Name: series and parallel impedance rules
Uploaded: 2024-04-11T12:48:49.000Z
Duration: 1 min 21 s
Channel: JoVE

Stellen Sie sich eine Weihnachtsbeleuchtungskette vor, bei der jede Glühbirne eine Impedanz darstellt. Diese Reihenanordnung der Impedanzen gewährleistet einen gleichmäßigen Strom über jedes Bauteil.
Unter Anwendung des Kirchhoffschen Spannungsgesetzes entspricht die äquivalente Impedanz der Summe einzelner Impedanzen, ähnlich wie bei Reihenwiderständen.
Die Quellspannung wird proportional auf mehrere Komponenten verteilt, basierend auf ihren jeweiligen Impedanzen, wobei das Prinzip der Spannungsteilung eingehalten wird.
Bei einer Reihenschaltung löst die Fehlfunktion einer einzelnen Glühbirne eine Unterbrechung aus, wodurch der Stromfluss unterbrochen wird.
Daher wird die Weihnachtsbeleuchtung in der Regel parallel verdrahtet, um eine konstante Spannung über jede Komponente zu gewährleisten.
Wendet man das Kirchhoffsche Gesetz auf diese Parallelschaltung an, so zeigt sich, dass der Kehrwert der äquivalenten Impedanz gleich der Summe der Kehrwerte der einzelnen Impedanzen ist, ähnlich wie bei parallelen Widerständen.
Die äquivalente Aufnahme ergibt sich also aus der Summe der einzelnen Aufnahmen.
Der Quellstrom teilt sich unter den Komponenten im umgekehrten Verhältnis zu ihren Impedanzen auf, was das Stromteilungsprinzip demonstriert.
Dabei baut jede Komponente einen unabhängigen Weg zur Stromquelle auf, der einen isolierten Stromfluss ermöglicht.

impedanzkombination

Stellen Sie sich eine Weihnachtslichterkette vor, wobei jede Glühbirne ein Impedanzelement symbolisiert. In dieser Reihenschaltung bleibt der Stromfluss über alle Komponenten hinweg gleichmäßig. Dieses Verhalten steht im Einklang mit dem Kirchhoffschen Spannungsgesetz (KVL), das besagt, dass die Gesamtimpedanz in einem solchen Aufbau der Summe der einzelnen Impedanzen entspricht – ähnlich wie bei in Reihe geschalteten Widerständen. Daraus folgt, dass die Spannung der Stromquelle nach dem Spannungsteilungsprinzip proportional auf diese Komponenten verteilt wird. <img alt="Equation1" src="/files/ftp_upload/15569/15569_PT_Equation_1.svg" style="text-align: center; height: 48px;"> Der Nachteil dieser Reihenschaltung zeigt sich jedoch, wenn eine einzelne Glühbirne ausfällt und ein offener Stromkreis entsteht, der den gesamten Stromfluss unterbricht. Weihnachtsbeleuchtungen werden typischerweise parallel angeordnet, um eine kontinuierliche und stabile Stromversorgung zu gewährleisten. Dieser Aufbau garantiert eine konstante Spannung an jeder Glühbirne gemäß dem Kirchhoffschen Stromgesetz (KCL), bei dem der Kehrwert der äquivalenten Impedanz der Summe der Kehrwerte der einzelnen Impedanzen entspricht – ähnlich wie bei parallel geschalteten Widerständen. Daraus folgt, dass die äquivalente Zulassung die Summe der einzelnen Zulassungen ist. In dieser Parallelanordnung teilt sich der Quellenstrom umgekehrt basierend auf den Impedanzen der einzelnen Lampen, was ein Beispiel für das Stromteilungsprinzip ist. Insbesondere stellt jede Glühbirne einen unabhängigen Weg zur Stromquelle her und ermöglicht so einen isolierten und unterbrechungsfreien Stromfluss. <img alt="Equation2" src="/files/ftp_upload/15569/15569_PT_Equation_2.svg" style="text-align: center; height: 48px;"> <img alt="Equation3" src="/files/ftp_upload/15569/15569_PT_Equation_3.svg" style="text-align: center; height: 40px;"> Darüber hinaus können in komplexeren Schaltkreisen mit sowohl Reihen- als auch Parallelimpedanzen die Delta-zu-Y- und Y-zu-Delta-Transformationen auch für Impedanzschaltungen verwendet werden und bieten wertvolle Werkzeuge für die Schaltungsanalyse und den Entwurf. Diese Transformationen erleichtern die Konvertierung zwischen verschiedenen Impedanzkonfigurationen und erhöhen die Vielseitigkeit impedanzbasierter Schaltkreise.

Impedanzkombination

Stellen Sie sich eine Weihnachtsbeleuchtungskette vor, bei der jede Glühbirne eine Impedanz darstellt. Diese Reihenanordnung der Impedanzen gewährleistet einen gleichmäßigen Strom über ...

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Impedance Combination

series and parallel impedance rules

Impedance in series and parallel circuits follows the same rules used for resistors. A string of Christmas lights is a simple example. Each bulb represents one impedance element. In a series connection, the current stays the same through every component.

This series behavior matches Kirchhoff’s Voltage Law, or KVL. The total impedance in the circuit is the sum of the individual impedances. The source voltage is then divided among the components based on their values. This is the voltage division principle. One weak point of a series circuit is that one failed bulb can open the circuit and stop current flow.

Christmas lights are often wired in parallel to avoid that problem. In a parallel circuit, each bulb keeps its own path to the power source. The voltage across each bulb stays constant. This matches Kirchhoff’s Current Law, or KCL. For parallel impedance, the reciprocal of the equivalent impedance equals the sum of the reciprocals of the individual impedances.

The equivalent admittance is the sum of the individual admittances. Admittance is the inverse of impedance. In this setup, the source current splits according to the impedances of the branches. This is the current division principle. Because each bulb has an independent path, current can keep flowing even if one branch fails.

For circuits that mix series and parallel impedances, delta-to-wye and wye-to-delta transformations are useful. These methods let students convert one impedance network into another form. They make circuit analysis and design more flexible.

Series and Parallel Impedance Rules

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impedance combination

Impedance in series and parallel circuits follows the same rules used for resistors. A string of Christmas lights is a simple example. Each bulb represents one impedance element. In a series connection, the current stays the same through every component. This series behavior matches Kirchhoff’s Voltage Law, or KVL. The total impedance in the circuit is the sum of the individual impedances. The source voltage is then divided among the components based on their values. This is the voltage...

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electrical engineering

Series and Parallel Impedance Rules

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