https://file.aiquickdraw.com/mathbot/file/172735693681489u3y2xb.jpg

To find the total inductance of the given combination of inductors, we need to analyze the circuit configuration. From the image:

1. **L1 (10H)** is in series with the parallel combination of the inductors on the right side.
2. The right side shows **L2 (20H)** in parallel with **L3 (40H)**, which in turn is in parallel with the series combination of **L4 (30H)** and **L5 (60H)**.

Let's break this down step by step:

### Step 1: Simplify the inductors in series
- **L4** and **L5** are in series, so their total inductance is simply their sum:
  \[
  L_{45} = L_4 + L_5 = 30 \, H + 60 \, H = 90 \, H
  \]

### Step 2: Simplify the parallel combination of L2, L3, and L45
- Now, we have **L2 (20H)**, **L3 (40H)**, and **L45 (90H)** in parallel.
  The formula for the total inductance of inductors in parallel is:
  \[
  \frac{1}{L_{\text{parallel}}} = \frac{1}{L_2} + \frac{1}{L_3} + \frac{1}{L_{45}}
  \]
  Substituting the values:
  \[
  \frac{1}{L_{\text{parallel}}} = \frac{1}{20} + \frac{1}{40} + \frac{1}{90}
  \]

  Let's compute the equivalent inductance of this parallel combination.

### Step 3: Add L1 in series
- Once the equivalent inductance of the parallel combination is found, we will add **L1 (10H)**, since inductors in series simply add up.

Let me calculate the result.The total inductance of the given combination of inductors is approximately **21.61 H**.

Would you like further details or have any questions?

Here are 5 related questions to consider:
1. How do series and parallel combinations of inductors affect the overall inductance in a circuit?
2. What is the physical meaning of inductance, and how does it impact the behavior of circuits?
3. How would the total inductance change if the values of inductors were altered?
4. Why does adding inductors in parallel reduce the overall inductance, unlike in series?
5. What are some practical applications of inductors in electrical circuits?

**Tip:** When working with inductors, always remember that series combinations increase inductance, while parallel combinations decrease it.

Find the total inductance of the combination of the inductors shown below.

Learn how to find the total inductance of a combination of inductors arranged in both series and parallel configurations. This step-by-step guide covers key electrical circuit concepts and includes detailed calculations for inductors in series and parallel. Suitable for high school students in Grades 10-12.

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