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current passing through

current passing through

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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**Question 2: Finding the Current Through Resistor (R3 = 4Ω) Using Superposition Theorem** --- For this question, you are required to determine the current passing through the resistor \( R3 \) (4Ω) using the superposition theorem. The circuit diagram provided consists of the following components: - A voltage source (E) of 12V. - Four resistors with the following values: - \( R1 = 6Ω \), - \( R2 = 2Ω \), - \( R3 = 4Ω \), - \( R4 = 3Ω \). - A current source (Is) supplying 8A. ### Circuit Diagram Overview: The circuit diagram shows a parallel series combination as follows: 1. The voltage source (E) of 12V is connected in parallel to two branches: - The first branch contains resistor \( R1 \) (6Ω). - The second branch contains resistors \( R2 \) (2Ω) in series with \( R3 \) (4Ω) and \( R4 \) (3Ω) and the current source \( Is \) of 8A in series. ### Applying Superposition Theorem: Superposition theorem states that in a linear circuit with multiple sources, the total current in any branch is the algebraic sum of the currents caused by each source acting independently while all other sources are replaced by their internal resistances. #### Steps to Find the Current Through \( R3 \) Using Superposition Theorem: 1. **Consider the effect of the 12V voltage source alone:** - Replace the current source \( Is \) with an open circuit. - Calculate the current through \( R3 \) due to the voltage source alone. 2. **Consider the effect of the 8A current source alone:** - Replace the voltage source (12V) with a short circuit (0V). - Calculate the current through \( R3 \) due to the current source alone. 3. **Sum the individual currents:** - Add the currents obtained from step 1 and step 2 to get the total current passing through \( R3 \). By following these steps and calculations, you will be able to find the current through \( R3 \) using the superposition theorem. ---
Transcribed Image Text:**Question 2: Finding the Current Through Resistor (R3 = 4Ω) Using Superposition Theorem** --- For this question, you are required to determine the current passing through the resistor \( R3 \) (4Ω) using the superposition theorem. The circuit diagram provided consists of the following components: - A voltage source (E) of 12V. - Four resistors with the following values: - \( R1 = 6Ω \), - \( R2 = 2Ω \), - \( R3 = 4Ω \), - \( R4 = 3Ω \). - A current source (Is) supplying 8A. ### Circuit Diagram Overview: The circuit diagram shows a parallel series combination as follows: 1. The voltage source (E) of 12V is connected in parallel to two branches: - The first branch contains resistor \( R1 \) (6Ω). - The second branch contains resistors \( R2 \) (2Ω) in series with \( R3 \) (4Ω) and \( R4 \) (3Ω) and the current source \( Is \) of 8A in series. ### Applying Superposition Theorem: Superposition theorem states that in a linear circuit with multiple sources, the total current in any branch is the algebraic sum of the currents caused by each source acting independently while all other sources are replaced by their internal resistances. #### Steps to Find the Current Through \( R3 \) Using Superposition Theorem: 1. **Consider the effect of the 12V voltage source alone:** - Replace the current source \( Is \) with an open circuit. - Calculate the current through \( R3 \) due to the voltage source alone. 2. **Consider the effect of the 8A current source alone:** - Replace the voltage source (12V) with a short circuit (0V). - Calculate the current through \( R3 \) due to the current source alone. 3. **Sum the individual currents:** - Add the currents obtained from step 1 and step 2 to get the total current passing through \( R3 \). By following these steps and calculations, you will be able to find the current through \( R3 \) using the superposition theorem. ---
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