Bigger Capacitor Slower - Electronic Circuits Step by Step

Increasing capacitance increases the exact time scale and final stored charge in this RC model. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Start with the smaller capacitor

The smaller capacitor gives time constant 12 seconds and final charge 24 coulombs.

\tau_{\text{small}} = 12\ \text{s},\quad Q_{\text{small}} = 24\ \text{C}

Increase only the capacitance

Increase the capacitance from 4 farads to 8 farads.

C: 4\ \text{F} \rightarrow 8\ \text{F}

The time scale and final storage grow

The time constant changes from 12 seconds to 24 seconds, and the final charge changes from 24 coulombs to 48 coulombs. The final energy changes from 72 joules to 144 joules.

\tau: 12\ \text{s} \rightarrow 24\ \text{s},\quad Q_{\text{final}}: 24\ \text{C} \rightarrow 48\ \text{C},\quad U_{\text{final}}: 72\ \text{J} \rightarrow 144\ \text{J}

Capacitance stretches time and storage

At fixed resistance and source voltage, capacitance increases the time constant, final charge, and final stored energy in the same exact rows.

\begin{array}{c|c|c|c|c|c}R&C&V&\tau&Q_f&U_f\\3\ \text{ohm}&4\ \text{F}&6\ \text{V}&12\ \text{s}&24\ \text{C}&72\ \text{J}\\3\ \text{ohm}&8\ \text{F}&6\ \text{V}&24\ \text{s}&48\ \text{C}&144\ \text{J}\\3\ \text{ohm}&12\ \text{F}&6\ \text{V}&36\ \text{s}&72\ \text{C}&216\ \text{J}\\\end{array}