Name: equivalent inductance in circuit networks
Uploaded: 2024-04-11T12:48:39.000Z
Duration: 1 min 17 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.6

IPC.6.A

Series and Parallel Inductors

Les inductances connectées en série et/ou en parallèle peuvent être simplifiées en une seule inductance équivalente.
Considérons une connexion en série d’inductances avec le même courant qui les traverse.
Lorsque la loi de tension de Kirchhoff est appliquée à la boucle et que l'expression des tensions de l'inductance est substituée, l'expression résultante indique que l'inductance équivalente de ces inductances connectées en série est égale à la somme des inductances individuelles.
Ensuite, considérez une connexion parallèle d’inductances, où chaque inductance subit la même tension à ses bornes. La loi de courant de Kirchhoff est appliquée à la boucle et l'expression du courant d'inductance est substituée.
Étant donné que le courant initial traversant l’inductance équivalente est la somme des courants d’inductance individuels, la somme des inverses des inductances individuelles est égale à l’inverse de l’inductance équivalente.
Les combinaisons d’inductances en série et en parallèle suivent des règles similaires à celles des résistances.
Considérons un circuit avec des inductances en série et en parallèle. L’inductance équivalente de la combinaison parallèle d’inductances est calculée et ajoutée à l’inductance série pour obtenir l’inductance équivalente totale.

inductances série et parallèle

Dans les circuits électriques, l’intégration d’inductances dans la boîte à outils d’éléments passifs nécessite de naviguer dans les subtilités des combinaisons série et parallèle impliquant ces composants. Les circuits pratiques comportent souvent des configurations de plusieurs inductances, et il est essentiel de comprendre comment déterminer leur inductance équivalente. Pour une connexion en série de N inductances, chacune transportant le même courant, l'application de la loi de tension de Kirchhoff révèle une relation cruciale. La substitution de l'expression des tensions d'inductance conduit à une conclusion perspicace : l'inductance équivalente de cet arrangement en série est la simple sommation des inductances individuelles. Ce phénomène reflète la façon dont les résistances se combinent en série, soulignant une similitude fondamentale entre ces éléments passifs. <img alt="Equation1" src="/files/ftp_upload/15090/15090_Equation_1.svg" style="text-align: center; height: 16px;"> Dans une connexion parallèle d'inducteurs, chacun supporte une tension identique ; La loi actuelle de Kirchhoff peut être appliquée. Cela conduit à une révélation significative : l’inverse de l’inductance équivalente est égal à la somme des inverses des inductances individuelles. Cette règle de combinaison parallèle reflète le comportement des résistances en parallèle, illustrant une approche harmonieuse du traitement des différents éléments passifs. <img alt="Equation2" src="/files/ftp_upload/15090/15090_Equation_2.svg" style="text-align: center; height: 34px;"> Dans la pratique, les circuits comportent souvent un mélange d'inductances série et parallèle. Face à de tels scénarios, l'inductance équivalente des inductances parallèles est calculée et ajoutée à l'inductance série pour obtenir l'inductance équivalente globale du circuit.

Inductances série et parallèle

Les inductances connectées en série et/ou en parallèle peuvent être simplifiées en une seule inductance équivalente.
Considérons une connexion en série d’inductances ...

Education

Enseignement

JoVE Core

Electrical Engineering

Génie électrique

Unit 1

Unité 1

Energy Storage Elements

Éléments de stockage d'énergie

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

equivalent inductance in circuit networks

Equivalent inductance in circuit networks helps simplify circuits with multiple inductors. When inductors are combined, the circuit can often be replaced by one inductor with the same effect on the current and voltage.

For inductors in series, the same current flows through each component. Applying Kirchhoff's voltage law shows that the total voltage is the sum of the inductor voltages. As a result, the equivalent inductance of a series group is the sum of the individual inductances. This is the same pattern used for resistors in series.

For inductors in parallel, each branch has the same voltage. Kirchhoff's current law gives the key relationship for this arrangement. The reciprocal of the equivalent inductance equals the sum of the reciprocals of the individual inductances. This matches the rule used for resistors in parallel.

Many practical circuits use a mix of series and parallel inductors. In those cases, the parallel inductors are first combined into one equivalent inductance. That result is then added to the inductance in series to find the total equivalent inductance of the circuit.

Equivalent Inductance in Circuit Networks

equivalent-inductance-in-circuit-networks

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Equivalent inductance in circuit networks helps simplify circuits with multiple inductors. When inductors are combined, the circuit can often be replaced by one inductor with the same effect on the current and voltage. For inductors in series, the same current flows through each component. Applying Kirchhoff's voltage law shows that the total voltage is the sum of the inductor voltages. As a result, the equivalent inductance of a series group is the sum of the individual inductances. This is...

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Learn how series and parallel inductors combine in circuits. See how Kirchhoff's laws give the rules for equivalent inductance in mixed networks.

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Equivalent Inductance in Circuit Networks

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