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:

• \(𝑄=𝑄_0𝑒^{−𝑡/𝑅𝐶}\)

• \(V=V_0𝑒^{−𝑡/𝑅𝐶}\)

• \(I=I_0𝑒^{−𝑡/𝑅𝐶}\)

Where:

𝑅 is the resistance in the circuit,

𝐶 is the capacitance of the capacitor,

𝑡 is time,

𝑄 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,

𝑄₀ 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 𝜏 which is given by the formula:

• 𝜏 = 𝑅𝐶

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.