Fixed Charge Energy Inverse Scan - Capacitors & Stored Charge Step by Step

At fixed stored charge, larger capacitance lowers voltage and stored energy through exact inverse rows. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Hold charge fixed and change capacitance

Keep stored charge fixed at 12 coulombs. A larger capacitance needs less voltage for that same charge, so the stored energy falls.

V=\frac{Q}{C}\qquad U=\tfrac{1}{2}QV

More capacitance lowers energy at fixed charge

Each row first solves voltage from Q divided by C, then computes one-half Q V. This makes the inverse dependence on capacitance visible without decimals.

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

The same result is Q squared over two C

Substituting voltage equals Q over C into one-half Q V gives the fixed-charge route. The capacitance sits in the denominator.

U=\frac{Q^{2}}{2C}

The middle row closes both energy routes

For the checked middle row, the charge, capacitance, voltage, and energy all agree before rendering.

Q=12\ \text{C}\qquad C=3\ \text{F}\qquad U=24\ \text{J}