Problem $1$: $/20$

A series RLC resonant circuit has component values of R $=5,$ L $=20$ mH$,$ and C $=0\mathrm{.}5$ F$.$

Determine the following quantities: a$)$ the circuit$$s resonant frequency $0$; b$)$ the circuit$$s quality

factor Q; c$)$ the circuit$$s bandwidth BW; and d$)$ the circuit$$s half$-$power frequencies LO and HI$.$

Ans: a$)$ $0=104$ rad$/$s; b$)$ Q $=40$; c$)$ BW $=250$ rad$/$s; d$)$ LO $=9875$ rad$/$s$,$ HI $=10125$ rad$/$s$.$