Input RC Time Three-Row Scan - Electronic Circuits III: Comparators and Interfaces Step by Step

An input capacitor scan separates time constant, final charge, and stored energy without inventing an exponential midpoint. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Input timing has a resistance scale and a storage scale

The battery voltage is fixed while resistance and capacitance are scanned. Tau tracks their product, while final charge and energy come from the capacitor value.

\tau=RC,\quad Q_f=CV,\quad U_f=\frac{1}{2}CV^{2}

Three rows keep timing and stored state together

The table gives a minimum set of points for both dependencies: resistance changes the time scale, and capacitance changes both time scale and stored state.

\begin{array}{c|c|c|c|c}R&C&\tau&Q_f&U_f\\2\ \text{ohm}&3\ \text{F}&6\ \text{s}&36\ \text{C}&216\ \text{J}\\3\ \text{ohm}&4\ \text{F}&12\ \text{s}&48\ \text{C}&288\ \text{J}\\4\ \text{ohm}&6\ \text{F}&24\ \text{s}&72\ \text{C}&432\ \text{J}\\\end{array}

The large row has the longest time constant

For the large row, tau is 24 seconds and final charge is 72 coulombs.

4\ \text{ohm}\cdot6\ \text{F}=24\ \text{s}

The RC helper still refuses exponential midpoint claims

This deeper scan adds more points, but it still claims only tau, final charge, and final energy. Midpoint voltages need a separate sampled-response helper.

48\ \text{C},\quad288\ \text{J}