$1.$ Consider the circuits described:

$($a$)$ If a parallel RLC circuit has a $3$k Ohm resistor and a $2$ H inductor, what are the possible values of

the capacitor for $(1)$ overdamped; $(2)$ critically damped, and $(3)$ underdamped circuit

behaviors?

$($b$)$ What if that was a series circuit instead?

$($c$)$ Consider the damped circuit in series, and add a voltage supply of $10$V aligned with the

capacitor so that the plus of both are on the same side $($i$.$e$.$ short those two terminals$).$ If that

voltage supply turns on at t$=0+,$ what is the ic$($t$)$ for t$>0$ if the dvc$(0)/$dt$=100$V$/$s and vc$(0)=0?$