Energy in a Capacitor
A camera flash, a supercapacitor in a bus, the capacitor that keeps a clock running: how much energy does a capacitor hold, and how quickly can it give it away? Solve for the energy, capacitance or voltage, or follow a discharge through a resistor.
Capacitors as Energy Stores
A charged capacitor holds energy in the electric field between its plates. Because the energy grows with the square of the voltage, a small capacitor at high voltage can hold a surprising amount: the 330 V capacitor of a camera flash stores several joules.
Compared with a battery, a capacitor stores little energy, but it can release it extremely quickly: through a small resistor the power can reach kilowatts for a fraction of a millisecond. Supercapacitors hold thousands of farads at a few volts and are used where short, powerful bursts are needed, such as regenerative braking.
Energy and Voltage
ESome Capacitors
E = ½CV²| Capacitor | C and V | Energy |
|---|---|---|
| Small ceramic | 100 nF at 5 V | 1.25 µJ |
| Power-supply electrolytic | 1000 µF at 25 V | 0.31 J |
| Camera flash | 120 µF at 330 V | 6.5 J |
| Supercapacitor cell | 3000 F at 2.7 V | 10.9 kJ (3.0 Wh) |
Worked Techniques
The work done to push the charge onto the plates against the growing voltage.
Doubling the stored energy only takes 41% more voltage.
The energy falls with e−2t/RC, twice as fast as the voltage. x is the share released.
Sources & Verification
- A. R. Hambley, Electrical Engineering: Principles and Applications, 7th ed., Pearson, 2018 — Ch. 3 (Inductance and Capacitance) and Ch. 4 (Transients).