# Energy Stored in Capacitors

## 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 V^{2}(1)

where

W = energy stored - or work done in establishing the electric field (joules, J)

C = capacitance (farad, F,)µF

V = 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 (V _{s}^{2} - V_{f}^{2}) / P (3)*

*where *

*dt = discharge time (s)*

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

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

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