A capacitor with an initial potential difference of $167$ V is discharged through a resistor when a switch between them is closed at t$=0$t $=0$t$=0$ s$.$ At t$=10\mathrm{.}0$t $=10\mathrm{.}0$t$=10\mathrm{.}0$ s$,$ the potential difference across the capacitor is $1\mathrm{.}66$ V$.($a$)$ What is the time constant of the circuit? $($b$)$ What is the potential difference across the capacitor at t$=19\mathrm{.}1$t $=19\mathrm{.}1$t$=19\mathrm{.}1$ s