What is the Energy Stored in a Capacitor?
A capacitor is an electronic component used in circuits to store electrical charge. In a standard parallel-plate capacitor, equal but opposite charges accumulate on adjacent plates, creating an electric field between them. This stored charge represents potential energy.
Capacitor Energy Formula
The energy E stored in a capacitor with capacitance C charged to voltage V is:
E = ½ × C × V²
Using the charge relationship Q = C × V, this can also be written as:
- E = ½ × Q² / C
- E = ½ × Q × V
Units and Measurement Systems
This calculator supports both the Metric (SI) and American unit systems:
- Capacitance: F (farad), mF, µF (microfarad), nF (nanofarad), pF (picofarad)
- Voltage: kV (kilovolt), V (volt), mV (millivolt)
- Energy: kJ, J (joule), mJ, µJ, nJ, Wh, mWh
- Charge: C (coulomb), mC, µC, nC, pC
Electrical Energy in a Capacitor — Example
How much energy is stored in a capacitor with C = 300 µF charged to V = 20 V?
- Convert to SI base units: C = 3×10⁻⁴ F
- Apply the formula: E = ½ × 3×10⁻⁴ F × (20 V)² = 0.06 J = 60 mJ
- Charge accumulated: Q = 3×10⁻⁴ F × 20 V = 6 mC
Energy Transformations in an LC Circuit
In an LC circuit (inductor + capacitor), energy oscillates between the capacitor's electric field and the inductor's magnetic field. At maximum charge, all energy resides in the capacitor (E = ½CV²). At maximum current, all energy resides in the inductor (E = ½LI²). The total energy is conserved in an ideal lossless circuit.
Practical Applications
- Flash photography: Capacitors store energy to power camera flashes
- Power supplies: Smoothing voltage ripple in rectifier circuits
- Defibrillators: High-voltage capacitors deliver precisely controlled energy pulses
- Hybrid vehicles: Supercapacitors store regenerative braking energy
- DRAM memory: Each memory cell is a tiny capacitor storing 1 bit
Capacitor Color Code and Value Reading
Ceramic capacitors are often labeled with a 3-digit code (e.g., "104" means 10 × 10⁴ pF = 100 nF = 0.1 µF). Electrolytic capacitors are typically labeled directly in µF. When working with unknown capacitors, a capacitance meter or LCR meter gives the most accurate reading.
FAQs
What unit is capacitance measured in?
Capacitance is measured in farads (F). In practice, most capacitors range from picofarads (pF) to millifarads (mF). Supercapacitors can reach hundreds or thousands of farads.
Does a capacitor with more capacitance always store more energy?
Not necessarily — energy depends on both C and V². Increasing voltage has a stronger effect because energy scales with V². Doubling voltage quadruples energy; doubling capacitance only doubles it.
What is the difference between energy and charge in a capacitor?
Charge (Q = C×V) is the amount of electric charge stored, measured in coulombs. Energy (E = ½CV²) is the work needed to charge the capacitor, measured in joules. A fully charged capacitor can release this energy back into a circuit.
Why is there a factor of ½ in the energy formula?
As a capacitor charges, the voltage increases from 0 to V. The first charges are added at low voltage (little work needed), while the last charges are added at full voltage (more work needed). The average voltage is V/2, so the total work done is E = Q × (V/2) = ½QV = ½CV².