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

Rozważmy złożoną sieć kondensatorów z trzema grupami kondensatorów połączonych równolegle, a grupy te są następnie połączone szeregowo ze sobą. Określ równoważną pojemność między zaciskami tego skomplikowanego obwodu.
Aby rozwiązać ten problem, najpierw analizowana jest grupa na dole obwodu, składająca się z czterech kondensatorów połączonych równolegle. Suma ich pojemności daje pojemność równoważną, reprezentowaną przez pojedynczy kondensator C3.
Następnie rozważana jest środkowa grupa, mająca trzy kondensatory równolegle. Ponownie, zsumowanie ich pojemności daje równoważną pojemność C2.
Na koniec rozważ górną grupę, która ma dwa kondensatory połączone równolegle. Pojemność równoważna jest obliczana i reprezentowana przez jeden kondensator, C1.
Teraz złożony obwód został uproszczony do trzech kondensatorów połączonych szeregowo.
Aby określić pojemność zastępczą dla tej kombinacji szeregowej, bierze się pod uwagę sumę odwrotności każdej pojemności, co daje odwrotność pojemności równoważnej.
Po przegrupowaniu warunków uzyskuje się równoważną pojemność całego obwodu między zaciskami.

pojemność zastępcza

Z badań nad obwodami rezystancyjnymi wynika, że wykorzystanie kombinacji szeregowo-równoległej jest skuteczną metodą upraszczania obwodów. Kondensatory w obwodzie mogą być połączone na jeden z dwóch sposobów: w konfiguracji szeregowej lub równoległej. Sposób, w jaki kondensatory są podłączone do baterii, wpływa zarówno na spadek napięcia na każdym kondensatorze, jak i na ilość ładunku, jaki może zgromadzić każdy z nich. Aby uprościć ten przypadek, kombinację kondensatorów można zastąpić jednym kondensatorem zastępczym. Kondensator ten może magazynować taką samą ilość ładunku jak pierwotna kombinacja, gdy poddany jest temu samemu napięciu.

W przypadku połączenia równoległego N kondensatorów wszystkie mają to samo napięcie. Pojemność zastępcza dla takiej konfiguracji jest dana wzorem:

<img alt="Equation1" src="/files/ftp_upload/15087/15087_PT_Equation_1.svg" style="text-align: center; height: 14px;" />

Należy zauważyć, że pojemność zastępcza N kondensatorów połączonych równolegle jest równa sumie ich indywidualnych pojemności.

Przechodząc teraz do sytuacji, w której N kondensatorów jest połączonych szeregowo, obserwujemy, że przez wszystkie kondensatory płynie ten sam prąd i tym samym zgromadzony ładunek jest identyczny. Pojemność zastępcza tego układu wyraża się jako:

<img alt="Equation2" src="/files/ftp_upload/15087/15087_PT_Equation_2.svg" style="text-align: center; height: 32px;" />

W przeciwieństwie do konfiguracji równoległej, pojemność zastępcza kondensatorów połączonych szeregowo jest obliczana jako odwrotność sumy odwrotności pojemności poszczególnych kondensatorów.

Pojemność zastępcza

Rozważmy złożoną sieć kondensatorów z trzema grupami kondensatorów połączonych równolegle, a grupy te są następnie połączone szeregowo ze sobą. ...

Education

JoVE Core

Electrical Engineering

Elektrotechnika

Unit 1

Jednostka 1

Energy Storage Elements

Elementy magazynowania energii

KEY TERMS AND CONCEPTS

KLUCZOWE TERMINY I POJĘCIA

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.

Capacitors in Series and Parallel

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Capacitance in Series and Parallel

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equivalent capacitance

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...

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key terms and concepts

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

Capacitors in Series and Parallel | JoVE K12

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Capacitors in Series and Parallel

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