Req13 3kn 3kn 3kn 3kz 3kn Reqgz

Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
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Section: Chapter Questions
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Please help find the equivalent resistance of each resistive network. Specifically Req 11, 12, and 13 here.

### Series and Parallel Resistor Network Analysis

In the provided circuit diagram, we need to determine the equivalent resistances between points A and B, which are represented as \( R_{eq12} \) and \( R_{eq13} \).

#### Description:

- **Resistors in Series and Parallel:**
  - Several resistors with resistances of 3kΩ are arranged in both series and parallel configurations.

- **Analyzing the Network:**
  - The topmost path includes two resistors in series, both marked as 3kΩ.
  - The bottommost path also contains two resistors in series, each 3kΩ.
  - These two series paths create a parallel network:
    - The central part of the network connects the two horizontal paths with three vertical 3kΩ resistors arranged in series.
    - Additionally, there is a diagonal 3kΩ resistor linking the middle junction points of the vertical and horizontal resistors.
  - This configuration needs to be simplified to find the overall equivalent resistance.

#### Approach to Simplification:

1. **Identify Parallel and Series Connections:**
   - Combine series resistors first:
     - The top two resistors add up to form \( 3kΩ + 3kΩ = 6kΩ \) in total.
     - Similarly, the bottom two resistors also form \( 3kΩ + 3kΩ = 6kΩ \).

2. **Reduce the Combined Resistors in Parallel:**
   - Calculate the equivalent resistance of the two series pairs in parallel:
     - Formula for parallel resistors: 
       \[
       \frac{1}{R_{equivalent}} = \frac{1}{R_1} + \frac{1}{R_2}
       \]
     - Applying for our pairs:
       \[
       \frac{1}{R_{parallel}} = \frac{1}{6kΩ} + \frac{1}{6kΩ}
       \]
       \[
       R_{parallel} = 3kΩ
       \]

3. **Considering Other Resistors in the Network:**
   - The vertical 3kΩ resistors are positioned to form new series and parallel combinations that need further steps for consolidation.
   - The diagonal resistor provides an additional path affecting the equivalent resistance.

#### Final Equivalent Resistance:

- The final equivalent resistance calculation may require iterative simplification steps considering both series and
Transcribed Image Text:### Series and Parallel Resistor Network Analysis In the provided circuit diagram, we need to determine the equivalent resistances between points A and B, which are represented as \( R_{eq12} \) and \( R_{eq13} \). #### Description: - **Resistors in Series and Parallel:** - Several resistors with resistances of 3kΩ are arranged in both series and parallel configurations. - **Analyzing the Network:** - The topmost path includes two resistors in series, both marked as 3kΩ. - The bottommost path also contains two resistors in series, each 3kΩ. - These two series paths create a parallel network: - The central part of the network connects the two horizontal paths with three vertical 3kΩ resistors arranged in series. - Additionally, there is a diagonal 3kΩ resistor linking the middle junction points of the vertical and horizontal resistors. - This configuration needs to be simplified to find the overall equivalent resistance. #### Approach to Simplification: 1. **Identify Parallel and Series Connections:** - Combine series resistors first: - The top two resistors add up to form \( 3kΩ + 3kΩ = 6kΩ \) in total. - Similarly, the bottom two resistors also form \( 3kΩ + 3kΩ = 6kΩ \). 2. **Reduce the Combined Resistors in Parallel:** - Calculate the equivalent resistance of the two series pairs in parallel: - Formula for parallel resistors: \[ \frac{1}{R_{equivalent}} = \frac{1}{R_1} + \frac{1}{R_2} \] - Applying for our pairs: \[ \frac{1}{R_{parallel}} = \frac{1}{6kΩ} + \frac{1}{6kΩ} \] \[ R_{parallel} = 3kΩ \] 3. **Considering Other Resistors in the Network:** - The vertical 3kΩ resistors are positioned to form new series and parallel combinations that need further steps for consolidation. - The diagonal resistor provides an additional path affecting the equivalent resistance. #### Final Equivalent Resistance: - The final equivalent resistance calculation may require iterative simplification steps considering both series and
This is a schematic diagram representing a complex resistor network. Below is a detailed transcription and explanation suitable for an educational website:

