# Superposition Theorem Application on Circuit Analysis## Problem StatementUsing the Superposition Theorem, analyze the given circuit to find:(i) Current flowing through \( R_3 \) due to the voltage source (\( V_S \)) acting alone.(ii) Current flowing through \( R_3 \) due to the current source (\( I_{S1} \)) acting alone.(iii) Current flowing through \( R_3 \) due to the current source (\( I_{S2} \)) acting alone.(iv) Total current flowing through \( R_3 \) due to all the sources.## Circuit Diagram DescriptionThe circuit comprises of:- **Voltage Source (\( V_S \))**: 10V- **Current Source 1 (\( I_{S1} \))**: 15 mA- **Current Source 2 (\( I_{S2} \))**: 7.5 mA### Resistors:- \( R_1 = 1 \text{k}\Omega \)- \( R_2 = 3 \text{k}\Omega \)- \( R_3 = 1 \text{k}\Omega \)- \( R_4 = 2 \text{k}\Omega \)### Connections:- The voltage source \( V_S \) is connected to \( R_1 \).- \( R_2 \) connects \( R_1 \) in parallel to form a mixed configuration with the current sources.- \( R_3 \) is connected in series with \( R_4 \) and across the adjunction formed by \( I_{S1} \) and \( I_{S2} \).## ObjectiveCalculate the currents in \( R_3 \) using the Superposition Theorem, deactivating all sources but one at each step, and then summing the results for a total current assessment.

(i) step-1:-only voltagr source(vs) acting alone⇒De-eneergize other two current source by open…

For the following circuit use Superposition Theorem to find (i) current flowing through R3 due to the voltage source (Vs) acting alone. (ii) current flowing through R3 due to the current source (Is1) acting alone. (iii)current flowing through R3 due to the current source (I,2) acting alone. (iv)Total current flowing through R3 due to all the sources.

For the following circuit use Superposition Theorem to find (i) current flowing through R3 due to the voltage source (Vs) acting alone. (ii) current flowing through R3 due to the current source (Is1) acting alone. (iii)current flowing through R3 due to the current source (I,2) acting alone. (iv)Total current flowing through R3 due to all the sources.

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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Concept explainers

Superposition Theorem

The superposition theorem is applied to linear systems. For such systems, the output from two different inputs equals the sum of the outputs from each input separately. On applying this theorem many times we get the output from any number of inputs equal to the sum of the outputs from the individual inputs separately.

Question

# Superposition Theorem Application on Circuit Analysis

## Problem Statement
Using the Superposition Theorem, analyze the given circuit to find:

(i) Current flowing through \( R_3 \) due to the voltage source (\( V_S \)) acting alone.

(ii) Current flowing through \( R_3 \) due to the current source (\( I_{S1} \)) acting alone.

(iii) Current flowing through \( R_3 \) due to the current source (\( I_{S2} \)) acting alone.

(iv) Total current flowing through \( R_3 \) due to all the sources.

## Circuit Diagram Description

The circuit comprises of:
- **Voltage Source (\( V_S \))**: 10V
- **Current Source 1 (\( I_{S1} \))**: 15 mA
- **Current Source 2 (\( I_{S2} \))**: 7.5 mA

### Resistors:
- \( R_1 = 1 \text{k}\Omega \)
- \( R_2 = 3 \text{k}\Omega \)
- \( R_3 = 1 \text{k}\Omega \)
- \( R_4 = 2 \text{k}\Omega \)

### Connections:
- The voltage source \( V_S \) is connected to \( R_1 \).
- \( R_2 \) connects \( R_1 \) in parallel to form a mixed configuration with the current sources.
- \( R_3 \) is connected in series with \( R_4 \) and across the adjunction formed by \( I_{S1} \) and \( I_{S2} \).

## Objective
Calculate the currents in \( R_3 \) using the Superposition Theorem, deactivating all sources but one at each step, and then summing the results for a total current assessment.

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