An input capacitance gives an exact time constant and final stored state without claiming an exponential curve. 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 capacitance sets an exact time constant
The input resistance is 3 ohm and the capacitance is 4 farads, so tau is 12 seconds.
τ=RC=12s
Final charge and energy are exact
At the final 12 volt level, the charge is 48 coulombs and the stored energy is 288 joules. Exponential midpoints and filter cutoff values are deferred.