Energy stored by a capacitor

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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