parallel-sharing-conserves-charge - Electronic Circuits XVI: Switched-Capacitor Charge and Conversion Step by Step

Parallel connection makes one final voltage from total 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

Two parallel capacitors first contribute source charges

The final voltage is downstream of the two source snapshots, not an independent label.

54\ \text{C}+0\ \text{C}=54\ \text{C}

The final voltage tracks total starting charge

The capacitances stay fixed; only the first capacitor's initial voltage changes.

\begin{array}{c|c|c}V_a&Q_{\text{total}}&V_f\\3\ \text{V}&18\ \text{C}&2\ \text{V}\\6\ \text{V}&36\ \text{C}&4\ \text{V}\\9\ \text{V}&54\ \text{C}&6\ \text{V}\\\end{array}

Parallel sharing conserves total charge

The final voltage is total charge divided by total capacitance, not a hand-authored label.

54\ \text{C}+0\ \text{C}=54\ \text{C}\quad54\ \text{C}/9\ \text{F}=6\ \text{V}