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

Gli induttori collegati in configurazioni in serie e/o in parallelo possono essere semplificati in un singolo induttore equivalente.
Si consideri un collegamento in serie di induttori con la stessa corrente che li attraversa.
Quando la legge della tensione di Kirchhoff viene applicata all'anello e l'espressione per le tensioni dell'induttore viene sostituita, l'espressione risultante indica che l'induttanza equivalente di questi induttori collegati in serie è uguale alla somma delle singole induttanze.
Successivamente, si consideri un collegamento in parallelo di induttori, in cui ogni induttore subisce la stessa tensione attraverso di esso. L'attuale legge di Kirchhoff viene applicata al loop e l'espressione per la corrente dell'induttore viene sostituita.
Poiché la corrente iniziale attraverso l'induttore equivalente è la somma delle correnti dei singoli induttori, la somma dei reciproci delle singole induttanze è uguale al reciproco dell'induttanza equivalente.
Le combinazioni di induttori in serie e in parallelo seguono regole simili a quelle dei resistori.
Si consideri un circuito con induttori sia in serie che in parallelo. L'induttanza equivalente della combinazione parallela di induttori viene calcolata e aggiunta all'induttanza in serie per ottenere l'induttanza equivalente totale.

induttori in serie e in parallelo

Nei circuiti elettrici, l'integrazione degli induttori nel kit di elementi passivi, richiede l'esplorazione delle complessità delle combinazioni in serie e in parallelo che coinvolgono questi componenti. I circuiti pratici spesso presentano configurazioni di più induttori e, capire come determinare la loro induttanza equivalente, è vitale.

Per un collegamento in serie di N induttori, ciascuno trasportato dalla stessa corrente, l'applicazione della legge sulla tensione di Kirchhoff, svela una relazione cruciale. Sostituendo l'espressione con le tensioni dell'induttore, si arriva ad una conclusione illuminante: l'induttanza equivalente di questa disposizione in serie, è la semplice somma delle singole induttanze. Questo fenomeno rispecchia il modo in cui i resistori si combinano in serie, sottolineando una somiglianza fondamentale tra questi elementi passivi.

<img alt="Equation1" src="/files/ftp_upload/15090/15090_Equation_1.svg" style="text-align: center; height: 16px;">

In una connessione parallela di induttori, ciascuno porta una tensione identica; Può essere applicata l'attuale legge di Kirchhoff. Ciò porta ad una rivelazione significativa: il reciproco dell'induttanza equivalente, è pari alla somma dei reciproci delle singole induttanze. Questa regola di combinazione parallela, rispecchia il comportamento dei resistori in parallelo, illustrando un approccio armonioso alla gestione dei diversi elementi passivi.

<img alt="Equation2" src="/files/ftp_upload/15090/15090_Equation_2.svg" style="text-align: center; height: 34px;">

In pratica, i circuiti spesso presentano una miscela di induttori in serie e in parallelo. Di fronte a tali scenari, l'induttanza equivalente degli induttori paralleli, viene calcolata e aggiunta all'induttanza in serie, per ottenere l'induttanza equivalente complessiva del circuito.

Induttori in Serie e in Parallelo

Gli induttori collegati in configurazioni in serie e/o in parallelo possono essere semplificati in un singolo induttore equivalente.
Si consideri un collegamento in serie di induttori ...

Education

Didattica

JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

Energy Storage Elements

Elementi di accumulo di energia

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

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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series and parallel inductors

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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JoVE Core Electrical Engineering offers easy-to-understand animated videos that cover fundamental concepts of electric circuits along with circuit analysis techniques. It incorporates first-order and second-order circuits using operational amplifiers and circuit transformation concepts. The inclusion of practical design examples and real-world applications through scientist-in-action videos adds significant educational value, making complex concepts accessible.

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Equivalent Inductance in Circuit Networks

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