27.16
Circuitos RC: Descargando un capacitor
Una de las aplicaciones de un circuito RC es el oscilador de relajación. El oscilador de relajación está compuesto por una fuente de voltaje, un capac…
Cuando un condensador está completamente cargado, la diferencia de potencial a través del condensador es igual a la fuente de voltaje.
Si la batería se desconecta del circuito, el condensador se descarga.
Usando la regla del bucle de Kirchhoff se obtiene una ecuación. Aquí, la corriente es la velocidad a la que la carga sale del condensador. Dado que el condensador pierde carga con el tiempo, el signo es negativo.
Sustituyendo la definición de corriente se obtiene una ecuación. Esta ecuación se integra aún más para obtener la carga en el condensador en función del tiempo.
Para un condensador de descarga, la carga en el condensador disminuye exponencialmente desde la carga inicial, que es la carga máxima adquirida por el condensador durante la carga.
La derivada del tiempo de la ecuación de la carga en un condensador da como resultado la expresión actual en función del tiempo.
El signo negativo en la expresión significa la dirección opuesta de la corriente en comparación con el caso de carga del condensador.
El decaimiento actual tiene un comportamiento exponencial. Su magnitud disminuye exponencialmente y tiende a cero a medida que el tiempo tiende al infinito.
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Q1: What happens to a capacitor when the battery is disconnected from an RC circuit?
When the battery disconnects, the capacitor discharges through the resistor. The charge decreases exponentially from its initial maximum value toward zero. The circuit reduces to a simple series connection of the resistor, capacitor, and switch, with the voltage source completely removed from the circuit.
Q2: How does the current behave during capacitor discharge?
The discharge current decays exponentially with time, starting at its maximum value and approaching zero as time increases. The negative sign in the current expression indicates the current flows opposite to the charging direction. The current magnitude decreases continuously throughout the discharge process.
Q3: Why is there a negative sign in the capacitor discharge current equation?
The negative sign signifies that the current direction during discharge is opposite to the current direction during charging. Since the capacitor loses charge with time, the negative sign reflects this opposite flow direction compared to when the capacitor was acquiring charge from the voltage source.
Q4: What mathematical relationship describes charge decay in a discharging capacitor?
The charge on a discharging capacitor decreases exponentially as a function of time, starting from the maximum charge acquired during charging. Using Kirchhoff's loop rule and integrating the resulting equation yields this exponential decay relationship, where charge approaches zero as time approaches infinity.
Q5: How does a relaxation oscillator use capacitor discharge?
A relaxation oscillator comprises a voltage source, capacitor, resistor, and neon lamp. The lamp acts as an open circuit until voltage reaches a threshold, then acts as a short circuit, allowing the capacitor to discharge through it and produce light. The process repeats as the capacitor recharges, creating flashing controlled by R and C values.
Q6: What is the relationship between voltage and charge during capacitor discharge?
Both voltage and charge magnitudes decrease exponentially during discharge, approaching zero as time increases. Since voltage across the capacitor is proportional to the charge stored, they decay together at the same exponential rate determined by the RC time constant of the circuit.
Q7: How does the discharge process differ from charging in an RC circuit?
During charging, a voltage source drives charge onto the capacitor; during discharge, no external source exists and the capacitor releases stored charge through the resistor. The current direction reverses, indicated by the negative sign in the discharge current equation, though both processes follow exponential behavior.