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5. Calculate is using current divider rule. 0.5A 120Ω 4002 60Ω 80Ω 20Ω 10Ω

5. Calculate is using current divider rule. 0.5A 120Ω 4002 60Ω 80Ω 20Ω 10Ω

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
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**Problem 5: Calculate \(i_3\) Using the Current Divider Rule** The image above is a circuit diagram with the following components and connections: - The circuit contains a current source supplying 0.5 A. - There are multiple resistors with the following resistances: 120Ω, 40Ω, 10Ω, 60Ω, 20Ω, and 80Ω. - The resistors are arranged in a network with certain parallel and series configurations: - The 120Ω and 40Ω resistors are in parallel. - This parallel combination is in series with the 10Ω resistor. - The combined series-parallel setup is in parallel with the two series groups: one with 60Ω and 20Ω resistors, and the other with a single 80Ω resistor. - The objective is to calculate the current \(i_3\) through the 40Ω resistor using the current divider rule. **Explanation of Current Divider Rule:** The current divider rule is used to determine the current flowing through a particular branch in a parallel circuit. It is given by: \[ i_x = \frac{R_{total}}{R_x} \times i_{total} \] where: - \(i_x\) is the current through the branch of interest. - \(R_{total}\) is the equivalent resistance of the total parallel network. - \(R_x\) is the resistance of the branch of interest. - \(i_{total}\) is the total current entering the parallel network. Apply this rule to determine \(i_3\).
Transcribed Image Text:**Problem 5: Calculate \(i_3\) Using the Current Divider Rule** The image above is a circuit diagram with the following components and connections: - The circuit contains a current source supplying 0.5 A. - There are multiple resistors with the following resistances: 120Ω, 40Ω, 10Ω, 60Ω, 20Ω, and 80Ω. - The resistors are arranged in a network with certain parallel and series configurations: - The 120Ω and 40Ω resistors are in parallel. - This parallel combination is in series with the 10Ω resistor. - The combined series-parallel setup is in parallel with the two series groups: one with 60Ω and 20Ω resistors, and the other with a single 80Ω resistor. - The objective is to calculate the current \(i_3\) through the 40Ω resistor using the current divider rule. **Explanation of Current Divider Rule:** The current divider rule is used to determine the current flowing through a particular branch in a parallel circuit. It is given by: \[ i_x = \frac{R_{total}}{R_x} \times i_{total} \] where: - \(i_x\) is the current through the branch of interest. - \(R_{total}\) is the equivalent resistance of the total parallel network. - \(R_x\) is the resistance of the branch of interest. - \(i_{total}\) is the total current entering the parallel network. Apply this rule to determine \(i_3\).
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