27.16
RC-circuits: een condensator ontladen
Een van de toepassingen van een RC-circuit is de relaxatie-oscillator. De relaxatie-oscillator omvat een spanningsbron, een condensator, een weerstand…
When a capacitor is fully charged, the potential difference across the capacitor is equal to the voltage source.
If the battery gets disconnected from the circuit, the capacitor discharges.
Using Kirchhoff's loop rule yields an equation. Here, the current is the rate at which the charge is leaving the capacitor. Since the capacitor is losing charge with time, the sign is negative.
Substituting the definition of current yields an equation. This equation is further integrated to get the charge on the capacitor as a function of time.
For a discharging capacitor, the charge on the capacitor decreases exponentially from the initial charge, which is the maximum charge acquired by the capacitor while charging.
The time derivative of the— charge on a capacitor— equation results in the current expression as a function of time.
The negative sign in the expression signifies the opposite direction of the current compared to the capacitor's charging case.
The current decay has an exponential behavior. Its magnitude decreases exponentially and tends to zero as time tends to infinity.
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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.