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Find the currents I1, I2, I3 flowing in the circuit.

Find the currents I1, I2, I3 flowing in the circuit.

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Find the currents I1, I2, I3 flowing in the circuit.

### Electrical Circuit Analysis #### Introduction: This section provides an analysis of an electrical circuit with multiple branches and components including resistors, voltage sources, and internal resistances. #### Circuit Components: - **Resistors:** - \( R_1 = 20 \, \Omega \) - \( R_2 = 6 \, \Omega \) - \( R_3 = 8 \, \Omega \) - \( R_4 = 15 \, \Omega \) - **Voltage Sources:** - \( \mathcal{E}_1 = 18 \, \text{V} \) - \( \mathcal{E}_2 = 3.0 \, \text{V} \) - \( \mathcal{E}_3 = 12 \, \text{V} \) - \( \mathcal{E}_4 = 24 \, \text{V} \) - **Internal Resistances:** - \( r_1 = 0.5 \, \Omega \) - \( r_2 = 0.25 \, \Omega \) - \( r_3 = 0.5 \, \Omega \) - \( r_4 = 0.75 \, \Omega \) #### Node Analysis: - **Node A:** Connected to voltage source \( \mathcal{E}_1 \), resistor \( R_1 \), and internal resistance \( r_1 \). - **Node B:** Between resistors \( R_1 \) and \( R_2 \), and carrying current \( I_1 \) to \( I_2 \) and \( I_3 \). - **Node C:** Connected to resistor \( R_3 \) and voltage source \( \mathcal{E}_3 \). - **Node D:** Connected to internal resistance \( r_4 \) and voltage source \( \mathcal{E}_4 \). - **Node E:** Between resistor \( R_4 \) and internal resistance \( r_4 \). - **Node F:** Connected to resistor \( R_4 \). - **Node G:** Connected to voltage source \( \mathcal{E}_2 \) and internal resistance \( r_2 \). #### Currents in the Circuit: - \( I_1 \) flows through \( R_1 \) from
Transcribed Image Text:### Electrical Circuit Analysis #### Introduction: This section provides an analysis of an electrical circuit with multiple branches and components including resistors, voltage sources, and internal resistances. #### Circuit Components: - **Resistors:** - \( R_1 = 20 \, \Omega \) - \( R_2 = 6 \, \Omega \) - \( R_3 = 8 \, \Omega \) - \( R_4 = 15 \, \Omega \) - **Voltage Sources:** - \( \mathcal{E}_1 = 18 \, \text{V} \) - \( \mathcal{E}_2 = 3.0 \, \text{V} \) - \( \mathcal{E}_3 = 12 \, \text{V} \) - \( \mathcal{E}_4 = 24 \, \text{V} \) - **Internal Resistances:** - \( r_1 = 0.5 \, \Omega \) - \( r_2 = 0.25 \, \Omega \) - \( r_3 = 0.5 \, \Omega \) - \( r_4 = 0.75 \, \Omega \) #### Node Analysis: - **Node A:** Connected to voltage source \( \mathcal{E}_1 \), resistor \( R_1 \), and internal resistance \( r_1 \). - **Node B:** Between resistors \( R_1 \) and \( R_2 \), and carrying current \( I_1 \) to \( I_2 \) and \( I_3 \). - **Node C:** Connected to resistor \( R_3 \) and voltage source \( \mathcal{E}_3 \). - **Node D:** Connected to internal resistance \( r_4 \) and voltage source \( \mathcal{E}_4 \). - **Node E:** Between resistor \( R_4 \) and internal resistance \( r_4 \). - **Node F:** Connected to resistor \( R_4 \). - **Node G:** Connected to voltage source \( \mathcal{E}_2 \) and internal resistance \( r_2 \). #### Currents in the Circuit: - \( I_1 \) flows through \( R_1 \) from
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