3 FIND THE EQUIVALENT INDUCTANCE (IN TERMS OF L), LE BETWEEN TERMINALS A AND B
3 FIND THE EQUIVALENT INDUCTANCE (IN TERMS OF L), LE BETWEEN TERMINALS A AND B
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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![**Instruction for Problem Solving**
**Title:** Inductor Network Analysis
**Objective:** Find the equivalent inductance between terminals A and B in terms of a given inductance value, L.
**Diagram Description:**
The diagram represents a network of inductors arranged between two terminals, labeled A and B. The inductors are connected as follows:
- At the top, there is one inductor labeled \(L_0\) connected longitudinally between terminal A and the junction point of two inductors.
- Below \(L_0\), there are three horizontal rows, each containing three inductors labeled \(L\) in series.
- Each row is connected in parallel to form a ladder-like structure.
- At the ends of these rows, the bottom-left inductor is connected to terminal B.
**Understanding the Setup:**
1. **Series Configuration:** Inductors in series within each row will sum up to a total inductance. For a series of three inductors, the equivalent inductance in each row is \(3L\).
2. **Parallel Configuration:** The overall equivalent inductance of the parallel rows needs to be calculated using the formula for parallel inductors:
\[
\frac{1}{L_{\text{eq}}} = \frac{1}{L_1} + \frac{1}{L_2} + \ldots + \frac{1}{L_n}
\]
3. **Overall Circuit:** After calculating \(L_{\text{eq}}\) for the parallel network, combine it with \(L_0\) in series for the final equivalent inductance between A and B.
**Solution Steps:**
1. Calculate the series inductance for each row.
2. Calculate the equivalent inductance of the three parallel branches.
3. Add \(L_0\) in series to find the total equivalent inductance.
This approach will allow you to find the overall inductance in terms of L and L_0 for the given network.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fabc5aa9d-951a-40e1-86a3-f092042c4046%2Fd87f24be-47c2-405b-b7c4-3f16cfefc9cc%2F2ak6zyh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Instruction for Problem Solving**
**Title:** Inductor Network Analysis
**Objective:** Find the equivalent inductance between terminals A and B in terms of a given inductance value, L.
**Diagram Description:**
The diagram represents a network of inductors arranged between two terminals, labeled A and B. The inductors are connected as follows:
- At the top, there is one inductor labeled \(L_0\) connected longitudinally between terminal A and the junction point of two inductors.
- Below \(L_0\), there are three horizontal rows, each containing three inductors labeled \(L\) in series.
- Each row is connected in parallel to form a ladder-like structure.
- At the ends of these rows, the bottom-left inductor is connected to terminal B.
**Understanding the Setup:**
1. **Series Configuration:** Inductors in series within each row will sum up to a total inductance. For a series of three inductors, the equivalent inductance in each row is \(3L\).
2. **Parallel Configuration:** The overall equivalent inductance of the parallel rows needs to be calculated using the formula for parallel inductors:
\[
\frac{1}{L_{\text{eq}}} = \frac{1}{L_1} + \frac{1}{L_2} + \ldots + \frac{1}{L_n}
\]
3. **Overall Circuit:** After calculating \(L_{\text{eq}}\) for the parallel network, combine it with \(L_0\) in series for the final equivalent inductance between A and B.
**Solution Steps:**
1. Calculate the series inductance for each row.
2. Calculate the equivalent inductance of the three parallel branches.
3. Add \(L_0\) in series to find the total equivalent inductance.
This approach will allow you to find the overall inductance in terms of L and L_0 for the given network.
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