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

Lorsqu’une source CC est soudainement déconnectée d’un circuit RL, elle devient sans source.
En supposant que l’inductance a un courant initial i0, l’énergie initiale stockée dans l’inductance peut être déterminée.
L'application de la loi de tension de Kirchhoff autour de la boucle et la substitution des tensions aux bornes de l'inductance et de la résistance donne une équation différentielle du premier ordre.
La réorganisation des termes, l’intégration et l’application des limites donnent une équation logarithmique.
En prenant exponentiel des deux côtés, l'expression finale de la réponse naturelle du circuit est déterminée.
Le graphique du courant en fonction du temps montre une diminution exponentielle du courant initial.
La réponse actuelle peut être exprimée en termes de constante de temps, qui est le rapport entre l’inductance et la résistance.
L’expression de courant est utilisée pour déterminer la tension et la puissance dissipées aux bornes de la résistance.
L’intégration de la puissance dissipée dans le temps permet d’exprimer l’énergie absorbée par la résistance.
Lorsque le temps approche de l’infini, l’énergie absorbée par la résistance se rapproche de l’énergie initiale stockée dans l’inductance, ce qui implique que l’énergie initiale est progressivement dissipée dans la résistance.

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circuit rl sans source

Lorsqu'une source CC est soudainement déconnectée d'un circuit RL (Résistance-Inductance), le circuit devient sans source. En supposant que l'inducteur a un courant initial noté I0, l'énergie initiale stockée dans l'inducteur peut être déterminée. L'application de la loi de tension de Kirchhoff autour de la boucle du circuit et la substitution des tensions aux bornes de l'inductance et de la résistance donnent une équation différentielle du premier ordre. Une équation logarithmique est obtenue en réorganisant les termes de cette équation, en l'intégrant et en en définissant les limites d'intégration. Prendre l'exponentielle des deux côtés de cette équation donne l'expression finale de la réponse naturelle du circuit. Si le courant est tracé en fonction du temps, une diminution exponentielle est observée dans le courant initial. Ce comportement peut être exprimé en termes de constante de temps, qui pour un circuit RL est le rapport entre l'inductance et la résistance. Cette constante de temps représente la vitesse à laquelle le circuit répond aux changements du signal d'entrée. En utilisant l'expression du courant, la tension aux bornes de la résistance et la puissance dissipée dans la résistance peuvent être calculées. La puissance dissipée correspond essentiellement à la vitesse à laquelle l’énergie est perdue sous forme de chaleur. Pour connaître l'énergie totale absorbée par la résistance, la puissance dissipée est intégrée au cours du temps. À mesure que le temps approche l'infini, l'énergie absorbée par la résistance se rapproche de l'énergie initiale stockée dans l'inducteur. Cela implique que l'énergie initiale stockée dans l'inducteur se dissipe progressivement dans la résistance jusqu'à ce que l'énergie de l'inducteur soit épuisée. En conclusion, comprendre le comportement des circuits RL lorsque la source CC est supprimée offre des informations précieuses sur la réponse transitoire de ces circuits. Ces connaissances sont fondamentales pour concevoir et analyser des circuits dans des applications telles que l'électronique de puissance et les systèmes de communication, où les inductances sont largement utilisées pour filtrer ou façonner les signaux.

Circuit RL sans source

Lorsqu’une source CC est soudainement déconnectée d’un circuit RL, elle devient sans source.
En supposant que l’inductance a un courant initial i0, l’énergie initiale ...

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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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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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