sharing-capacitance-voltage-final-scan - Electronic Circuits XV & XVI: Transformers and Switched-Capacitor Conversion Step by Step

Charge sharing sets the final voltage by dividing conserved total charge by total capacitance after the connection. This is an ideal charge-conservation voltage ledger, not a lossless-energy claim; real sharing includes switch resistance, parasitic capacitance, leakage, dielectric effects, timing, and measurement tolerance.

The final sharing voltage moves when source capacitance or source voltage changes. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Final voltage divides conserved charge by total capacitance

The final voltage is downstream of both source capacitors; changing either source capacitance or source voltage changes the quotient.

V_f={Q_{\text{total}}\over C_{\text{total}}}=24\ \text{C}/6\ \text{F}

Capacitance and voltage changes enter the same quotient

The table separates changing source capacitance from changing source voltage so the final-voltage quotient is visible both ways.

\begin{array}{c|c|c|c|c}\text{scan}&C_a&V_a&Q_{\text{total}}&V_f\\C_a\ \text{changes}&2\ \text{F}&6\ \text{V}&12\ \text{C}&3\ \text{V}\\C_a\ \text{changes}&4\ \text{F}&6\ \text{V}&24\ \text{C}&4\ \text{V}\\C_a\ \text{changes}&6\ \text{F}&6\ \text{V}&36\ \text{C}&\tfrac{9}{2}\ \text{V}\\V_a\ \text{changes}&4\ \text{F}&3\ \text{V}&12\ \text{C}&2\ \text{V}\\V_a\ \text{changes}&4\ \text{F}&6\ \text{V}&24\ \text{C}&4\ \text{V}\\V_a\ \text{changes}&4\ \text{F}&9\ \text{V}&36\ \text{C}&6\ \text{V}\\\end{array}

The final sharing row is a quotient of checked totals

This row is not a lossless-energy claim; it is only the charge-conservation voltage row.

24\ \text{C}/6\ \text{F}=4\ \text{V}