Name: rc circuit charging after a dc step
Uploaded: 2024-04-11T12:48:43.000Z
Duration: 1 min 15 s
Channel: JoVE

Quando uma fonte CC é aplicada abruptamente a um circuito RC, sua tensão é representada como uma função de passo unitário.
A tensão no capacitor é a resposta em degrau.
Como a tensão em um capacitor não pode mudar instantaneamente, seu valor imediatamente após a comutação permanece o mesmo que o valor imediatamente antes da comutação.
Aplicando a lei atual de Kirchhoff em um tempo igual a zero, reorganizando os termos e reescrevendo a equação para um tempo maior que zero, uma equação diferencial de primeira ordem é obtida.
Integrar a equação, aplicar os limites e obter o exponencial em ambos os lados produz a resposta do capacitor para tempos maiores que zero.
Combinando isso com a tensão inicial do capacitor como a resposta do circuito por um tempo menor que zero, obtém-se a resposta completa do circuito RC.
Com o tempo, a tensão do capacitor aumenta exponencialmente e se aproxima da tensão da fonte.
Se o capacitor estiver inicialmente descarregado, a resposta completa será modificada de acordo. A partir disso, a corrente através do capacitor é determinada e observa-se que diminui exponencialmente com o tempo.

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circuito rc com fonte

Quando uma fonte DC é aplicada abruptamente a um circuito RC (Resistor-Capacitor), a tensão pode ser representada como uma função de degrau unitário. A tensão no capacitor, conhecida como resposta ao degrau, caracteriza como o circuito reage a essa mudança repentina na entrada.

Devido às propriedades inerentes de um capacitor, sua tensão não pode mudar instantaneamente. Isso significa que imediatamente após o fechamento da chave, a tensão do capacitor permanece a mesma que era antes do fechamento da chave.

Aplicando a Lei dos Nós de Kirchhoff no momento em que a chave é fechada (t=0), reorganizando os termos e reescrevendo a equação para os tempos t>0, obtém-se uma equação diferencial de primeira ordem. Esta equação descreve como a corrente através do circuito muda com o tempo após a aplicação abrupta da fonte DC.

Esta equação diferencial é resolvida integrando-a, aplicando os limites e tomando a exponencial em ambos os lados. Isso produz a resposta ao degrau do capacitor para tempos t>0. A combinação desta resposta ao degrau com a tensão inicial no capacitor (para t<0) fornece a resposta completa do circuito RC.

Conforme o tempo passa, a tensão no capacitor aumenta exponencialmente e se aproxima da tensão da fonte aplicada. Este processo representa o carregamento do capacitor.

Se o capacitor estiver inicialmente descarregado, a resposta completa do circuito será modificada de acordo. A partir desta resposta modificada, a corrente através do capacitor é calculada. Observa-se que esta corrente diminui exponencialmente com o tempo, representando o carregamento gradual do capacitor até atingir a tensão da fonte.

Concluindo, a compreensão da resposta ao degrau de um circuito RC fornece informações valiosas sobre como esses circuitos respondem a mudanças repentinas na tensão de entrada. Este conhecimento é essencial para projetar e analisar circuitos eletrônicos, particularmente em aplicações como processamento de sinais, onde capacitores são amplamente utilizados para filtrar ou moldar sinais.

Circuito RC com Fonte

Quando uma fonte CC é aplicada abruptamente a um circuito RC, sua tensão é representada como uma função de passo unitário.
A tensão através do capacitor é o passo ...

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JoVE Core

Electrical Engineering

Engenharia Elétrica

Unit 1

Unidade 1

First and Second-Order Circuits

Circuitos de Primeira e Segunda Ordem

KEY TERMS AND CONCEPTS

TERMOS-CHAVE E CONCEITOS

RC Circuit with Source

rc circuit charging after a dc step

An RC circuit with a DC source shows how a capacitor charges after a sudden voltage step. The applied source is treated as a unit step function, and the capacitor voltage is the step response of the circuit. This response describes how the circuit reacts right after the input changes.

A capacitor cannot change its voltage instantly. So, immediately after the switch closes at t=0, the capacitor voltage stays at its initial value. Kirchhoff’s current law is then applied at that moment and rewritten for times t&gt;0. This produces a first-order differential equation for the circuit current.

The differential equation is solved by integration. After applying the limits and taking the exponential form, the capacitor’s step response is found for t&gt;0. When this result is combined with the capacitor voltage for t&lt;0, it gives the complete response of the RC circuit. If the capacitor starts uncharged, the response is adjusted accordingly.

As time passes, the capacitor voltage rises exponentially and approaches the source voltage. This is the charging process of the capacitor. The current through the capacitor can also be calculated from the modified response. It decreases exponentially with time as the capacitor gradually charges until it reaches the source voltage.

Understanding the step response of an RC circuit helps explain how the circuit reacts to a sudden DC input. This is useful for analyzing and designing electronic circuits. It is especially important in signal processing, where capacitors are often used to filter or shape signals.

RC Circuit Charging After a DC Step

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key terms and concepts

Study how an RC circuit responds to a sudden DC step, including capacitor charging, the exponential voltage rise, and the decreasing current over time.

RC Circuit Charging After a DC Step | 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

RC Circuit Charging After a DC Step

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