---
title: "Discharging a Capacitor and the Time Constant"
description: "A capacitor discharging through a resistor loses charge at a rate set by the charge still on it, so voltage, charge and current all fall exponentially. The product RC is the time taken to fall to abou"
canonical: https://lightmysky.com/learn/science/discharging-a-capacitor-and-the-time-constant-mt_5sjDPudyad
source: https://lightmysky.com/learn/science/discharging-a-capacitor-and-the-time-constant-mt_5sjDPudyad.md
retrieved: 2026-09-12
---

> **Agent view.** This is the Markdown twin of the page, for tools and assistants.
> When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md
> API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md
> Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt
> Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json
> Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`.

# Discharging a Capacitor and the Time Constant

A capacitor discharging through a resistor loses charge at a rate set by the charge still on it, so voltage, charge and current all fall exponentially. The product RC is the time taken to fall to about 37 per cent.

Subject: Science · Area: Energy · Ages 17 to 18
Page: https://lightmysky.com/learn/science/discharging-a-capacitor-and-the-time-constant-mt_5sjDPudyad

## Ready when they can

- Predicts the voltage after a stated number of time constants and reads RC off a decay curve
- Uses the exponential form to find either a remaining charge or an elapsed time
- Plots the natural log of voltage against time and takes RC from the gradient of the straight line

## Lesson: Capacitors let go slowly

A resistor in series with a capacitor sets the pace of discharge. The time constant tau equals R times C, in seconds for ohms times farads. After one constant the voltage has fallen to about 37 percent. After five it is effectively zero.

Discharge runs on an exponential: voltage equals start voltage times e to the minus t over R C. A 10 microfarad capacitor through a 100 kilohm resistor gives R C equal to 1 second. These fixed fractions predict the voltage after any count of constants with no heavy lifting.

**Tip.** Take the natural log of voltage and plot it against time to get a straight line. Its gradient is minus one over R C, so R C drops out with a ruler. Keep units strict: convert milliseconds and microfarads before they meet.

**Recap.** Price discharge in time constants, trust the 37 percent rule, and read R C off logged data.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Recognising Cubic, Reciprocal and Exponential Graphs](https://lightmysky.com/learn/mathematics/recognising-cubic-reciprocal-and-exponential-graphs-mt_2IJJ51rmq9)
- [Resistance in Series and Parallel](https://lightmysky.com/learn/science/resistance-in-series-and-parallel-mt_B29m3h5B75)
- [Capacitance and the Energy Stored in a Capacitor](https://lightmysky.com/learn/science/capacitance-and-the-energy-stored-in-a-capacitor-mt_j1Eltr9z6l)

## Opens up

- [Magnetic Flux Density and the Force on a Current-Carrying Wire](https://lightmysky.com/learn/science/magnetic-flux-density-and-the-force-on-a-current-carrying-wire-mt_zuqc4gjBVh)