A single$-$loop circuit consists of a $7\mathrm{.}1$ resistor, $12\mathrm{.}1$ H inductor, and a $3\mathrm{.}1F$ capacitor. Initially the capacitor has a charge of $6\mathrm{.}2C$ and the current is zero. Calculate the charge on the capacitor $N$ complete cycles later for $($a$)N=5,($b$)N=10,$ and $($c$)N=100.$

$($a$)$ Number $$ Units $$

$($b$)$ Number $$ Units $$

$($c$)$ Number $$ Units $$