Stored Energy

Energy From Charge

A charged ideal capacitor stores energy equal to one half of charge times voltage. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Use charge and voltage

The capacitor stores 12 coulombs at 6 volts.

Q=12 CV=6 VQ = 12\ \text{C}\qquad V = 6\ \text{V}
Stored energyThe capacitor value is the one used in the energy check.2 F

Energy is half charge times voltage

For an ideal capacitor, stored energy is one half of charge times voltage.

U=12QVU = \tfrac{1}{2} QV

Compute stored energy

One half of 12 times 6 gives 36 joules.

U=12⋅12 C⋅6 V=36 JU = \tfrac{1}{2}\cdot 12\ \text{C}\cdot 6\ \text{V} = 36\ \text{J}
Stored energyThe capacitor value is the one used in the energy check.2 F

Charge and voltage both enter the budget

The checked diagram is the middle row. Other exact rows show the same one-half charge-voltage budget without using decimals.

QVU6 C4 V12 J12 C6 V36 J18 C8 V72 J\begin{array}{c|c|c}Q&V&U\\6\ \text{C}&4\ \text{V}&12\ \text{J}\\12\ \text{C}&6\ \text{V}&36\ \text{J}\\18\ \text{C}&8\ \text{V}&72\ \text{J}\\\end{array}
Stored energyThe middle table row is the checked diagram.2 F