Lessons · Engineering · energy in a capacitor
A capacitor stores energy, and the energy goes as the square of the volts
A capacitor C charged to V holds charge Q = C V and energy E = ½ C V².
Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.
What it is for
A drive's DC bus capacitors are still charged ten minutes after the power is off, and the energy in them is enough to weld a screwdriver. The number on the warning label came from this line.
How to think about it
Convert microfarads to farads first: 470 µF is 470e-6 F. Then a half, times C, times the volts squared. Doubling the voltage quadruples the energy, which is why high-voltage capacitors are the dangerous ones.
Worked example
E = ½ C V²; also Q = C VEnergy and charge. Both need C in farads.
A 470 µF capacitor charged to 24 VThe numbers on the can and the meter.
E = 0.5 × 470e-6 × 24² = 0.5 × 470e-6 × 576 = 0.1354 JAbout an eighth of a joule.
At 48 V: 0.5 × 470e-6 × 48² = 0.5414 J, four times as muchTwice the volts, four times the energy. The square is the whole warning.
Your turn
1000 µF at 10 V. Write the energy.
E = 0.5 × 1000e-6 × ² = 0.05 J
Solve one, graded on the server
The trap
Leaving C in microfarads, or forgetting the half. 470 × 576 is 270,720 of nothing. Convert to farads first, and remember the half is not decoration.