Homework Help is Here – Start Your Trial Now!
Engineering
Electrical Engineering
A) State superposition theorem. B) Use superposition to determine the current i2 if vs=10V, is=2A, R1=522, R2=2Q2, R3= R₂ www. VS R₁ www is 12 R3

A) State superposition theorem. B) Use superposition to determine the current i2 if vs=10V, is=2A, R1=522, R2=2Q2, R3= R₂ www. VS R₁ www is 12 R3

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

Please help. 

### State Superposition Theorem #### Explanation and Application **A) State Superposition Theorem:** The superposition theorem states that in any linear circuit with multiple independent sources, the response (voltage or current) in any element of the circuit is the algebraic sum of the responses caused by each independent source acting alone, while all other independent sources are turned off (replaced by their internal impedances). **B) Use Superposition to Determine the Current \( i_2 \):** Given: - Voltage source, \( v_s = 10V \) - Current source, \( i_s = 2A \) - Resistor \( R_1 = 5Ω \) - Resistor \( R_2 = 2Ω \) - Resistor \( R_3 = 4Ω \) #### Steps to Determine the Current \( i_2 \): **1. Circuit Analysis with \( v_s \) Active and \( i_s \) Deactivated:** - Replace \( i_s \) with an open circuit. - Analyze the resulting series-parallel circuit to find \( i_2 \). **2. Circuit Analysis with \( i_s \) Active and \( v_s \) Deactivated:** - Replace \( v_s \) with a short circuit. - Analyze the resulting circuit to find the contribution of current \( i_2 \). **3. Combine the Results:** - Sum the individual currents to find the total \( i_2 \) in the original circuit utilizing the principle of superposition. #### Detailed Analysis: **Step 1:** When considering \( v_s = 10V \) and \( i_s \) deactivated (open circuit): - The circuit reduces to a simple voltage divider between \( R_1 \), \( R_2 \), and \( R_3 \). - Calculate the equivalent resistance seen by the voltage source. - Find the voltage across \( R_3 \) and then compute the current \( i_{2(v_s)} \). **Step 2:** When considering \( i_s = 2A \) and \( v_s \) deactivated (short circuit): - The current divides between \( R_2 \) and \( R_3 \) when \( R_1 \) is bypassed by the short. - Analyze the current distribution and find the effective current \( i_{2(i_s)} \). **Step 3:** Add
Transcribed Image Text:### State Superposition Theorem #### Explanation and Application **A) State Superposition Theorem:** The superposition theorem states that in any linear circuit with multiple independent sources, the response (voltage or current) in any element of the circuit is the algebraic sum of the responses caused by each independent source acting alone, while all other independent sources are turned off (replaced by their internal impedances). **B) Use Superposition to Determine the Current \( i_2 \):** Given: - Voltage source, \( v_s = 10V \) - Current source, \( i_s = 2A \) - Resistor \( R_1 = 5Ω \) - Resistor \( R_2 = 2Ω \) - Resistor \( R_3 = 4Ω \) #### Steps to Determine the Current \( i_2 \): **1. Circuit Analysis with \( v_s \) Active and \( i_s \) Deactivated:** - Replace \( i_s \) with an open circuit. - Analyze the resulting series-parallel circuit to find \( i_2 \). **2. Circuit Analysis with \( i_s \) Active and \( v_s \) Deactivated:** - Replace \( v_s \) with a short circuit. - Analyze the resulting circuit to find the contribution of current \( i_2 \). **3. Combine the Results:** - Sum the individual currents to find the total \( i_2 \) in the original circuit utilizing the principle of superposition. #### Detailed Analysis: **Step 1:** When considering \( v_s = 10V \) and \( i_s \) deactivated (open circuit): - The circuit reduces to a simple voltage divider between \( R_1 \), \( R_2 \), and \( R_3 \). - Calculate the equivalent resistance seen by the voltage source. - Find the voltage across \( R_3 \) and then compute the current \( i_{2(v_s)} \). **Step 2:** When considering \( i_s = 2A \) and \( v_s \) deactivated (short circuit): - The current divides between \( R_2 \) and \( R_3 \) when \( R_1 \) is bypassed by the short. - Analyze the current distribution and find the effective current \( i_{2(i_s)} \). **Step 3:** Add
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Superposition 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