7. For the circuit shown below, calculate the total resistance between points A & B.

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### Problem 7: Calculating Total Resistance in a Complex Circuit

**Objective:**

Calculate the total resistance between points A and B for the given circuit.

**Circuit Description:**

- **Resistors and Configuration:**
  - There is an 8 Ω resistor directly connected in series between points A and a junction.
  - At the first junction, the circuit splits into two parallel branches:
    - One branch has a 25 Ω resistor directly parallel.
    - The second branch connects to another junction.
  - Continuing from the second junction:
    - One path has a 30 Ω resistor.
    - Another path extends further and splits into an upper and lower branch.
  
- **Upper Branch:**
  - The upper branch has a 12 Ω resistor followed in series by a 15 Ω resistor.

- **Lower Branch:**
  - The lower branch contains an 8 Ω resistor and a 15 Ω resistor in series.

- **End Connection:**
  - All branches ultimately reconnect and lead back to point B.

**Steps to Calculate Total Resistance:**

1. **Parallel Combination:**
   - Calculate the combined resistance for resistors in parallel paths.
   
2. **Series Addition:**
   - Add series resistors where paths converged.

3. **Overall Resistance:**
   - Combine results from parallel and series calculations to determine total resistance. 

The task involves using the concepts of series and parallel circuits to find the equivalent resistance between two points by systematically simplifying the circuit.
Transcribed Image Text:### Problem 7: Calculating Total Resistance in a Complex Circuit **Objective:** Calculate the total resistance between points A and B for the given circuit. **Circuit Description:** - **Resistors and Configuration:** - There is an 8 Ω resistor directly connected in series between points A and a junction. - At the first junction, the circuit splits into two parallel branches: - One branch has a 25 Ω resistor directly parallel. - The second branch connects to another junction. - Continuing from the second junction: - One path has a 30 Ω resistor. - Another path extends further and splits into an upper and lower branch. - **Upper Branch:** - The upper branch has a 12 Ω resistor followed in series by a 15 Ω resistor. - **Lower Branch:** - The lower branch contains an 8 Ω resistor and a 15 Ω resistor in series. - **End Connection:** - All branches ultimately reconnect and lead back to point B. **Steps to Calculate Total Resistance:** 1. **Parallel Combination:** - Calculate the combined resistance for resistors in parallel paths. 2. **Series Addition:** - Add series resistors where paths converged. 3. **Overall Resistance:** - Combine results from parallel and series calculations to determine total resistance. The task involves using the concepts of series and parallel circuits to find the equivalent resistance between two points by systematically simplifying the circuit.
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