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Find the equivalent inductance between terminals A and B in the following figure. Assume no mutual inductance between any of the inductors.

Find the equivalent inductance between terminals A and B in the following figure. Assume no mutual inductance between any of the inductors.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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Find the equivalent inductance between terminals A and B in the following figure. Assume no mutual inductance between any of the inductors.

### Diagram Explanation: Inductor Network This diagram represents an inductor network circuit, specifically a combination of series and parallel inductor arrangements. #### Components: - **Inductors**: There are six inductors, each with an inductance value of 25 mH (millihenries). - **Nodes**: The circuit has two main nodes labeled A and B. #### Configuration: 1. **Series Inductors**: - The inductors between nodes A and B can be grouped into three pairs. - Each pair is connected in series. 2. **Parallel Inductors**: - The top and bottom series pairs are connected in parallel with the middle series pair. - This can be visualized as follows: - `L1 (25 mH)` and `L2 (25 mH)` are connected in series. - This is duplicated for the middle pair and bottom pair. - The branch with `L3 (25 mH)` and `L4 (25 mH)` in series lies in parallel with the two other branch pairs. #### Detailed Path: - Starting at node A: - First, a 25 mH inductor. - The connection then splits. - One path further splits into: - a top path with one 25 mH inductor followed by another 25 mH inductor. - a bottom path with two 25 mH inductors in series. - The middle path contains two 25 mH inductors in series. - These paths rejoin at node B. ### Explanation: - **Series Connection**: When inductors are connected in series, the total inductance (L_total) is the sum of the individual inductances. - **Parallel Connection**: When inductors are connected in parallel, the total inductance is given by the reciprocal of the sum of the reciprocals of the individual inductances. ### Application in Education: Understanding the combination of series and parallel inductor connections is crucial for students studying electrical engineering and physics. It helps in grasping the concepts of inductance and the effects on a circuit. This diagram can be used as an example problem for calculating equivalent inductance and analyzing complex circuits. ### Practice Problem: 1. **Calculate Equivalent Inductance**: Given the above circuit, calculate the total inductance between points A and B. 2. **Step-by-step Solution**: - Calculate
Transcribed Image Text:### Diagram Explanation: Inductor Network This diagram represents an inductor network circuit, specifically a combination of series and parallel inductor arrangements. #### Components: - **Inductors**: There are six inductors, each with an inductance value of 25 mH (millihenries). - **Nodes**: The circuit has two main nodes labeled A and B. #### Configuration: 1. **Series Inductors**: - The inductors between nodes A and B can be grouped into three pairs. - Each pair is connected in series. 2. **Parallel Inductors**: - The top and bottom series pairs are connected in parallel with the middle series pair. - This can be visualized as follows: - `L1 (25 mH)` and `L2 (25 mH)` are connected in series. - This is duplicated for the middle pair and bottom pair. - The branch with `L3 (25 mH)` and `L4 (25 mH)` in series lies in parallel with the two other branch pairs. #### Detailed Path: - Starting at node A: - First, a 25 mH inductor. - The connection then splits. - One path further splits into: - a top path with one 25 mH inductor followed by another 25 mH inductor. - a bottom path with two 25 mH inductors in series. - The middle path contains two 25 mH inductors in series. - These paths rejoin at node B. ### Explanation: - **Series Connection**: When inductors are connected in series, the total inductance (L_total) is the sum of the individual inductances. - **Parallel Connection**: When inductors are connected in parallel, the total inductance is given by the reciprocal of the sum of the reciprocals of the individual inductances. ### Application in Education: Understanding the combination of series and parallel inductor connections is crucial for students studying electrical engineering and physics. It helps in grasping the concepts of inductance and the effects on a circuit. This diagram can be used as an example problem for calculating equivalent inductance and analyzing complex circuits. ### Practice Problem: 1. **Calculate Equivalent Inductance**: Given the above circuit, calculate the total inductance between points A and B. 2. **Step-by-step Solution**: - Calculate
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