Name: rc capacitor discharge after power loss
Uploaded: 2024-04-11T12:48:43.000Z
Duration: 1 min 16 s
Channel: JoVE

Cuando una fuente de CC se retira abruptamente de un circuito RC, el circuito queda libre de fuente.
Suponiendo que el voltaje inicial del condensador completamente cargado es V0, se puede obtener su energía inicial, que estimula el circuito.
Aplicando la ley de corriente de Kirchhoff en el nodo superior y sustituyendo los valores de corriente en los componentes, se obtiene una ecuación diferencial de primer orden.
Reorganizando los términos, integrando y tomando la exponencial en ambos lados, se obtiene la respuesta natural del circuito, donde la constante de integración es igual al voltaje inicial.
El gráfico de voltaje versus tiempo muestra que el voltaje inicial decae exponencialmente con el tiempo.
La constante de tiempo, tau, significa el tiempo requerido para que el condensador se descargue al 36.8 por ciento de su voltaje inicial.
Al sustituir el valor de tau en la expresión de respuesta de voltaje, se pueden determinar la corriente y la potencia disipadas en la resistencia.
La integración de la potencia disipada a lo largo del tiempo proporciona la energía absorbida por la resistencia.
A medida que el tiempo se acerca al infinito, esta energía se acerca a la energía inicial almacenada en el condensador, lo que implica que la energía inicial del condensador se disipa gradualmente en la resistencia.

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circuito rc sin fuente

RC Circuit without Source

Cuando una fuente de CC se desconecta abruptamente de un circuito RC (resistencia-condensador), el circuito queda libre de fuente. Suponiendo que el condensador estaba completamente cargado antes de retirar la fuente, su voltaje inicial, denotado como V0, puede considerarse como la energía inicial que estimula el circuito. Al aplicar la ley de corriente de Kirchhoff en el nodo superior del circuito y sustituir los valores de corriente en los componentes, se obtiene una ecuación diferencial de primer orden. Reordenando los términos de esta ecuación, integrando y luego tomando la exponencial en ambos lados, se determina la respuesta natural del circuito. La constante de integración en esta ecuación es igual al voltaje inicial. El gráfico de voltaje versus tiempo muestra que el voltaje inicial decae exponencialmente con el tiempo. Esto significa que la carga del condensador disminuye gradualmente, lo que a su vez reduce el voltaje a través de él. La constante de tiempo del circuito, representada por la letra griega tau (τ), significa el tiempo necesario para que el condensador se descargue al 36,8% de su voltaje inicial. Esta constante de tiempo juega un papel fundamental en la determinación de la velocidad a la que se descarga el condensador y, como resultado, la velocidad a la que el circuito responde a los cambios. Al sustituir el valor de tau en la expresión de respuesta de voltaje, se puede calcular la corriente que fluye a través de la resistencia, así como la potencia disipada en la resistencia. La potencia disipada en la resistencia es la velocidad a la que se pierde energía en forma de calor. La integración de la potencia disipada en el tiempo proporciona la energía total absorbida por la resistencia. A medida que el tiempo se acerca al infinito, esta energía se acerca a la energía inicial almacenada en el condensador. Esto implica que la energía inicial del capacitor se disipa gradualmente en la resistencia, agotando eventualmente la carga del capacitor. En conclusión, comprender el comportamiento de los circuitos RC cuando se elimina la fuente de CC proporciona información valiosa sobre la respuesta transitoria de estos circuitos. Este conocimiento es esencial para diseñar y analizar circuitos en aplicaciones como procesamiento de señales, electrónica de potencia y sistemas de comunicación, donde la carga y descarga rápida de condensadores es un proceso fundamental.

Circuito RC sin Fuente

Cuando una fuente de CC se retira abruptamente de un circuito RC, el circuito queda libre de fuente.
Suponiendo que el voltaje inicial del condensador completamente cargado es ...

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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 this expression equals the initial voltage.

The voltage-time graph shows an exponential drop in voltage. As the capacitor loses charge, the voltage across it also falls. The time constant, tau (τ), is the time needed for the capacitor to discharge to 36.8% of its initial voltage. It helps determine how fast the capacitor discharges and how quickly the circuit responds to change.

Using tau in the voltage response expression also allows the current through the resistor to be found. From that current, the power dissipated in the resistor can be calculated. Power is the rate at which energy is lost as heat. When that power is integrated over time, the total energy absorbed by the resistor is obtained.

As time approaches infinity, the energy absorbed by the resistor approaches the initial energy stored in the capacitor. In other words, the capacitor’s initial energy is gradually converted into heat in the resistor until the charge is depleted. Understanding this transient response is useful for analyzing RC circuits in signal processing, power electronics, and communication systems, where capacitor charging and discharging are key processes.

RC Capacitor Discharge After Power Loss

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Learn how a source-free RC circuit discharges after the DC source is removed, including exponential voltage decay, time constant, current, and energy loss.

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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 Capacitor Discharge After Power Loss

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