Name: rl circuit decay after source removal
Uploaded: 2024-04-11T12:48:43.000Z
Duration: 1 min 14 s
Channel: JoVE

Quando una sorgente CC viene improvvisamente scollegata da un circuito RL, diventa priva di sorgente.
Supponendo che l'induttore abbia una corrente iniziale i0, è possibile determinare l'energia iniziale immagazzinata nell'induttore.
Applicando la legge della tensione di Kirchhoff attorno all'anello e sostituendo le tensioni attraverso l'induttore e il resistore si ottiene un'equazione differenziale del primo ordine.
Riorganizzando i termini, integrando e applicando i limiti si ottiene un'equazione logaritmica.
Prendendo l'esponenziale da entrambe le parti, viene determinata l'espressione finale della risposta naturale del circuito.
Il grafico della corrente rispetto al tempo mostra una diminuzione esponenziale della corrente iniziale.
La risposta di corrente può essere espressa in termini di costante di tempo, che è il rapporto tra induttanza e resistenza.
L'espressione di corrente viene utilizzata per determinare la tensione e la potenza dissipate attraverso il resistore.
L'integrazione della potenza dissipata nel tempo fornisce l'espressione dell'energia assorbita dal resistore.
Quando il tempo si avvicina all'infinito, l'energia assorbita dal resistore si avvicina all'energia iniziale immagazzinata nell'induttore, il che implica che l'energia iniziale viene gradualmente dissipata nel resistore.

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circuito rl senza sorgente

Quando una sorgente CC viene improvvisamente disconnessa da un circuito RL (Resistore-Induttore), il circuito diventa privo di sorgente. Supponendo che l'induttore abbia una corrente iniziale indicata come I0, è possibile determinare l'energia iniziale immagazzinata nell'induttore.

Applicando la legge sulla tensione di Kirchhoff attorno al loop del circuito e sostituendo le tensioni attraverso l'induttore e il resistore, si ottiene un'equazione differenziale di primo ordine. Riorganizzando i termini di questa equazione, integrandola e applicando i limiti, si ottiene un'equazione logaritmica. Prendendo l'esponenziale su entrambi i lati di questa equazione, si ottiene l'espressione finale della risposta naturale del circuito.

Se si traccia la corrente in funzione del tempo, si osserva una diminuzione esponenziale della corrente iniziale. Questo comportamento può essere espresso in termini di costante di tempo, che per un circuito RL è il rapporto tra induttanza e resistenza. Questa costante di tempo rappresenta la velocità con cui il circuito risponde ai cambiamenti nel segnale di ingresso.

Utilizzando l'espressione corrente, è possibile calcolare la tensione ai capi del resistore e la potenza che viene dissipata nel resistore. La potenza dissipata, è sostanzialmente la velocità con cui l'energia viene persa sotto forma di calore.

Per trovare l'energia totale assorbita dal resistore, si integra la potenza dissipata nel tempo. Man mano che il tempo si avvicina all'infinito, l'energia assorbita dal resistore, si avvicina all'energia iniziale immagazzinata nell'induttore. Ciò implica che l'energia iniziale immagazzinata nell'induttore si dissipa gradualmente nel resistore, finché l'energia dell'induttore non si esaurisce.

In conclusione, comprendere il comportamento dei circuiti RL quando la sorgente CC viene rimossa, offre preziose informazioni sulla risposta transitoria di questi circuiti. Questa conoscenza è fondamentale per progettare e analizzare circuiti in applicazioni quali l'elettronica di potenza e i sistemi di comunicazione, dove gli induttori vengono ampiamente utilizzati per filtrare o modellare i segnali.

Circuito RL senza Sorgente

Quando una sorgente CC viene improvvisamente scollegata da un circuito RL, diventa priva di sorgente.
Supponendo che l'induttore abbia una corrente iniziale i0, l'energia iniziale ...

Education

Didattica

JoVE Core

Electrical Engineering

Ingegneria elettrica

Unit 1

Unità 1

First and Second-Order Circuits

Circuiti del primo e del secondo ordine

KEY TERMS AND CONCEPTS

TERMINI E CONCETTI CHIAVE

RL Circuit without Source

rl circuit decay after source removal

An RL circuit begins to decay after the DC source is removed. At that moment, the circuit becomes source-free. If the inductor has an initial current, I0, it also stores initial energy. That stored energy drives the natural response of the circuit.

Kirchhoff’s voltage law is applied around the loop. The inductor voltage and resistor voltage are substituted into the equation. This gives a first-order differential equation for the current. Rearranging the terms produces a logarithmic form, which can then be integrated with limits. Taking the exponential of both sides gives the final current expression.

The current decreases exponentially with time. This drop can be described with the time constant of an RL circuit. The time constant is the ratio of inductance to resistance. It shows how quickly the circuit responds to a change in the input signal.

The current expression also lets us find the voltage across the resistor. It also lets us calculate the power dissipated in the resistor. Power is the rate at which energy is lost as heat. To find the total energy absorbed by the resistor, the power is integrated over time.

As time approaches infinity, the energy absorbed by the resistor approaches the initial energy stored in the inductor. This means the inductor’s energy is gradually transferred to the resistor until it is depleted. Understanding this transient response helps with circuit analysis. It is also useful in power electronics and communication systems, where inductors are used to filter or shape signals.

RL Circuit Decay After Source Removal

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rl circuit without source

An RL circuit begins to decay after the DC source is removed. At that moment, the circuit becomes source-free. If the inductor has an initial current, I0, it also stores initial energy. That stored energy drives the natural response of the circuit. Kirchhoff’s voltage law is applied around the loop. The inductor voltage and resistor voltage are substituted into the equation. This gives a first-order differential equation for the current. Rearranging the terms produces a logarithmic form, which...

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RLC Damping and Resonant Frequency

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Natural Response of a Source-Free RLC Circuit

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key terms and concepts

See how an RL circuit responds after the DC source is removed, with exponential current decay, time constant, resistor power, and energy loss as heat.

RL Circuit Decay After Source Removal | JoVE K12

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.

electrical engineering

RL Circuit Decay After Source Removal

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