Deeper Charge and Energy Budgets

Parallel Charge-Splitting Three-Row Scan

Parallel capacitors share voltage, so branch charges add to the equivalent stored 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

Parallel capacitors share voltage

In parallel, each branch sees the same voltage. Charge splits by capacitance, then the branch charges add at the terminals.

Qa=CaVQb=CbVQ_a=C_aV\qquad Q_b=C_bV
Parallel charge-splitting branchesThe middle table row is the checked parallel graph.2 F4 F

Each branch charge comes from the shared voltage

Hold voltage at 6 volts. Each branch charge is capacitance times that same voltage.

CaCbQaQb1 F3 F6 C18 C2 F4 F12 C24 C4 F4 F24 C24 C\begin{array}{c|c|c|c}C_a&C_b&Q_a&Q_b\\1\ \text{F}&3\ \text{F}&6\ \text{C}&18\ \text{C}\\2\ \text{F}&4\ \text{F}&12\ \text{C}&24\ \text{C}\\4\ \text{F}&4\ \text{F}&24\ \text{C}&24\ \text{C}\\\end{array}
Parallel charge-splitting branchesThe displayed graph is the middle budget row.2 F4 F

Branch charges add to the total

Now add the two branch charges. The total charge is the amount stored by the equivalent capacitor at the same voltage.

QaQbQt6 C18 C24 C12 C24 C36 C24 C24 C48 C\begin{array}{c|c|c}Q_a&Q_b&Q_t\\6\ \text{C}&18\ \text{C}&24\ \text{C}\\12\ \text{C}&24\ \text{C}&36\ \text{C}\\24\ \text{C}&24\ \text{C}&48\ \text{C}\\\end{array}
Parallel charge-splitting branchesThe displayed graph is the middle total-charge row.2 F4 F

The equivalent capacitor stores the same charge

The parallel equivalent is honest only when equivalent capacitance times voltage equals the branch-charge total.

Qt=Qa+Qb=CeqVQ_t=Q_a+Q_b=C_{\text{eq}}V
Parallel charge-splitting branchesThe graph decides the equivalent capacitance.2 F4 F