### Circuit Analysis Problem**Objective:** Find the current ($i_3$) for the following circuit scenarios.**Diagram Descriptions:**Each subfigure (a, b, c, d) represents a point in the circuit with the following parameters: - $i_1$: Current in the first branch- $i_2$: Current in the second branch- $i_3$: Current in the third branch (to be determined)**Scenarios:**- **(a)** - $i_1 = 8A$ (to the right) - $i_2 = 6A$ (to the right) - $i_3 = ?$ - The currents $i_1$ and $i_2$ are adding to the right, and $i_3$ is directed downwards.- **(b)** - $i_1 = 8A$ (to the right) - $i_2 = -2A$ (to the left) - $i_3 = ?$ - The current $i_1$ is to the right, while $i_2$ is opposing to the left, and $i_3$ is directed upwards.- **(c)** - $i_1 = -4A$ (to the left) - $i_2 = -3A$ (to the left) - $i_3 = ?$ - Both currents $i_1$ and $i_2$ flow to the left, with $i_3$ directed upwards.- **(d)** - $i_1 = -4A$ (to the left) - $i_2 = 2A$ (to the right) - $i_3 = ?$ - The current $i_1$ is to the left, $i_2$ is to the right, and $i_3$ is directed downwards.**Note:**To find $i_3$, apply Kirchhoff's Current Law (KCL), which states that the total current entering a junction equals the total current leaving the junction.

Answered: 1. Find the current (is) for the…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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### Circuit Analysis Problem

**Objective:** Find the current ($i_3$) for the following circuit scenarios.

**Diagram Descriptions:**

Each subfigure (a, b, c, d) represents a point in the circuit with the following parameters:

- $i_1$: Current in the first branch
- $i_2$: Current in the second branch
- $i_3$: Current in the third branch (to be determined)

**Scenarios:**

- **(a)**
- $i_1 = 8A$ (to the right)
- $i_2 = 6A$ (to the right)
- $i_3 = ?$
- The currents $i_1$ and $i_2$ are adding to the right, and $i_3$ is directed downwards.

- **(b)**
- $i_1 = 8A$ (to the right)
- $i_2 = -2A$ (to the left)
- $i_3 = ?$
- The current $i_1$ is to the right, while $i_2$ is opposing to the left, and $i_3$ is directed upwards.

- **(c)**
- $i_1 = -4A$ (to the left)
- $i_2 = -3A$ (to the left)
- $i_3 = ?$
- Both currents $i_1$ and $i_2$ flow to the left, with $i_3$ directed upwards.

- **(d)**
- $i_1 = -4A$ (to the left)
- $i_2 = 2A$ (to the right)
- $i_3 = ?$
- The current $i_1$ is to the left, $i_2$ is to the right, and $i_3$ is directed downwards.

**Note:**

To find $i_3$, apply Kirchhoff's Current Law (KCL), which states that the total current entering a junction equals the total current leaving the junction.

Expert Solution

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Now according to Kirchhoff's current law, the algebraic sum of current entering any junction is always the algebraic sum of current leaving the junction, so with the help of this principle, we can find the value of current in each case.

So by applying Kirchhoff's current law (KCL) in every case we can find the value of $i_{3}$ in every case.

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