Energy Stored in a Capacitor
Simple Explanation
A charged capacitor stores energy in the electric field between its plates: E=½CV² — this energy grows with the capacitance, and steeply (as the square) with the voltage applied.
Why Do We Need It?
This stored energy is exactly what makes capacitors useful for quick energy release — from a camera flash to backup power for electronics during brief power interruptions.
Formula
Energy Stored in a Capacitor
E = ½CV²
A charged capacitor stores energy in the electric field between its plates — this energy grows with capacitance, and with the SQUARE of the voltage across it.
- E
- — energy stored, in joules (J)
- C
- — capacitance, in farads (F)
- V
- — voltage across the capacitor, in volts (V)
When to use it: Whenever the energy stored by a charged capacitor needs to be found from its capacitance and voltage.
Worked Example
Find the energy stored in a charged capacitor
A 100 μF capacitor is charged to 12 V. Find the energy it stores.
Why Does This Work?
Charging a capacitor requires doing work against the growing electric field as more charge is added — the first bit of charge takes little work (the field starts at zero), but each successive bit of charge requires more work as the field grows, and integrating this increasing effort over the whole charging process produces exactly the ½CV² result.
Real-Life Example
A defibrillator delivering a controlled shock
A medical defibrillator charges an internal capacitor over several seconds, then discharges it almost instantly through a patient to restart a normal heart rhythm.
The energy calculated from E=½CV² is precisely calibrated by the device to deliver a therapeutic (not dangerous) amount of energy — capacitors are used specifically because they can release that stored energy in an extremely short, controlled pulse.
Practice
A 200 μF capacitor is charged to 10 V. Find the energy it stores, in mJ.
MediumCommon mistake
Forgetting to square the voltage — since V is squared in the formula, DOUBLING the voltage QUADRUPLES the stored energy, not just doubles it.
Quick Review
- E = ½CV².
- Energy grows with the SQUARE of voltage.
- Enables quick, controlled release of stored energy (camera flashes, defibrillators).