College Physics
College Physics
11th Edition
ISBN: 9781305952300
Author: Raymond A. Serway, Chris Vuille
Publisher: Cengage Learning
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In the figure, the ideal battery has an emf \( \mathcal{E} = 32.0 \, \text{V} \), and the resistances are \( R_1 = R_2 = 21.0 \, \Omega \), \( R_3 = R_4 = R_5 = 9.1 \, \Omega \), \( R_6 = 3.3 \, \Omega \), and \( R_7 = 18.0 \, \Omega \). 

What are the currents \( (a) \, i_1 \), \( (b) \, i_2 \), \( (c) \, i_3 \), and \( (d) \, i_6 \)?

**Diagram Explanation:**

The diagram illustrates a complex electrical circuit with multiple resistors and an ideal battery. Here are the key points:

- **Resistor Configuration:**
  - Resistors \( R_1 \) and \( R_2 \) are connected in series.
  - Resistors \( R_3 \), \( R_4 \), and \( R_5 \) are in parallel.
  - Resistor \( R_6 \) is connected in series with the parallel combination of \( R_3, R_4, \) and \( R_5 \).
  - Resistor \( R_7 \) is connected in parallel to the combination of \( R_1, R_2, R_6, \) and the parallel group \( R_3, R_4, \) and \( R_5 \).

- **Battery Placement:**
  - The battery, with an emf \( \mathcal{E} \) of 32.0 V, is placed to provide power to this network of resistors.

This configuration is part of a typical circuit analysis problem requiring calculation of currents through different parts of the circuit using techniques such as Kirchoff's laws or equivalent resistance methods.
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Transcribed Image Text:In the figure, the ideal battery has an emf \( \mathcal{E} = 32.0 \, \text{V} \), and the resistances are \( R_1 = R_2 = 21.0 \, \Omega \), \( R_3 = R_4 = R_5 = 9.1 \, \Omega \), \( R_6 = 3.3 \, \Omega \), and \( R_7 = 18.0 \, \Omega \). What are the currents \( (a) \, i_1 \), \( (b) \, i_2 \), \( (c) \, i_3 \), and \( (d) \, i_6 \)? **Diagram Explanation:** The diagram illustrates a complex electrical circuit with multiple resistors and an ideal battery. Here are the key points: - **Resistor Configuration:** - Resistors \( R_1 \) and \( R_2 \) are connected in series. - Resistors \( R_3 \), \( R_4 \), and \( R_5 \) are in parallel. - Resistor \( R_6 \) is connected in series with the parallel combination of \( R_3, R_4, \) and \( R_5 \). - Resistor \( R_7 \) is connected in parallel to the combination of \( R_1, R_2, R_6, \) and the parallel group \( R_3, R_4, \) and \( R_5 \). - **Battery Placement:** - The battery, with an emf \( \mathcal{E} \) of 32.0 V, is placed to provide power to this network of resistors. This configuration is part of a typical circuit analysis problem requiring calculation of currents through different parts of the circuit using techniques such as Kirchoff's laws or equivalent resistance methods.
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