Dicharging a Capacitor
Key Stage 5
Meaning
Capacitor discharge is the process of releasing the stored energy in a capacitor through a circuit.
About Capacitor Discharge
- The charge, voltage and current all decrease exponentially during discharge.
- The time constant of a circuit determines how quickly a capacitor discharges.
- A large time constant means a slow discharge, while a small time constant means a rapid discharge.
- Capacitor discharge curves are used to analyze the behaviour of RC circuits.
- Safety precautions are necessary when discharging large capacitors to avoid electric shock.
Formula
The discharge through a resistor follows an exponential decay described by the formulae:
- \(π=π_0π^{βπ‘/π πΆ}\)
- \(V=V_0π^{βπ‘/π πΆ}\)
- \(I=I_0π^{βπ‘/π πΆ}\)
Where:
π is the resistance in the circuit,
πΆ is the capacitance of the capacitor,
π‘ is time,
π is the charge stored at time t,
V is the potential difference across the capacitor at time t,
I is the current being discharged by the capacitor at time t,
π0 is the initial charge stored,
V0 is the initial potential difference across the capacitor,
I0 is the initial current through the circuit,
A capacitor's rate of discharge in a circuit is characterised by the time constant π which is given by the formula:
- π = π πΆ
Examples
- In a defibrillator, the capacitor discharges its energy quickly to deliver a shock to a patient's heart.
- In RC timing circuits, capacitors discharge to control the timing intervals.