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Find the equivalent inductance, Leq, where L1 = 9.9 H, L2 = 9.9 H, L3 = 9.7 H, L4 = 6.8 H, L5 = 1.3 H, L6 = 7.6 H, L7 = 7.4 H, and L8 = 9.2 H. Don't forget to include a unit in your answer.

To find the equivalent inductance \( L_{eq} \) of the circuit, we need to follow these steps:

### 1. Analyze the Circuit Configuration
- **Identify Series and Parallel Combinations:**
  - **L4** and **L5** are in parallel.
  - The result of \( L4 \) and \( L5 \) in parallel is in series with \( L3 \).
  - The result of \( L3 \), \( L4 \), and \( L5 \) is in parallel with \( L1 \).
  - The result of the above parallel combination is in series with \( L2 \).
  - \( L6 \), \( L7 \), and \( L8 \) are in series.

### 2. Compute the Combinations
- **L4** and **L5** in parallel:
  \[
  \frac{1}{L_{45}} = \frac{1}{L4} + \frac{1}{L5}
  \]
  \[
  L_{45} = \frac{L4 \times L5}{L4 + L5}
  \]
  Substituting values:
  \[
  L_{45} = \frac{6.8 \times 1.3}{6.8 + 1.3} = \frac{8.84}{8.1} \approx 1.0914 \text{ H}
  \]

- **L_{45}** in series with \( L3 \):
  \[
  L_{345} = L_{45} + L3 = 1.0914 + 9.7 \approx 10.7914 \text{ H}
  \]

- **L_{345}** in parallel with \( L1 \):
  \[
  \frac{1}{L_{1345}} = \frac{1}{L1} + \frac{1}{L_{345}}
  \]
  \[
  L_{1345} = \frac{L1 \times L_{345}}{L1 + L_{345}} = \frac{9.9 \times 10.7914}{9.9 + 10.7914} \approx 5.1448 \text{ H}
  \]

- **L_{1345}** in series with \( L2 \):
  \[
  L_{12345} = L_{1345} + L2 = 5.1448 + 9.9 = 15.0448 \text{ H}
  \]

- **L6**, **L7**, and **L8** are in series:
  \[
  L_{678} = L6 + L7 + L8 = 7.6 + 7.4 + 9.2 = 24.2 \text{ H}
  \]

- **Finally, \( L_{eq} \) is the series combination of \( L_{12345} \) and \( L_{678} \):**
  \[
  L_{eq} = L_{12345} + L_{678} = 15.0448 + 24.2 = 39.2448 \text{ H}
  \]

### Final Answer
The equivalent inductance \( L_{eq} \) is approximately \( \mathbf{39.2448 \, H} \).

Would you like more details on any step or have any other questions?

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### Follow-up Questions:
1. How do you find the equivalent inductance of inductors in series?
2. How do you find the equivalent inductance of inductors in parallel?
3. What are the general steps to simplify complex inductance circuits?
4. Why is the reciprocal method used for parallel inductances?
5. How does the equivalent inductance change if additional inductors are added in series?
6. How does the equivalent inductance change if additional inductors are added in parallel?
7. Can you explain why inductance in parallel is less than the smallest individual inductance?
8. How do we use Kirchhoff's laws to analyze inductance in more complex circuits?

### Tip:
When working with inductors, remember that the total inductance decreases in parallel combinations and increases in series combinations, which is opposite to resistors.

Learn how to calculate the equivalent inductance (Leq) of a complex circuit using series and parallel combinations of inductors. This example involves determining Leq from given inductance values (L1 = 9.9 H, L2 = 9.9 H, L3 = 9.7 H, L4 = 6.8 H, L5 = 1.3 H, L6 = 7.6 H, L7 = 7.4 H, L8 = 9.2 H). Detailed step-by-step solution provided.

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