Name: capacitors in series and parallel
Uploaded: 2024-04-11T12:48:39.000Z
Duration: 1 min 19 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry and Physics

IPC.6

IPC.6.A

Equivalent Capacitance

Stellen Sie sich ein komplexes Kondensatornetzwerk vor, in dem drei Gruppen von Kondensatoren parallel geschaltet sind, die dann in Reihe geschaltet werden. Bestimmen Sie die äquivalente Kapazität zwischen den Anschlüssen dieser komplizierten Schaltung.
Um dies zu lösen, wird zunächst die Gruppe am unteren Ende der Schaltung, bestehend aus vier parallel geschalteten Kondensatoren, analysiert. Die Summe ihrer Kapazität ergibt eine äquivalente Kapazität, die durch einen einzelnen Kondensator C3 dargestellt wird.
Als nächstes wird die mittlere Gruppe mit drei Kondensatoren parallel betrachtet. Auch hier ergibt die Addition ihrer Kapazitäten die äquivalente Kapazität C2.
Betrachten Sie schließlich die obere Gruppe, die zwei Kondensatoren parallel hat. Die äquivalente Kapazität wird berechnet und mit einem Kondensator, C1, dargestellt.
Jetzt wurde die komplexe Schaltung in drei in Reihe geschaltete Kondensatoren vereinfacht.
Um die äquivalente Kapazität für diese Reihenkombination zu bestimmen, wird die Summe der Kehrwerte jeder Kapazität genommen, was den Kehrwert der äquivalenten Kapazität ergibt.
Durch Neuanordnen der Terme erhält man die äquivalente Kapazität der gesamten Schaltung zwischen den Klemmen.

Äquivalente kapazität

Aus der Untersuchung von Widerstandsschaltungen geht hervor, dass der Einsatz einer Serien-Parallel-Kombination eine wirksame Strategie zur Vereinfachung von Schaltungen darstellt. Kondensatoren können innerhalb eines Stromkreises auf zwei Arten angeordnet werden: in Reihenschaltung oder in Parallelschaltung. Die Art und Weise, wie diese Kondensatoren an eine Batterie angeschlossen sind, beeinflusst sowohl den Potentialabfall an jedem einzelnen Kondensator als auch die Größe der Ladung, die jeder Kondensator speichern kann. Dies wird durch die spezifische Art der vorhandenen Verbindung bestimmt. Um dieses Szenario zu vereinfachen, kann die Kombination von Kondensatoren durch einen einzigen äquivalenten Kondensator ersetzt werden. Dieser äquivalente Kondensator ist in der Lage, eine identische Ladungsmenge wie die ursprüngliche Kombination zu speichern, wenn er der gleichen Potentialdifferenz ausgesetzt wird. Bei einer Parallelschaltung von N Kondensatoren liegt an allen die gleiche Spannung an. Die äquivalente Kapazität für eine solche Konfiguration ist gegeben durch <img alt="Equation1" src="/files/ftp_upload/15087/15087_PT_Equation_1.svg" style="text-align: center; height: 14px;"> Es ist wichtig zu beachten, dass die äquivalente Kapazität von N parallel geschalteten Kondensatoren der Summe ihrer Einzelkapazitäten entspricht. Geht man nun zu dem Szenario über, in dem N Kondensatoren in Reihe miteinander verbunden sind, stellt man fest, dass durch alle Kondensatoren der gleiche Strom i und folglich die gleiche Ladung fließt. Die äquivalente Kapazität dieses Aufbaus wird dargestellt als <img alt="Equation2" src="/files/ftp_upload/15087/15087_PT_Equation_2.svg" style="text-align: center; height: 32px;"> Im Gegensatz zur Parallelkonfiguration wird die äquivalente Kapazität von in Reihe geschalteten Kondensatoren als Kehrwert der Summe der Kehrwerte der einzelnen Kapazitäten jedes Kondensators berechnet.

Äquivalente Kapazität

Stellen Sie sich ein komplexes Kondensatornetzwerk vor, in dem drei Gruppen von Kondensatoren parallel geschaltet sind, die dann in Reihe geschaltet werden. ...

Education

Lehre

JoVE Core

Electrical Engineering

Elektrotechnik

Unit 1

Einheit 1

Energy Storage Elements

Energiespeicherelemente

KEY TERMS AND CONCEPTS

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capacitors in series and parallel

Capacitors in series and parallel can be simplified by replacing the group with one equivalent capacitor. This equivalent capacitor stores the same charge as the original network when the same potential difference is applied. The idea helps make complex capacitor circuits easier to analyze.

In a parallel connection, capacitors share the same voltage across each branch. The equivalent capacitance of N capacitors in parallel is the sum of their individual capacitances. This type of connection increases the total ability of the circuit to store charge.

In a series connection, the same current flows through each capacitor, and the same charge passes through them. The equivalent capacitance for N capacitors in series is found from the reciprocal of the sum of the reciprocals of each capacitance. This result is different from the parallel case and gives a smaller effective capacitance.

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Learn how capacitors behave in series and parallel, and how to find equivalent capacitance by adding capacitances in parallel or using reciprocals in series.

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Capacitors in Series and Parallel

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