capacitor-charge-snapshot-is-cv - Electronic Circuits XV & XVI: Transformers and Switched-Capacitor Conversion Step by Step

A capacitor-charge-snapshot-is-CV scan holds the capacitance fixed and varies the voltage across three rows, checking that charge Q = C * V and stored energy U = C * V^2 / 2 recompute from the pinned voltage row by row. The arithmetic is exact only for the stated capacitances, voltages, charges, stored energies, and rows in the ideal capacitor model. Real circuits add ESR, switch on-resistance, parasitics, dielectric loss, switching-timing errors, probe/calibration limits, finite precision, and measurement uncertainty.

A switched-capacitor lesson starts with a finite capacitor state. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A capacitor snapshot binds one finite state

The displayed state is a checked capacitance and voltage row before any scan changes the voltage.

C=2\ \text{F}\quad V=6\ \text{V}

More voltage increases both charge and stored energy

The capacitance is fixed; each row recomputes charge and stored energy from the pinned voltage.

\begin{array}{c|c|c}V&Q&U\\3\ \text{V}&6\ \text{C}&9\ \text{J}\\6\ \text{V}&12\ \text{C}&36\ \text{J}\\9\ \text{V}&18\ \text{C}&81\ \text{J}\\\end{array}

A capacitor snapshot computes charge and energy

The checked row binds capacitance, voltage, charge, and stored energy before display.

Q=CV=2\ \text{F}\cdot6\ \text{V}=12\ \text{C}\quad U=36\ \text{J}