In an RC series circuit, E$=12\mathrm{.}0$ V$,$ R$=1\mathrm{.}86$ M$,$ and C$=1\mathrm{.}53$ mF$.($a$)$ Calculate the time constant. $($b$)$ Find the maximum charge that will appear on the capacitor during charging. $($c$)$ How long does it take for the charge to build up to $6\mathrm{.}87$ mC$?$