A capacitor with an initial potential difference of $158$ V is discharged through a resistor when a switch between them is closed at $\backslash ($ t$=0\backslash )$ s $.$ At $\backslash ($ t$=10\mathrm{.}0\backslash$mathrm$\{$~s$\}\backslash ),$ the potential difference across the capacitor is $1\mathrm{.}13$ V $.($a$)$ What is the time constant of the circuit? $($b$)$ What is the potential difference across the capacitor at $\backslash ($ t$=18\mathrm{.}5\backslash$mathrm$\{$~s$\}\backslash )?$