A $15\mathrm{.}2$ kOhm resistor and a capacitor are connected in series and then a $12\mathrm{.}0$V potential difference is suddenly applied across them. The potential difference across the capacitor rises to $3\mathrm{.}08$V in $1\mathrm{.}84$ us$.($a$)$ Calculate the time constant of the circuit. $($b$)$ Find the capacitance of the capacitor.