A capacitor with an initial potential difference of $133$ 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 $1\mathrm{.}52$V$.($a$)$ what is the time constant of the circuit? $($b$)$ What is the potential difference across the capacitor at t$=19\mathrm{.}9$s$?$