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 voltage and current also decrease exponentially during discharge.
• The time constant 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 formula:

• \(𝑄=𝑄_0𝑒^{−𝑡/𝑅𝐶}\)
• \(𝑄=𝑄_0𝑒^\frac{−𝑡}{𝑅𝐶}\)

Where:

𝑄 is the charge stored,

𝑄₀ is the initial charge stored,

𝑅 is the resistance in the circuit,

𝐶 is the capacitance of the capacitor

and

𝑡 is time

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.