19.3 Discharging a Capacitor

2026 Syllabus Objectives

By the end of these notes, you should be able to:

  1. Analyse graphs of the variation with time of potential difference, charge, and current for a capacitor discharging through a resistor.
  2. Recall and use τ = RC for the time constant of a discharging capacitor.
  3. Use equations of the form x = x₀ e^(−t/RC) where x can represent current, charge, or potential difference.

1. What Happens When a Capacitor Discharges?

https://cambridgeassistant.com

A capacitor is a component that stores electrical charge on two conducting plates. When you connect a charged capacitor to a resistor (and disconnect the battery), the capacitor begins to discharge — it pushes its stored charge around the circuit through the resistor.

Here is what happens physically, step by step:

  • At the very start of discharge, there is a large amount of charge on the plates. This means there is a large potential difference (voltage) across the plates, which drives a large current through the resistor.
  • As charge flows off the plates, the amount of charge stored decreases. This means the potential difference also decreases, so the current decreases too.
  • Eventually, the plates have equal numbers of electrons on each side — the charge is zero, the voltage is zero, and the current is zero. The capacitor is fully discharged.

Key idea: As the capacitor discharges, the charge, potential difference, and current all decrease together. They do not drop at a steady rate — they fall quickly at first, then more and more slowly. This type of decrease is called exponential decay.

2. The Discharge Circuit

https://cambridgeassistant.com

A typical discharge circuit contains:

  • A capacitor (C) — the component being discharged
  • A resistor (R) — the component the charge flows through
  • An ammeter — to measure the current at different times

When the circuit is closed (the switch is flipped to disconnect the battery and connect the resistor), discharge begins immediately.

The resistance affects how quickly the capacitor discharges:

  • A high resistance means the current is small, so charge flows slowly off the plates. The capacitor takes a long time to discharge.
  • A low resistance means the current is large, so charge flows quickly. The capacitor discharges rapidly.

Sign in to view full notes