RC Time Coupled Axes Scan - Electronic Circuits Step by Step

A three-row RC scan separates resistance's timing role from capacitance's timing and storage roles. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

Resistance and capacitance affect different reads

The time constant uses both resistance and capacitance. Final charge and final stored energy use capacitance and voltage, not resistance. This scan keeps the exact time constant and final state; it does not claim a sampled exponential midpoint voltage.

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

A three-row scan separates timing from storage

The first change raises resistance only, so only the time scale changes. The second change raises capacitance, so time scale, final charge, and final energy all change.

\begin{array}{c|c|c|c|c|c}R&C&V&\tau&Q_f&U_f\\1\ \text{ohm}&1\ \text{F}&6\ \text{V}&1\ \text{s}&6\ \text{C}&18\ \text{J}\\2\ \text{ohm}&1\ \text{F}&6\ \text{V}&2\ \text{s}&6\ \text{C}&18\ \text{J}\\2\ \text{ohm}&2\ \text{F}&6\ \text{V}&4\ \text{s}&12\ \text{C}&36\ \text{J}\\\end{array}

The rendered row closes all three formulas

For the rendered row, resistance 2 ohms and capacitance 2 farads give a time constant of 4 seconds. The same capacitance gives final charge 12 coulombs.

4\ \text{s},\quad 12\ \text{C},\quad 36\ \text{J}

The scan keeps resistance out of stored energy

Resistance changes the timing path, but final stored energy is set by capacitance and voltage. The three rows make that separation scannable.

R\uparrow\Rightarrow\tau\uparrow,\quad C\uparrow\Rightarrow\tau,Q_f,U_f\uparrow