# Energy stored by a capacitor

From Wikiversity

The energy (measured in Joules) stored in a capacitor is equal to the *work* done to charge it. Consider a capacitance *C*, holding a charge *+q* on one plate and *-q* on the other. Moving a small element of charge from one plate to the other against the potential difference *V = q/C* requires the work :

where

*W*is the work measured in joules

*q*is the charge measured in coulombs

*C*is the capacitance, measured in farads

We can find the energy stored in a capacitance by integrating this equation. Starting with an uncharged capacitance (*q*=0) and moving charge from one plate to the other until the plates have charge *+Q* and *-Q* requires the work *W*:

Combining this with the above equation for the capacitance of a flat-plate capacitor, we get:

- .

where

*W*is the energy measured in joules

*C*is the capacitance, measured in farads

*V*is the voltage measured in volts