27.16
Circuits RC : Décharge d'un condensateur
L'un des usages d'un circuit RC est l'oscillateur de relaxation. L'oscillateur de relaxation est composé d'une source de tension, d'un condensateur, d…
Lorsqu’un condensateur est complètement chargé, la différence de potentiel aux bornes du condensateur est égale à la source de tension.
Si la batterie est déconnectée du circuit, le condensateur se décharge.
L'utilisation de la règle de la boucle de Kirchhoff donne une équation. Ici, le courant est la vitesse à laquelle la charge quitte le condensateur. Étant donné que le condensateur perd de sa charge avec le temps, le signe est négatif.
En substituant la définition du courant, on obtient une équation. Cette équation est ensuite intégrée pour obtenir la charge sur le condensateur en fonction du temps.
Pour un condensateur à décharge, la charge sur le condensateur diminue de façon exponentielle par rapport à la charge initiale, qui est la charge maximale acquise par le condensateur pendant la charge.
La dérivée temporelle de l’équation de la charge sur un condensateur donne l’expression du courant en fonction du temps.
Le signe négatif dans l'expression signifie la direction opposée du courant par rapport au boîtier de charge du condensateur.
La décroissance actuelle a un comportement exponentiel. Sa magnitude diminue de façon exponentielle et tend vers zéro comme le temps tend vers l’infini.
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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.