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Three resistors R1 = 86.1 Ω, R2 = 24.3 Ω, R3 = 70.0 Ω, and two batteries 1 = 40.0 V, and 2 = 351 V are connected as shown in the diagram below.   (a) What current flows through R1, R2, and R3?   I1 =   I2 =   I3= (b) What is the absolute value of the potential difference across R1, R2, and R3? In V

Three resistors R1 = 86.1 Ω, R2 = 24.3 Ω, R3 = 70.0 Ω, and two batteries 1 = 40.0 V, and 2 = 351 V are connected as shown in the diagram below.   (a) What current flows through R1, R2, and R3?   I1 =   I2 =   I3= (b) What is the absolute value of the potential difference across R1, R2, and R3? In V

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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Three resistors R1 = 86.1 Ω, R2 = 24.3 Ω, R3 = 70.0 Ω, and two batteries 1 = 40.0 V, and 2 = 351 V are connected as shown in the diagram below.

 

(a) What current flows through R1, R2, and R3?

 

I1 =  

I2 =  

I3=


(b) What is the absolute value of the potential difference across R1, R2, and R3? In V

|ΔVR1| = 

|ΔVR2| = 

|ΔVR3| =

 
### Series-Parallel Circuit Diagram Explanation The diagram above illustrates a series-parallel electrical circuit containing the following components: 1. **Two Batteries (Sources of EMF):** - \( \mathcal{E}_1 \) and \( \mathcal{E}_2 \), which provide the electromotive force to the circuit. They are in series with each other and the resistors. 2. **Three Resistors:** - \( R_1 \), \( R_2 \), and \( R_3 \). - \( R_1 \) and \( R_2 \) are parallel to each other. - \( R_3 \) is in series with the parallel combination of \( R_1 \) and \( R_2 \). ### Detailed Explanation: - **Parallel Connection:** - In the parallel section, both resistors \( R_1 \) and \( R_2 \) have the same potential difference as they are connected across the same nodes. - **Series Connection:** - The resistor \( R_3 \) is connected in series with the combined parallel resistors \( R_1 \) and \( R_2 \). Therefore, the total resistance in the circuit is the sum of the resistance of \( R_3 \) and the equivalent resistance of \( R_1 \) and \( R_2 \). - **Application:** - Such circuits are commonly analyzed to find the total resistance, current through each component, and the voltage across different parts using Ohm's Law and Kirchhoff’s laws. This configuration illustrates the combination of resistors in series and parallel, providing a foundation for analyzing more complex circuits.
Transcribed Image Text:### Series-Parallel Circuit Diagram Explanation The diagram above illustrates a series-parallel electrical circuit containing the following components: 1. **Two Batteries (Sources of EMF):** - \( \mathcal{E}_1 \) and \( \mathcal{E}_2 \), which provide the electromotive force to the circuit. They are in series with each other and the resistors. 2. **Three Resistors:** - \( R_1 \), \( R_2 \), and \( R_3 \). - \( R_1 \) and \( R_2 \) are parallel to each other. - \( R_3 \) is in series with the parallel combination of \( R_1 \) and \( R_2 \). ### Detailed Explanation: - **Parallel Connection:** - In the parallel section, both resistors \( R_1 \) and \( R_2 \) have the same potential difference as they are connected across the same nodes. - **Series Connection:** - The resistor \( R_3 \) is connected in series with the combined parallel resistors \( R_1 \) and \( R_2 \). Therefore, the total resistance in the circuit is the sum of the resistance of \( R_3 \) and the equivalent resistance of \( R_1 \) and \( R_2 \). - **Application:** - Such circuits are commonly analyzed to find the total resistance, current through each component, and the voltage across different parts using Ohm's Law and Kirchhoff’s laws. This configuration illustrates the combination of resistors in series and parallel, providing a foundation for analyzing more complex circuits.
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