---

### Resistor Network Diagram

The image above illustrates a network of resistors arranged in both series and parallel combinations. The goal is to determine the equivalent resistance (\( R_{eq} \)) of the network as indicated by \( R_{eq11} \). Here are the details of the components and their connections:

1. **Resistors:**
   - **2 kΩ Resistor**: Connected in series at the top left of the network.
   - **4 kΩ Resistor**: Connected in series after the 2 kΩ resistor.
   - **12 kΩ Resistor**: Placed in parallel with the combined network of the 4 kΩ, 3 kΩ, and 6 kΩ resistors.
   - **3 kΩ Resistor**: In series with an intermediate node.
   - **6 kΩ Resistor**: In parallel with the 3 kΩ resistor from the intermediate node.

2. **Connections:**
   - The 4 kΩ and 3 kΩ resistors form a series combination.
   - This series combination (4 kΩ + 3 kΩ) is in parallel with the 6 kΩ resistor.
   - The 12 kΩ resistor is in parallel with the entire combination mentioned above.
   - Finally, this combined parallel set-up is connected in series with the initial 2 kΩ resistor.

### Steps to Calculate Equivalent Resistance (\( R_{eq} \)):

1. **Series and Parallel Combinations**
   - First, compute the equivalent resistance of the 3 kΩ and 6 kΩ resistors in parallel:
     \[
     R_{\text{parallel}} = \left(\frac{1}{3 kΩ} + \frac{1}{6 kΩ}\right)^{-1} = 2 kΩ
     \]
   
   - Next, add the 4 kΩ resistor in series with the above combination:
     \[
     R_{\text{series}} = 2 kΩ + 4 kΩ = 6 kΩ
     \]
   
   - Then, calculate the equivalent resistance of the 12 kΩ resistor in parallel with the 6 kΩ obtained above:
     \[
     R_{\text{parallel total}} = \left(\frac{1}{6 kΩ}
Transcribed Image Text:This is a schematic diagram representing a complex resistor network. Below is a detailed transcription and explanation suitable for an educational website: --- ### Resistor Network Diagram The image above illustrates a network of resistors arranged in both series and parallel combinations. The goal is to determine the equivalent resistance (\( R_{eq} \)) of the network as indicated by \( R_{eq11} \). Here are the details of the components and their connections: 1. **Resistors:** - **2 kΩ Resistor**: Connected in series at the top left of the network. - **4 kΩ Resistor**: Connected in series after the 2 kΩ resistor. - **12 kΩ Resistor**: Placed in parallel with the combined network of the 4 kΩ, 3 kΩ, and 6 kΩ resistors. - **3 kΩ Resistor**: In series with an intermediate node. - **6 kΩ Resistor**: In parallel with the 3 kΩ resistor from the intermediate node. 2. **Connections:** - The 4 kΩ and 3 kΩ resistors form a series combination. - This series combination (4 kΩ + 3 kΩ) is in parallel with the 6 kΩ resistor. - The 12 kΩ resistor is in parallel with the entire combination mentioned above. - Finally, this combined parallel set-up is connected in series with the initial 2 kΩ resistor. ### Steps to Calculate Equivalent Resistance (\( R_{eq} \)): 1. **Series and Parallel Combinations** - First, compute the equivalent resistance of the 3 kΩ and 6 kΩ resistors in parallel: \[ R_{\text{parallel}} = \left(\frac{1}{3 kΩ} + \frac{1}{6 kΩ}\right)^{-1} = 2 kΩ \] - Next, add the 4 kΩ resistor in series with the above combination: \[ R_{\text{series}} = 2 kΩ + 4 kΩ = 6 kΩ \] - Then, calculate the equivalent resistance of the 12 kΩ resistor in parallel with the 6 kΩ obtained above: \[ R_{\text{parallel total}} = \left(\frac{1}{6 kΩ}
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