### Problem StatementIn the figure below, what is the potential difference $ V_{ab} $ between points $ a $ and $ b $ if $ \varepsilon_1 = 5.4 \, \text{V}, \varepsilon_2 = 1.5 \, \text{V}, R_1 = 14.0 \, \Omega, $ and $ R_2 = 5.7 \, \Omega, $ and the batteries are ideal?### Circuit Diagram ExplanationIn the accompanying circuit diagram, a complex circuit is presented with the following elements:- **Batteries**: - $ \varepsilon_1 = 5.4 \, \text{V} $ - $ \varepsilon_2 = 1.5 \, \text{V} $- **Resistors**: - $ R_1 = 14.0 \, \Omega $ - $ R_2 = 5.7 \, \Omega $- **Currents**: - $ i_1 $: Current through the branch with $ R_1 $ - $ i_2 $: Current through the branch with $ R_2 $- **Points**: - $ a $ and $ b $: Points between which the potential difference $ V_{ab} $ is calculated.This diagram presents a typical series and parallel circuit where resistors and batteries are arranged to determine the voltage difference across designated points. The currents $ i_1 $ and $ i_2 $ split at the junctions and merge again, forming a loop. The parameters given are to be used in Ohm's Law and Kirchhoff’s rules to find the required potential difference $ V_{ab} $.

Answered: In the figure below, what is the…

College Physics

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ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

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### Problem Statement

In the figure below, what is the potential difference $ V_{ab} $ between points $ a $ and $ b $ if $ \varepsilon_1 = 5.4 \, \text{V}, \varepsilon_2 = 1.5 \, \text{V}, R_1 = 14.0 \, \Omega, $ and $ R_2 = 5.7 \, \Omega, $ and the batteries are ideal?

### Circuit Diagram Explanation

In the accompanying circuit diagram, a complex circuit is presented with the following elements:

- **Batteries**:
- $ \varepsilon_1 = 5.4 \, \text{V} $
- $ \varepsilon_2 = 1.5 \, \text{V} $

- **Resistors**:
- $ R_1 = 14.0 \, \Omega $
- $ R_2 = 5.7 \, \Omega $

- **Currents**:
- $ i_1 $: Current through the branch with $ R_1 $
- $ i_2 $: Current through the branch with $ R_2 $

- **Points**:
- $ a $ and $ b $: Points between which the potential difference $ V_{ab} $ is calculated.

This diagram presents a typical series and parallel circuit where resistors and batteries are arranged to determine the voltage difference across designated points. The currents $ i_1 $ and $ i_2 $ split at the junctions and merge again, forming a loop. The parameters given are to be used in Ohm's Law and Kirchhoff’s rules to find the required potential difference $ V_{ab} $.

Expert Solution

Step 1: Kirchhoff's current law

Apply Kirchhoff's current law at junction b.

$table row cell sum I subscript b equals 0 end cell row cell i subscript 2 minus i subscript 1 minus i subscript 3 equals 0 end cell row cell i subscript 3 equals i subscript 2 minus i subscript 1 text end text ..... text end text left parenthesis 1 right parenthesis end cell end table$

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