# Capacitors - Stored Energy

### 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 U^{ 2 }(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 (U _{ s } ^{ 2 } - U _{ f } ^{ 2 } ) / P (3) *

* where *

* dt = discharge time (s) *

* U _{ s } = start voltage (V) *

* U _{ f } = final voltage (V) *

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