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

Quando uma fonte CC é repentinamente desconectada de um circuito RL, ela se torna livre de fonte.
Supondo que o indutor tenha uma corrente inicial i0, a energia inicial armazenada no indutor pode ser determinada.
Aplicando a lei de tensão de Kirchhoff ao redor do loop e substituindo as tensões no indutor e no resistor produz uma equação diferencial de primeira ordem.
Reorganizar termos, integrar e aplicar os limites fornece uma equação logarítmica.
Ao tomar exponencial em ambos os lados, a expressão final da resposta natural do circuito é determinada.
O gráfico de corrente versus tempo mostra uma diminuição exponencial na corrente inicial.
A resposta atual pode ser expressa em termos da constante de tempo, que é a razão entre a indutância e a resistência.
A expressão de corrente é usada para determinar a tensão e a potência dissipadas pelo resistor.
A integração da potência dissipada ao longo do tempo fornece a expressão da energia absorvida pelo resistor.
À medida que o tempo se aproxima do infinito, a energia absorvida pelo resistor se aproxima da energia inicial armazenada no indutor, o que implica que a energia inicial é gradualmente dissipada no resistor.

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circuito rl sem fonte

Quando uma fonte DC é repentinamente desconectada de um circuito RL (Resistor-Indutor), o circuito fica sem fonte. Supondo que o indutor tenha uma corrente inicial indicada como I0, a energia inicial armazenada no indutor pode ser determinada.

Aplicar a Lei das Malhas de Kirchhoff ao redor do circuito e substituir as tensões no indutor e no resistor produz uma equação diferencial de primeira ordem. Uma equação logarítmica é obtida reorganizando os termos desta equação, integrando-a e aplicando os limites. Tomar a exponencial em ambos os lados desta equação produz a expressão final da resposta natural do circuito.

Se a corrente for plotada em função do tempo, uma diminuição exponencial será observada na corrente inicial. Este comportamento pode ser expresso em termos da constante de tempo, que para um circuito RL é a razão entre indutância e resistência. Esta constante de tempo representa a velocidade com que o circuito responde às mudanças no sinal de entrada.

Usando a expressão da corrente, a tensão no resistor e a potência que é dissipada no resistor podem ser calculadas. A potência dissipada é essencialmente a taxa na qual a energia é perdida na forma de calor.

Para encontrar a energia total absorvida pelo resistor, a potência dissipada é integrada ao longo do tempo. À medida que o tempo se aproxima do infinito, a energia absorvida pelo resistor se aproxima da energia inicial armazenada no indutor. Isto implica que a energia inicial armazenada no indutor se dissipa gradualmente no resistor até que a energia do indutor se esgote.

Concluindo, compreender o comportamento dos circuitos RL quando a fonte DC é removida oferece informações valiosas sobre a resposta transitória desses circuitos. Este conhecimento é fundamental para projetar e analisar circuitos em aplicações como eletrônica de potência e sistemas de comunicação, onde os indutores são amplamente utilizados para filtrar ou moldar sinais.

Circuito RL sem Fonte

Quando uma fonte CC é repentinamente desconectada de um circuito RL, ela se torna livre de fonte.
Supondo que o indutor tenha uma corrente inicial i0, a energia inicial ...

Education

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

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

first-order circuits

First-Order Circuits in Flashing Lamps

First-order circuits use a resistor and one energy storage element, either a capacitor or an inductor. They are common in electronic systems and are described by a first-order differential equation that links the input and output signals. One important example is the RC circuit, which uses a resistor and a capacitor. In a relaxation oscillator such as a neon lamp circuit, the capacitor starts charging when voltage is applied. At first, the lamp behaves like an open circuit. When the capacitor...

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RC Capacitor Discharge After Power Loss

An RC circuit discharges after the DC source is removed. If the capacitor was fully charged first, its initial voltage, V0, provides the energy that drives the source-free circuit. Kirchhoff’s current law is applied at the top node of the circuit. The current terms for the resistor and capacitor are then substituted, which leads to a first-order differential equation. Rearranging, integrating, and taking the exponential gives the natural response of the circuit. The integration constant in...

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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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RL Step Response Under a DC Source

An RL circuit connected to a DC source has a step response that changes over time. The response has two parts: the transient response and the steady-state response. The transient response is the short-lived reaction that happens right after the source is applied. During the transient phase, the current changes exponentially. If the circuit starts with current in the inductor, that current decays toward zero as time goes on. At this stage, the inductor acts like a short circuit, so the source...

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RL Circuit and Frog Leg Current Response

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RLC Damping and Resonant Frequency

Second-order circuits use two energy storage elements, such as a capacitor and an inductor, to shape how current and voltage change over time. These circuits include RLC circuits, along with RC and RL circuits that have two capacitors or two inductors. Their behavior is described by second-order differential equations that connect the input signal to the output signal. The input usually comes from a voltage source or a current source. The output is often the voltage across the capacitor, the...

series rlc circuit without source

Natural Response of a Source-Free RLC Circuit

A source-free RLC circuit is a series circuit with a resistor, inductor, and capacitor, but no external energy source. It begins with the energy already stored in the capacitor and inductor. That stored energy drives the circuit at first. The circuit is described by a second-order differential equation. This equation shows how the resistor, inductor, and capacitor interact over time. The resistor removes energy from the circuit, so the solution has an exponential form. When the exponential...

types of responses of series rlc circuits

types-of-responses-of-series-rlc-circuits

Damping in Series RLC Circuit Responses

A source-free series RLC circuit shows three response patterns based on damping. The circuit is described by a second-order differential equation. Its complete solution is made from two distinct solutions. Those solutions depend on the roots, which are written in terms of the damping factor and the resonant frequency. When the damping factor is greater than the resonant frequency, both roots are real and negative. This gives an overdamped response. The circuit output decays slowly over time. <br...

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Forced Response in a Series RLC Circuit

A series RLC circuit with a DC source can model an automobile ignition system. The circuit shows how a battery can produce the high voltage needed for a spark. In this case, the input DC voltage acts like a forcing step function. Applying Kirchhoff's voltage law leads to a second-order differential equation. A second-order differential equation is an equation with a term for the second derivative. The form of this equation is very similar to the one used for a source-free RLC circuit, so the...

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Parallel RLC circuits help explain how a surge protector works in a street lamp. The circuit model uses a DC input source that creates a step response when the switch is turned on. This setup shows how the lamp’s components can be protected from sudden voltage spikes. When the switch closes, Kirchhoff’s current law is applied to the parallel RLC circuit. That leads to a second-order differential equation. The solution has two parts: a transient response and a steady-state response. The...

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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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