix using superposition. 9 V 402 ww 3 A 6 Ω ww 802 ww Ix 4.5 V

For the circuit below, find Ix using superposition. 9 V 402 ww 3 A 6 Ω ww 802 ww Ix 4.5 V

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...
See similar textbooks
icon
Related questions
Question
**Circuit Analysis Using Superposition** In the given circuit, our goal is to find the current \( I_x \) through the 8-ohm resistor using the superposition theorem. The circuit includes the following components: 1. A voltage source of 9V. 2. A voltage source of 4.5V. 3. A current source of 3A. 4. Resistors with resistances of 4Ω, 6Ω, and 8Ω. **Circuit Description:** - The 9V voltage source is connected in series with a 4Ω resistor. - Following the 4Ω resistor, a parallel connection includes a 3A current source and a 6Ω resistor. - The parallel connection leads to the series connection of an 8Ω resistor and a 4.5V voltage source. - The current \( I_x \) that we need to find flows through the 8Ω resistor, directed towards the 4.5V voltage source. **Superposition Theorem Application:** To apply the superposition theorem, we will consider each source independently while replacing all other voltage sources with short circuits and all other current sources with open circuits. The total current \( I_x \) will be the sum of the currents due to each independent source. 1. **Considering the 9V Voltage Source:** - Open circuit the 3A current source. - Short circuit the 4.5V voltage source. - Analyze the current \( I_x' \) through the 8Ω resistor. 2. **Considering the 4.5V Voltage Source:** - Open circuit the 3A current source. - Short circuit the 9V voltage source. - Analyze the current \( I_x'' \) through the 8Ω resistor. 3. **Considering the 3A Current Source:** - Short circuit both the 9V and 4.5V voltage sources. - Analyze the current \( I_x''' \) through the 8Ω resistor. Finally, sum the currents from the three cases to find the total \( I_x \): \[ I_x = I_x' + I_x'' + I_x''' \] This method allows us to determine the effect of each individual source on the current through the specified resistor and thus find the total current \( I_x \) in the circuit.
Transcribed Image Text:**Circuit Analysis Using Superposition** In the given circuit, our goal is to find the current \( I_x \) through the 8-ohm resistor using the superposition theorem. The circuit includes the following components: 1. A voltage source of 9V. 2. A voltage source of 4.5V. 3. A current source of 3A. 4. Resistors with resistances of 4Ω, 6Ω, and 8Ω. **Circuit Description:** - The 9V voltage source is connected in series with a 4Ω resistor. - Following the 4Ω resistor, a parallel connection includes a 3A current source and a 6Ω resistor. - The parallel connection leads to the series connection of an 8Ω resistor and a 4.5V voltage source. - The current \( I_x \) that we need to find flows through the 8Ω resistor, directed towards the 4.5V voltage source. **Superposition Theorem Application:** To apply the superposition theorem, we will consider each source independently while replacing all other voltage sources with short circuits and all other current sources with open circuits. The total current \( I_x \) will be the sum of the currents due to each independent source. 1. **Considering the 9V Voltage Source:** - Open circuit the 3A current source. - Short circuit the 4.5V voltage source. - Analyze the current \( I_x' \) through the 8Ω resistor. 2. **Considering the 4.5V Voltage Source:** - Open circuit the 3A current source. - Short circuit the 9V voltage source. - Analyze the current \( I_x'' \) through the 8Ω resistor. 3. **Considering the 3A Current Source:** - Short circuit both the 9V and 4.5V voltage sources. - Analyze the current \( I_x''' \) through the 8Ω resistor. Finally, sum the currents from the three cases to find the total \( I_x \): \[ I_x = I_x' + I_x'' + I_x''' \] This method allows us to determine the effect of each individual source on the current through the specified resistor and thus find the total current \( I_x \) in the circuit.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Maximum power transfer theorem
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, electrical-engineering and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,
SEE MORE TEXTBOOKS