Discharging capacitor Calculator
Voltage across a discharging capacitor.
Formula first
Overview
This equation describes the exponential decay of voltage across a capacitor as it discharges its stored energy through a resistor. It is a fundamental model for first-order transient circuits, illustrating how the electric field between capacitor plates weakens over time when the charging source is removed.
Symbols
Variables
= Initial Voltage, t = Time, R = Resistance, C = Capacitance, V(t) = Capacitor Voltage
Apply it well
When To Use
When to use: Use this formula when analyzing a passive circuit where a previously charged capacitor is allowed to bleed charge through a resistive path. It assumes the circuit has no active voltage sources during the discharge phase and that components behave ideally.
Why it matters: Understanding discharge rates is critical for designing safety circuits that bleed off high voltage, timing mechanisms in electronics, and filtering stages in power supplies. It determines how long a device can maintain operation during a power loss or how quickly a camera flash can reset.
Avoid these traps
Common Mistakes
- Using 1 - instead of .
- Mixing milliseconds and seconds.
One free problem
Practice Problem
A 100 μF capacitor is initially charged to 12V and then discharged through a 50 kΩ resistor. What is the voltage across the capacitor after exactly 2 seconds of discharging?
Solve for: Vt
Hint: Calculate the time constant RC first, then use the exponential decay formula Vt = V0 × e^(-t/RC).
The full worked solution stays in the interactive walkthrough.
References
Sources
- Halliday, Resnick, and Walker, Fundamentals of Physics
- Wikipedia: RC circuit
- Halliday, Resnick, Walker - Fundamentals of Physics, 10th ed.
- Griffiths - Introduction to Electrodynamics, 4th ed.
- NIST Guide for the Use of the International System of Units (SI)
- Halliday, Resnick, and Walker Fundamentals of Physics
- Horowitz and Hill The Art of Electronics
- Alexander and Sadiku Fundamentals of Electric Circuits