## Circuit Analysis using Kirchhoff's Current Law (KCL)### Problem Statement:Consider the circuit shown in Figure E1.3.1 and determine the unknown currents using KCL.### Diagram Explanation:The circuit diagram includes the following elements:- A power source is connected, marked with a "+" and "−" indicating polarity.- Several nodes are marked for reference: - **Node a** - **Node b** - **Node c** (indicated with a blue dotted line)- The circuit contains currents labeled at different points: - \( i_S = 10 \, \text{A} \) - \( i_1 = 5 \, \text{A} \) - \( i_4 = 3 \, \text{A} \) - \( i_2 = 4 \, \text{A} \) - Unknown currents are marked as \( i_5 \) and \( i_3 \), represented with "?" indicating they need to be determined.### Circuit Layout:- Current \( i_S \) enters the circuit.- There's a branch between \( i_S \) and \( i_1 \).- Node b is the junction where additional branches intersect.- Node c is the loop through which multiple currents pass, indicating potential calculation paths for solving using KCL.### Objective:Apply Kirchhoff's Current Law at the specified nodes to solve for unknown currents \( i_5 \) and \( i_3 \).### Key Concepts:Kirchhoff's Current Law states that the total current entering a junction must equal the total current leaving the junction. Use this principle to set up equations that will allow solving for unknown quantities within the circuit.

The given problem can be solved with the help of Kirchhoff's current law (KCL). According to this law, the sum of all the currents entering a node in a circuit is equal to the sum of all the currents leaving the node. Application of KCL at node a gives is=i1+i4+i5=>i5=is-i1-i4=>i5=10-5-3 A=>i5=2 A Application of KCL at node b gives i1=i2+i3=>i3=i1-i2=>i3=5-4 A=>i3=1 A Thus, the value of the unknown currents will be i3=1 A i5=2 A

Answered: Consider the circuit shown in Figure…

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Consider the circuit shown in Figure E1.3.1 and determine the unknown currents using KCL. Figure El.3.1 iş= 10A i| = 5A Node a Node b 7 i, = 3 A 7 iz= 4 A is = ? Node

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

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Question

## Circuit Analysis using Kirchhoff's Current Law (KCL)

### Problem Statement:
Consider the circuit shown in Figure E1.3.1 and determine the unknown currents using KCL.

### Diagram Explanation:
The circuit diagram includes the following elements:

- A power source is connected, marked with a "+" and "−" indicating polarity.
- Several nodes are marked for reference:
- **Node a**
- **Node b**
- **Node c** (indicated with a blue dotted line)
- The circuit contains currents labeled at different points:
- \( i_S = 10 \, \text{A} \)
- \( i_1 = 5 \, \text{A} \)
- \( i_4 = 3 \, \text{A} \)
- \( i_2 = 4 \, \text{A} \)
- Unknown currents are marked as \( i_5 \) and \( i_3 \), represented with "?" indicating they need to be determined.

### Circuit Layout:
- Current \( i_S \) enters the circuit.
- There's a branch between \( i_S \) and \( i_1 \).
- Node b is the junction where additional branches intersect.
- Node c is the loop through which multiple currents pass, indicating potential calculation paths for solving using KCL.

### Objective:
Apply Kirchhoff's Current Law at the specified nodes to solve for unknown currents \( i_5 \) and \( i_3 \).

### Key Concepts:
Kirchhoff's Current Law states that the total current entering a junction must equal the total current leaving the junction. Use this principle to set up equations that will allow solving for unknown quantities within the circuit.

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