= Capacitor bridging a divider and a return resistor
{title2=$V_{\rm th}=2V/3,\quad R_{\rm th}=5R/3$}
Feed a node through resistance $R$ from an ideal voltage $V$, connect that node to ground through $2R$, and connect a capacitor from it to a second node grounded through $R$. The capacitor sees a <Thévenin equivalent> with open-circuit voltage $2V/3$ and resistance $(R\parallel2R)+R=5R/3$. For zero initial capacitor voltage, $I_C=2V e^{-t/\tau}/(5R)$ and $\tau=5RC/3$. The $2R$ branch current is $V/(3R)-I_C/3$, so the two branch currents coincide at $t=\tau\log(8/5)$. This illustrates why the source-side resistor alone does not determine a charging time constant.
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