Capacitor Energy
Energy stored in a capacitor.
Formula
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Example
Stored in the electric field
How it works
A capacitor stores energy by separating positive and negative charge on its plates, creating an electric field between them. The factor of 1/2 appears because the voltage is not constant while the capacitor charges; the first bit of charge is added when the voltage is low, and later bits are added against a higher voltage, so the average charging voltage is V/2. That is why the stored energy depends on both the capacitance and the square of the final voltage.
When to use it
Use this formula when you need the energy held in a charged capacitor, such as in flash units, power supplies, timing circuits, or safety calculations for high-voltage capacitors. It is also useful when comparing how much energy changes if capacitance or voltage changes.
Worked example, step by step
A capacitor has a capacitance of 470 bcF and is charged to 12 V. Step 1: Write the formula: E = (1/2)CV^2 Step 2: Convert capacitance to farads: 470 bcF = 470 d7 10^-6 F = 0.000470 F Step 3: Substitute values: E = (1/2)(0.000470)(12^2) Step 4: Square the voltage: 12^2 = 144 Step 5: Multiply: E = 0.5 d7 0.000470 d7 144 Step 6: Calculate: E = 0.03384 J Final answer: The capacitor stores about 0.0338 J, or 33.8 mJ, of energy.
Common mistakes to avoid
- Using the capacitance value in microfarads without converting to farads
- Forgetting to square the voltage
- Leaving out the 1/2 factor from the energy formula
Did You Know?
Supercapacitors store so much energy they can now start car engines and buffer power grids.
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