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

Cewki indukcyjne połączone szeregowo i/lub równolegle można uprościć do równoważnej pojedynczej cewki indukcyjnej.
Rozważmy szeregowe połączenie cewek indukcyjnych, przez które przepływa ten sam prąd.
Gdy prawo napięcia Kirchhoffa zostanie zastosowane do pętli i podstawione zostanie wyrażenie dla napięć cewki indukcyjnej, otrzymane wyrażenie wskazuje, że równoważna indukcyjność tych szeregowo połączonych cewek indukcyjnych jest równa sumie poszczególnych indukcyjności.
Następnie rozważ równoległe połączenie cewek indukcyjnych, w którym każda cewka indukcyjna doświadcza tego samego napięcia. Do pętli stosuje się prawo prądu Kirchhoffa i podstawia się wyrażenie na prąd cewki indukcyjnej.
Ponieważ prąd początkowy płynący przez cewkę zastępczą jest sumą poszczególnych prądów cewki indukcyjnej, suma odwrotności poszczególnych indukcyjności jest równa odwrotności równoważnej indukcyjności.
Kombinacje cewek indukcyjnych szeregowo i równolegle podlegają podobnym zasadom jak rezystory.
Rozważ obwód z cewkami indukcyjnymi zarówno szeregowymi, jak i równoległymi. Równoważna indukcyjność równoległej kombinacji cewek indukcyjnych jest obliczana i dodawana do indukcyjności szeregowej w celu uzyskania całkowitej równoważnej indukcyjności.

cewki połączone szeregowo i równolegle

W obwodach elektrycznych integrowanie cewek indukcyjnych z zestawem narzędzi składającym się z elementów pasywnych wymaga poruszania się po zawiłościach kombinacji szeregowych i równoległych obejmujących te elementy. Praktyczne obwody często zawierają konfiguracje wielu cewek i zrozumienie, w jaki sposób określić ich równoważną indukcyjność, jest niezbędne.

W przypadku szeregowego połączenia N cewek indukcyjnych, z których każda przewodzi ten sam prąd, zastosowanie napięciowego prawa Kirchhoffa ujawnia kluczową zależność. Podstawienie wyrażenia dla napięć cewek indukcyjnych prowadzi do wnikliwego wniosku: odwrotność równoważnej indukcyjności jest równa sumie odwrotności poszczególnych indukcyjności. Ta reguła kombinacji równoległej odzwierciedla zachowanie równoległych rezystorów, ilustrując harmonijne podejście do radzenia sobie z różnymi elementami pasywnymi.

<img alt="Equation1" src="/files/ftp_upload/15090/15090_Equation_1.svg" style="text-align: center; height: 16px;" />

W przypadku równoległego połączenia cewek na każdej z nich panuje identyczne napięcie; można zastosować prądowe prawo Kirchhoffa. Prowadzi to do istotnego odkrycia: odwrotność indukcyjności równoważnej jest równa sumie odwrotności poszczególnych indukcyjności. Ta zasada kombinacji równoległej odzwierciedla zachowanie rezystorów połączonych równolegle, ilustrując harmonijne podejście do radzenia sobie z różnymi elementami pasywnymi.

<img alt="Equation2" src="/files/ftp_upload/15090/15090_Equation_2.svg" style="text-align: center; height: 34px;" />

W praktyce obwody często zawierają mieszankę cewek połączonych szeregowo i równolegle. W obliczu takich scenariuszy obliczana jest równoważna indukcyjność równoległych cewek i dodawana do indukcyjności szeregowej w celu uzyskania całkowitej równoważnej indukcyjności obwodu.

Cewki połączone szeregowo i równolegle

Cewki indukcyjne połączone szeregowo i/lub równolegle można uprościć do równoważnej pojedynczej cewki indukcyjnej.
Rozważ szeregowe połączenie cewek indukcyjnych ...

Education

JoVE Core

Electrical Engineering

Elektrotechnika

Unit 1

Jednostka 1

Energy Storage Elements

Elementy magazynowania energii

KEY TERMS AND CONCEPTS

KLUCZOWE TERMINY I POJĘCIA

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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IPC.6.B

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Equivalent Inductance in Circuit Networks

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