**Title: Techniques for Determining Thévenin and Norton Equivalents****Objective:**Learn how to use appropriate techniques to identify both the Thévenin and Norton equivalents for the given electrical network.**Description:**The circuit diagram displays a current source $ I_x = 2 \, \text{A} $ with a configuration of resistors. The resistors are labeled as:- $2 \, \Omega$- $3 \, \Omega$- $4 \, \Omega$- $6 \, \Omega$The resistors form a parallel and series arrangement as shown:- The $2 \, \Omega$ resistor is in parallel with the network containing the $4 \, \Omega$ and $6 \, \Omega$ resistors in series.**Task:**Calculate the following:- The Thévenin equivalent voltage and resistance.- The Norton equivalent current and resistance.**Results:**1. **The Thévenin Equivalent:** - Fill in the calculated Thévenin voltage in volts (V) for the series configuration with $8 \, \Omega$. 2. **The Norton Equivalent:** - Fill in the calculated Norton current in milliamps (mA) for the parallel configuration with $8 \, \Omega$.**Understanding Thévenin and Norton Equivalents:**- **Thévenin's Theorem:** Converts a complex network into a simple voltage source $ V_{\text{th}} $ in series with a single resistance $ R_{\text{th}} $.- **Norton's Theorem:** Converts a complex network into a simple current source $ I_{\text{n}} $ in parallel with a single resistance $ R_{\text{n}} $.Apply these methodologies to simplify analysis of electrical networks.

Answered: The Thévenin equivalent is |V in series…

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

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**Title: Techniques for Determining Thévenin and Norton Equivalents**

**Objective:**
Learn how to use appropriate techniques to identify both the Thévenin and Norton equivalents for the given electrical network.

**Description:**
The circuit diagram displays a current source $ I_x = 2 \, \text{A} $ with a configuration of resistors. The resistors are labeled as:
- $2 \, \Omega$
- $3 \, \Omega$
- $4 \, \Omega$
- $6 \, \Omega$

The resistors form a parallel and series arrangement as shown:
- The $2 \, \Omega$ resistor is in parallel with the network containing the $4 \, \Omega$ and $6 \, \Omega$ resistors in series.

**Task:**
Calculate the following:
- The Thévenin equivalent voltage and resistance.
- The Norton equivalent current and resistance.

**Results:**
1. **The Thévenin Equivalent:**
- Fill in the calculated Thévenin voltage in volts (V) for the series configuration with $8 \, \Omega$.

2. **The Norton Equivalent:**
- Fill in the calculated Norton current in milliamps (mA) for the parallel configuration with $8 \, \Omega$.

**Understanding Thévenin and Norton Equivalents:**
- **Thévenin's Theorem:** Converts a complex network into a simple voltage source $ V_{\text{th}} $ in series with a single resistance $ R_{\text{th}} $.
- **Norton's Theorem:** Converts a complex network into a simple current source $ I_{\text{n}} $ in parallel with a single resistance $ R_{\text{n}} $.

Apply these methodologies to simplify analysis of electrical networks.

Expert Solution

Step 1

Thevenin theorem states that any linear network with multiple number of sources and multiple resistances it can be replaced by a single voltage source and a single resistance.

The voltage source is called Thevenin voltage, and it is found by open circuiting the load terminals and finding the open circuit voltage at that point.

The resistance is called Thevenin resistance/impedance it is the open circuit resistance/impedance looking back into the network from load side when all the sources are replaced by their internal resistances. For voltage sources they are replaced by short circuit and for current sources they are replaced by an open circuit.

The Norton's equivalent circuit is the dual of the Thevenin circuit, means Thevenin circuit can be also derived if Norton's equivalent circuit is known.

Relations between Norton and Thevenin Circuit:

$\begin{array}{rcl} R_{T h} & = & R_{N} \\ V_{T h} & = & I_{N} * R_{T h} \end{array}$

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