Three Capacitor Topology Scan - Capacitors & Stored Charge Step by Step

Three-capacitor networks make the parallel-versus-series arithmetic visible as a topology-bound calculation. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Three capacitors make topology harder to fake

With three capacitors, the topology signal is even clearer. Parallel still adds storage directly; series still adds reciprocals.

\text{parallel adds }C\qquad\text{series adds }1/C

Parallel rows add all three capacitances

Read each row by adding the three capacitance values. The checked diagram is the middle row.

\begin{array}{c|c|c|c}C_a&C_b&C_c&C_{\text{eq}}\\1\ \text{F}&2\ \text{F}&3\ \text{F}&6\ \text{F}\\2\ \text{F}&4\ \text{F}&1\ \text{F}&7\ \text{F}\\3\ \text{F}&6\ \text{F}&9\ \text{F}&18\ \text{F}\\\end{array}

Series rows stay below any one equal branch

Read each row through reciprocal addition. Fractions are kept as fractions because the equivalent capacitance is exact, not a decimal estimate.

\begin{array}{c|c|c|c}C_a&C_b&C_c&C_{\text{eq}}\\1\ \text{F}&2\ \text{F}&2\ \text{F}&\tfrac{1}{2}\ \text{F}\\2\ \text{F}&2\ \text{F}&2\ \text{F}&\tfrac{2}{3}\ \text{F}\\3\ \text{F}&6\ \text{F}&6\ \text{F}&\tfrac{3}{2}\ \text{F}\\\end{array}

The graph chooses the arithmetic

The same component values can be wired into different graphs. The graph decides whether capacitance is summed directly or by reciprocal terms.

C_{\parallel}=C_a+C_b+C_c\qquad \frac{1}{C_s}=\frac{1}{C_a}+\frac{1}{C_b}+\frac{1}{C_c}