Energy Two Ways - Capacitors & Stored Charge Step by Step

The same stored energy is computed from capacitance or from charge. 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 capacitance and voltage

The first route uses capacitance 2 farads and voltage 6 volts.

U = \tfrac{1}{2} C V^{2}

Use charge and voltage

The same capacitor also has charge 12 coulombs.

U = \tfrac{1}{2} QV

Both routes agree

Both exact routes give 36 joules.

U = 36\ \text{J} = 36\ \text{J}

Several exact rows close both routes

Every row first computes charge from capacitance and voltage, then gives the same stored energy by either route. The checked diagram is the middle row.

\begin{array}{c|c|c|c}C&V&Q&U\\1\ \text{F}&4\ \text{V}&4\ \text{C}&8\ \text{J}\\2\ \text{F}&6\ \text{V}&12\ \text{C}&36\ \text{J}\\3\ \text{F}&4\ \text{V}&12\ \text{C}&24\ \text{J}\\\end{array}