You make a series LRC circuit with a $200-$ resistor, a $0\mathrm{.}400-$H inductor, and a $6\mathrm{.}00-$ F

$$ capacitor connected to a

voltage source that has amplitude $30\mathrm{.}0$ V and angular frequency $250$ rad$/$s$.$

$($a$)$ Find the impedance of the circuit. $(6$ points$)$

$($b$)$ Find the rms current. $(5$ points$)$

$($c$)$ Find the rms voltage across the capacitor. $(6$ points$)$