4. First-order transients
Capacitor discharging
Formula
Tags
Detail
Capacitor discharge: v(t)=V e^{−t/τ} falls exponentially toward 0.
Explore the idea
Variables
- voltages (V)
- currents (A)
- time constant (s)
- time (s)
- Ω, F, H.
Conditions
- Piecewise-constant linear first-order circuit; τ>0.
Intuitive explanation
For “Capacitor discharging”: the exponential interpolates the continuous initial value and the settled value with τ.
Worked example
A capacitor initially at , with , falls to in .
Common mistakes
- confusing 0⁺ with 0⁻
- using τ=L/R on an RC or τ=RC on an RL
- forgetting the settled value
Frequently asked questions
- What must be checked before using the Capacitor discharging relation?
- Fix 0⁺, the settled value and τ of the equivalent seen by C or L.
Also known as
- RC transient, RL transient, capacitor charging, exponential discharge
Related topics
Conventions
- V, A or s according to the left-hand side
Last reviewed: 2026-09-19