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

Si consideri una rete di condensatori complessa con tre gruppi di condensatori collegati in parallelo, e questi gruppi vengono quindi collegati in serie tra loro. Determinare la capacità equivalente tra i terminali di questo intricato circuito.
Per risolvere questo problema, viene analizzato per primo il gruppo alla base del circuito, costituito da quattro condensatori collegati in parallelo. La somma della loro capacità dà una capacità equivalente, rappresentata da un singolo condensatore C3.
Successivamente, viene considerato il gruppo intermedio, con tre condensatori in parallelo. Ancora una volta, sommando le loro capacità si ottiene la capacità equivalente C2.
Infine, considera il gruppo superiore, che ha due condensatori in parallelo. La capacità equivalente è calcolata e rappresentata con un condensatore, C1.
Ora, il complesso circuito è stato semplificato in tre condensatori collegati in serie.
Per determinare la capacità equivalente per questa combinazione di serie, si prende la somma dei reciproci di ciascuna capacità, risultando nell'inverso della capacità equivalente.
Dopo aver riorganizzato i termini, si ottiene la capacità equivalente dell'intero circuito tra i terminali.

capacità equivalente

Dallo studio dei circuiti resistivi, si comprende che l'utilizzo di una combinazione serie-parallelo, costituisce una strategia efficace per semplificare i circuiti. I condensatori possono essere disposti all'interno di un circuito in due modi: una configurazione in serie o una configurazione in parallelo. Il modo in cui questi condensatori sono collegati a una batteria, influenzerà sia la caduta di potenziale su ogni singolo condensatore, sia la dimensione della carica che ciascun condensatore può immagazzinare. Ciò è determinato dal tipo specifico di connessione in atto. Per semplificare questo scenario, la combinazione di condensatori può essere sostituita con un unico condensatore equivalente. Questo condensatore equivalente è in grado di immagazzinare una quantità di carica identica alla combinazione originale, quando sottoposto alla stessa differenza di potenziale.

Quando è presente una connessione parallela di N condensatori, tutti condividono la stessa tensione ai loro capi. La capacità equivalente per tale configurazione è data da

<img alt="Equation1" src="/files/ftp_upload/15087/15087_PT_Equation_1.svg" style="text-align: center; height: 14px;">

È fondamentale notare che la capacità equivalente di N condensatori collegati in parallelo, è uguale al totale delle loro capacità individuali.

Passando ora allo scenario in cui N condensatori sono collegati in serie, si osserva che la stessa corrente i, e di conseguenza la stessa carica, scorre attraverso tutti i condensatori. La capacità equivalente di questa configurazione è rappresentata come

<img alt="Equation2" src="/files/ftp_upload/15087/15087_PT_Equation_2.svg" style="text-align: center; height: 32px;">

A differenza della configurazione in parallelo, la capacità equivalente dei condensatori collegati in serie, viene calcolata come il reciproco della somma dei reciproci della capacità individuale di ciascun condensatore.

Capacità Equivalente

Si consideri una rete di condensatori complessa con tre gruppi di condensatori collegati in parallelo, e questi gruppi vengono quindi collegati in serie tra loro. ...

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

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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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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IPC.6.G

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Capacitors in Series and Parallel

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