Determine the equivalent inductance of the following circuit 10 mH ll 60 mH el 25 mH 20 mH a o ll ll o b 30 mH ll
Determine the equivalent inductance of the following circuit 10 mH ll 60 mH el 25 mH 20 mH a o ll ll o b 30 mH ll
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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![### Problem Statement
**a) Determine the equivalent inductance of the following circuit:**
### Circuit Description
The given circuit consists of inductors arranged in both series and parallel configurations:
- **Series Configuration on the Right Branch:**
- A 10 mH inductor is in series with a 60 mH inductor.
- **Parallel Configuration on the Middle Branch:**
- The combination of the 10 mH and 60 mH inductors is in parallel with a 20 mH inductor.
- **Parallel Configuration on the Bottom Branch:**
- The resulting parallel combination of the 10 mH, 60 mH, and 20 mH inductors is in parallel with a 30 mH inductor.
- **Series Configuration on the Left:**
- The entire right-side combination is in series with a 25 mH inductor between points `a` and `b`.
### Explanation
To determine the equivalent inductance between points `a` and `b`, follow these steps:
1. **Compute Inductance in Series:**
- Add the series inductors: \( L_{\text{series}} = 10 \, \text{mH} + 60 \, \text{mH} = 70 \, \text{mH} \).
2. **Compute Parallel Inductance (Top and Middle):**
- The total inductance for parallel inductors is given by:
\[
\frac{1}{L_{\text{parallel1}}} = \frac{1}{70 \, \text{mH}} + \frac{1}{20 \, \text{mH}}
\]
- Calculate \( L_{\text{parallel1}} \).
3. **Compute Parallel Inductance (Including Bottom):**
- Combine the result with 30 mH:
\[
\frac{1}{L_{\text{parallel2}}} = \frac{1}{L_{\text{parallel1}}} + \frac{1}{30 \, \text{mH}}
\]
- Calculate \( L_{\text{parallel2}} \).
4. **Add the Series Inductor on the Left:**
- Add the 25 mH series inductor to find the total equivalent inductance:
\[
L_{\text{eq}} = L_{\text{parallel2](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F406074af-a425-40d0-923c-17adedf14fc2%2F8b97b31d-b1d9-4412-afc6-e8b477232ef0%2Fxosg14u_processed.png&w=3840&q=75)
Transcribed Image Text:### Problem Statement
**a) Determine the equivalent inductance of the following circuit:**
### Circuit Description
The given circuit consists of inductors arranged in both series and parallel configurations:
- **Series Configuration on the Right Branch:**
- A 10 mH inductor is in series with a 60 mH inductor.
- **Parallel Configuration on the Middle Branch:**
- The combination of the 10 mH and 60 mH inductors is in parallel with a 20 mH inductor.
- **Parallel Configuration on the Bottom Branch:**
- The resulting parallel combination of the 10 mH, 60 mH, and 20 mH inductors is in parallel with a 30 mH inductor.
- **Series Configuration on the Left:**
- The entire right-side combination is in series with a 25 mH inductor between points `a` and `b`.
### Explanation
To determine the equivalent inductance between points `a` and `b`, follow these steps:
1. **Compute Inductance in Series:**
- Add the series inductors: \( L_{\text{series}} = 10 \, \text{mH} + 60 \, \text{mH} = 70 \, \text{mH} \).
2. **Compute Parallel Inductance (Top and Middle):**
- The total inductance for parallel inductors is given by:
\[
\frac{1}{L_{\text{parallel1}}} = \frac{1}{70 \, \text{mH}} + \frac{1}{20 \, \text{mH}}
\]
- Calculate \( L_{\text{parallel1}} \).
3. **Compute Parallel Inductance (Including Bottom):**
- Combine the result with 30 mH:
\[
\frac{1}{L_{\text{parallel2}}} = \frac{1}{L_{\text{parallel1}}} + \frac{1}{30 \, \text{mH}}
\]
- Calculate \( L_{\text{parallel2}} \).
4. **Add the Series Inductor on the Left:**
- Add the 25 mH series inductor to find the total equivalent inductance:
\[
L_{\text{eq}} = L_{\text{parallel2
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