Series Voltage-Sharing Three-Row Scan - Electric Fields, Electrostatics & Capacitors Step by Step

Series capacitors share the same charge, so each voltage drop is that charge divided by its own capacitance and the drops add back to the source. With 8 C held fixed, the three rows give source voltages 8, 6, and 4 V exactly for the ideal series-capacitor model; real series stacks add capacitance tolerance, leakage imbalance, dielectric absorption, ESR, voltage-rating limits, parasitics, and voltage/charge measurement uncertainty.

Series capacitors share charge, so each voltage drop is charge divided by that capacitor's capacitance. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Series capacitors share one charge ledger

In a series chain, the same stored charge passes through each capacitor ledger. Voltage then divides as charge divided by each capacitance.

V_a=\frac{Q}{C_a}\qquad V_b=\frac{Q}{C_b}

The two voltage drops add to the source

Hold charge at 8 coulombs. Each row computes the two capacitor voltages separately, then adds them to the source voltage.

\begin{array}{c|c|c|c|c}C_a&C_b&V_a&V_b&V_s\\2\ \text{F}&2\ \text{F}&4\ \text{V}&4\ \text{V}&8\ \text{V}\\2\ \text{F}&4\ \text{F}&4\ \text{V}&2\ \text{V}&6\ \text{V}\\4\ \text{F}&4\ \text{F}&2\ \text{V}&2\ \text{V}&4\ \text{V}\\\end{array}

The equivalent capacitor gives the same source

The series equivalent is allowed only because the source voltage from the two drops equals charge divided by equivalent capacitance.

V_s=V_a+V_b=\frac{Q}{C_{\text{eq}}}