Capacitors - Stored Energy
Potential power and energy stored in capacitors.
Capacitor - Energy Stored
The work done in establishing an electric field in a capacitor, and hence the amount of energy stored - can be expressed as
W = 1/2 C U2 (1)
where
W = energy stored - or work done in establishing the electric field (joules, J)
C = capacitance (farad, F, µF)
U = potential difference (voltage, V)
Capacitor - Power Generated
Since power is energy dissipated in time - the potential power generated by a capacitor can be expressed as
P = dW / dt (2)
where
P = potential power (watts, W)
dt = dissipation time (s)
Example - Capacitor, energy stored and power generated
The energy stored in a 10 μF capacitor charged to 230 V can be calculated as
W = 1/2 (10 10-6 F) (230 V)2
= 0.26 J
in theory - if this energy is dissipated within 5 μs the potential power generated can be calculated as
P = (0.26 Joules) / (5 10-6 s)
= 52000 W
= 52 kW
Be aware that in any real circuit, discharge starts at a peak value and declines. The energy dissipated is a very rough average power over the discharge pulse.
Capacitor - Time to Discharge at Constant Power Load
The time to discharge a capacitor at constant power load can be expressed as
dt = 1/2 C (Us2 - Uf2) / P (3)
where
dt = discharge time (s)
Us = start voltage (V)
Uf = final voltage (V)