Energy in the Electric Field
Capacitors do not store energy in the form of chemical reactions (like batteries); instead, they store potential energy ($U$) directly in the electric field created between their plates. This energy can be released almost instantly, making capacitors essential for high-power bursts.
The Square of Voltage
The most important relationship to note in the energy formula is that energy is proportional to the square of the voltage.
- If you double the capacitance, you double the energy.
- If you double the voltage, you quadruple the energy.
This is why high-voltage capacitors can be extremely dangerous. Even a small capacitor charged to several thousand volts can store enough energy to deliver a lethal shock.
The Formula
Where:
U=
Stored Energy (Joules, J)C=
Capacitance (Farads, F)V=
Voltage (Volts, V)Example Calculation
A $1,000 , \mu\text{F}$ ($0.001 , \text{F}$) capacitor is charged to $50 , \text{Volts}$.
- Square the Voltage: $50^2 = 2,500$.
- Multiply by Capacitance: $0.001 \times 2,500 = 2.5$.
- Divide by 2: $2.5 / 2 = 1.25 , \text{Joules}$.
The capacitor stores $1.25 , \text{J} of energy.