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

Lorsqu’une source CC est appliquée brusquement à un circuit RC, sa tension est représentée par une fonction de pas unitaire.
La tension aux bornes du condensateur est la réponse par paliers.
Étant donné que la tension aux bornes d’un condensateur ne peut pas changer instantanément, sa valeur immédiatement après la commutation reste la même que la valeur immédiatement avant la commutation.
En appliquant la loi du courant de Kirchhoff à un instant égal à zéro, en réarrangeant les termes et en réécrivant l'équation pour un temps supérieur à zéro, on obtient une équation différentielle du premier ordre.
En intégrant l’équation, en appliquant les limites et en prenant l’exponentielle des deux côtés, on obtient la réponse en pas du condensateur pour des fois supérieures à zéro.
En combinant cela avec la tension initiale du condensateur comme réponse du circuit pendant un temps inférieur à zéro, on obtient la réponse complète du circuit RC.
Avec le temps, la tension du condensateur augmente de façon exponentielle et se rapproche de la tension de la source.
Si le condensateur n’est pas chargé au départ, la réponse complète est modifiée en conséquence. À partir de là, le courant traversant le condensateur est déterminé et on observe qu’il diminue de façon exponentielle avec le temps.

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circuit rc avec source

Lorsqu'une source CC est appliquée brusquement à un circuit RC (Résistance-Condensateur), la tension peut être représentée comme une fonction de pas unitaire. La tension aux bornes du condensateur, connue sous le nom de réponse échelonnée, caractérise la façon dont le circuit réagit à ce changement soudain d'entrée. En raison des propriétés inhérentes d’un condensateur, sa tension ne peut pas changer instantanément. Cela signifie qu'immédiatement après la fermeture de l'interrupteur, la tension du condensateur reste la même qu'elle était juste avant la fermeture de l'interrupteur. En appliquant la loi actuelle de Kirchhoff au moment où l'interrupteur est fermé (t=0), en réorganisant les termes et en réécrivant l'équation pour les temps t>0, on obtient une équation différentielle du premier ordre. Cette équation décrit comment le courant traversant le circuit change avec le temps suite à l'application brusque de la source CC. Cette équation différentielle est résolue en l'intégrant, en appliquant les limites et en prenant l'exponentielle des deux côtés. Cela donne la réponse échelonnée du condensateur pour les temps t>0. La combinaison de cette réponse échelonnée avec la tension initiale aux bornes du condensateur (pour t <0) donne la réponse complète du circuit RC. Au fil du temps, la tension aux bornes du condensateur augmente de façon exponentielle et se rapproche de la tension source appliquée. Ce processus représente la charge du condensateur. Si le condensateur est initialement déchargé, la réponse complète du circuit est modifiée en conséquence. À partir de cette réponse modifiée, le courant traversant le condensateur est calculé. On observe que ce courant diminue de façon exponentielle avec le temps, ce qui représente la charge progressive du condensateur jusqu'à ce qu'il atteigne la tension source. En conclusion, comprendre la réponse échelonnée d’un circuit RC fournit des informations précieuses sur la façon dont ces circuits réagissent aux changements soudains de tension d’entrée. Ces connaissances sont essentielles pour concevoir et analyser des circuits électroniques, en particulier dans des applications telles que le traitement du signal, où les condensateurs sont largement utilisés pour filtrer ou mettre en forme les signaux.

Circuit RC avec Source

Lorsqu’une source CC est appliquée brusquement à un circuit RC, sa tension est représentée par une fonction de pas unitaire.
La tension aux bornes du condensateur est l’étape ...

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First and Second-Order Circuits

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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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