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Use superposition to find the currentio. Additionally, determine the power consumed by the 12 Ohm resistor. 1) 4.5 A Μ 12Ω γίο 2Ω 20 A( 4 14Ω +1 10 Ω 50 V Μ 15Ω.

Use superposition to find the currentio. Additionally, determine the power consumed by the 12 Ohm resistor. 1) 4.5 A Μ 12Ω γίο 2Ω 20 A( 4 14Ω +1 10 Ω 50 V Μ 15Ω.

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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### Superposition Theorem in Electrical Circuits **Objective:** Use superposition to find the current \(i_0\). Additionally, determine the power consumed by the 12 Ohm resistor. #### Circuit Description: The circuit comprises: - A 4.5 A current source. - A 12Ω resistor. - A 2Ω resistor. - A 20 A current source. - A 14Ω resistor. - A 10Ω resistor. - A 15Ω resistor. - A 50 V voltage source. These components are arranged as follows: 1. The 4.5 A current source is in series with the 12Ω resistor and the 2Ω resistor. 2. A 20 A current source is parallel to the series combination of the 4.5 A current source and the 2Ω resistor. 3. This combination is further in series with a 14Ω resistor which is parallel to a network containing a 10Ω resistor, a 50 V voltage source, and a 15Ω resistor. The main objective is to determine the current \(i_0\) passing through the 12Ω resistor using the superposition technique and then find the power consumed by that resistor. ### Steps to Solve Using Superposition: 1. **Superposition Principle**: - Temporarily remove all but one source (voltage and current sources) and solve the circuit. - Repeat for each source. - Combine the effects to get the total current \(i_0\). 2. **Removing Sources One at a Time**: - Replace each independent voltage source with a short circuit (wire). - Replace each independent current source with an open circuit (break). 3. **Calculating the Current \(i_0\)**: - Open circuit the 20A current source and short circuit the 50V voltage source. Solve for \(i_0\) using the 4.5 A current source. - Repeat the process for the other sources (one at a time). - Superimpose the results. 4. **Determine Power Consumption**: - Power consumed by the 12Ω resistor can be determined using \(P = i_0^2 \times R\). ### Graphical Representation: - **Circuit Diagram**: The provided diagram represents the electrical circuit with components as described, with specified values of current and voltage sources and resistances. #### Solving the Circuit: Detailed
Transcribed Image Text:### Superposition Theorem in Electrical Circuits **Objective:** Use superposition to find the current \(i_0\). Additionally, determine the power consumed by the 12 Ohm resistor. #### Circuit Description: The circuit comprises: - A 4.5 A current source. - A 12Ω resistor. - A 2Ω resistor. - A 20 A current source. - A 14Ω resistor. - A 10Ω resistor. - A 15Ω resistor. - A 50 V voltage source. These components are arranged as follows: 1. The 4.5 A current source is in series with the 12Ω resistor and the 2Ω resistor. 2. A 20 A current source is parallel to the series combination of the 4.5 A current source and the 2Ω resistor. 3. This combination is further in series with a 14Ω resistor which is parallel to a network containing a 10Ω resistor, a 50 V voltage source, and a 15Ω resistor. The main objective is to determine the current \(i_0\) passing through the 12Ω resistor using the superposition technique and then find the power consumed by that resistor. ### Steps to Solve Using Superposition: 1. **Superposition Principle**: - Temporarily remove all but one source (voltage and current sources) and solve the circuit. - Repeat for each source. - Combine the effects to get the total current \(i_0\). 2. **Removing Sources One at a Time**: - Replace each independent voltage source with a short circuit (wire). - Replace each independent current source with an open circuit (break). 3. **Calculating the Current \(i_0\)**: - Open circuit the 20A current source and short circuit the 50V voltage source. Solve for \(i_0\) using the 4.5 A current source. - Repeat the process for the other sources (one at a time). - Superimpose the results. 4. **Determine Power Consumption**: - Power consumed by the 12Ω resistor can be determined using \(P = i_0^2 \times R\). ### Graphical Representation: - **Circuit Diagram**: The provided diagram represents the electrical circuit with components as described, with specified values of current and voltage sources and resistances. #### Solving the Circuit: Detailed
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