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

Induktivitäten, die in Reihe und/oder parallel geschaltet sind, können zu einer gleichwertigen Einzelinduktivität vereinfacht werden.
Stellen Sie sich eine Reihenschaltung von Induktivitäten vor, durch die der gleiche Strom fließt.
Wenn das Kirchhoffsche Spannungsgesetz auf die Schleife angewendet wird und der Ausdruck für die Induktivitätsspannungen ersetzt wird, zeigt der resultierende Ausdruck an, dass die äquivalente Induktivität dieser in Reihe geschalteten Induktivitäten gleich der Summe der einzelnen Induktivitäten ist.
Betrachten Sie als Nächstes eine Parallelschaltung von Induktivitäten, bei der jede Induktivität die gleiche Spannung erfährt. Das Kirchhoffsche Stromgesetz wird auf die Schleife angewendet, und der Ausdruck für den Induktorstrom wird ersetzt.
Da der Anfangsstrom durch die äquivalente Induktivität die Summe der einzelnen Induktivitätsströme ist, ist die Summe der Kehrwerte der einzelnen Induktivitäten gleich dem Kehrwert der äquivalenten Induktivität.
Induktorkombinationen in Reihe und parallel folgen ähnlichen Regeln wie Widerstände.
Stellen Sie sich eine Schaltung mit seriellen und parallelen Induktivitäten vor. Die äquivalente Induktivität der parallelen Kombination von Induktivitäten wird berechnet und zur Serieninduktivität addiert, um die gesamte äquivalente Induktivität zu erhalten.

serien- und parallelinduktoren

In elektrischen Schaltkreisen erfordert die Integration von Induktivitäten in den Baukasten passiver Elemente die Beherrschung der Feinheiten von Reihen- und Parallelkombinationen dieser Komponenten. Praktische Schaltkreise verfügen häufig über Konfigurationen aus mehreren Induktivitäten, und es ist von entscheidender Bedeutung, zu verstehen, wie ihre äquivalente Induktivität bestimmt wird. Für eine Reihenschaltung von N Induktivitäten, von denen jede den gleichen Strom führt, offenbart die Anwendung des Kirchhoffschen Spannungsgesetzes einen entscheidenden Zusammenhang. Die Substitution des Ausdrucks für die Induktionsspannungen führt zu einer aufschlussreichen Schlussfolgerung: Die äquivalente Induktivität dieser Reihenschaltung ist die einfache Summe der einzelnen Induktivitäten. Dieses Phänomen spiegelt wider, wie Widerstände in Reihe geschaltet werden, und unterstreicht eine grundlegende Ähnlichkeit zwischen diesen passiven Elementen. <img alt="Equation1" src="/files/ftp_upload/15090/15090_Equation_1.svg" style="text-align: center; height: 16px;"> Bei einer Parallelschaltung von Induktoren führt jeder eine identische Spannung; Das Kirchhoffsche Stromgesetz kann angewendet werden. Dies führt zu einer wichtigen Erkenntnis: Der Kehrwert der äquivalenten Induktivität ist gleich der Summe der Kehrwerte der einzelnen Induktivitäten. Diese Parallelkombinationsregel spiegelt das Verhalten paralleler Widerstände wider und veranschaulicht einen harmonischen Ansatz für den Umgang mit verschiedenen passiven Elementen. <img alt="Equation2" src="/files/ftp_upload/15090/15090_Equation_2.svg" style="text-align: center; height: 34px;"> In der Praxis sind Schaltungen häufig mit einer Mischung aus Reihen- und Parallelinduktivitäten ausgestattet. Bei solchen Szenarien wird die äquivalente Induktivität der parallelen Induktivitäten berechnet und zur Serieninduktivität addiert, um die gesamte äquivalente Induktivität der Schaltung zu erhalten.

Serien- und Parallelinduktoren

Induktivitäten, die in Reihe und/oder parallel geschaltet sind, können zu einer gleichwertigen Einzelinduktivität vereinfacht werden.
Betrachten Sie eine Reihenschaltung von Induktivitäten ...

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

Energy Storage Elements

Energiespeicherelemente

KEY TERMS AND CONCEPTS

WICHTIGE BEGRIFFE UND KONZEPTE

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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