A capacitor with an initial potential difference of $112$ V is discharged through a resistor when a switch between them is closed at t $=0$ s$.$ At t $=10\mathrm{.}0$ s$,$ the potential difference across the capacitor is $1\mathrm{.}40$ V$.($a$)$ What is the time constant of the circuit? $($b$)$ What is the potential difference across the capacitor at t $=18\mathrm{.}4$ s$?$