Final Capacitor State - Electronic Circuits Step by Step

After a long time, the final capacitor charge and stored energy are exact static quantities. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

After a long time the capacitor reaches the source

This exact final-state lesson uses the source voltage 6 volts; it does not claim an intermediate charging voltage.

V_{\text{final}} = 6\ \text{V}

Final charge comes from C times V

With capacitance 4 farads and voltage 6 volts, the final charge is 24 coulombs.

Q_{\text{final}} = C V = 24\ \text{C}

Final stored energy is exact

The final stored energy is 72 joules.

U_{\text{final}} = \frac{1}{2} C V^{2} = 72\ \text{J}

Final charge and energy both depend on voltage

With resistance and capacitance fixed, final charge scales directly with voltage while final stored energy follows voltage squared.

\begin{array}{c|c|c|c|c|c}R&C&V&\tau&Q_f&U_f\\3\ \text{ohm}&4\ \text{F}&3\ \text{V}&12\ \text{s}&12\ \text{C}&18\ \text{J}\\3\ \text{ohm}&4\ \text{F}&6\ \text{V}&12\ \text{s}&24\ \text{C}&72\ \text{J}\\3\ \text{ohm}&4\ \text{F}&9\ \text{V}&12\ \text{s}&36\ \text{C}&162\ \text{J}\\\end{array}