The sinusoidal voltage source in the circuit shown in $($Figure $1)$ is generating the voltage v$\_$g$=1\mathrm{.}2$cos$(100$t$)$ V$.$ The capacitor is adjusted until the output voltage leads the input voltage by $120.$ Suppose that R $=4$ k$$

a$)$ Find the value of C in microfarads

b$)$ Write the steady$-$state expression for v$\_$o$($t$)$ as v$\_$o$($t$)=$ V$\_$o $*$ cos$($t$+),$ where Find the numerical value of V$\_$o when C has the value found in the previous part.

c$)$ Find the numerical value of $$ when C has the value found.

d$)$ Find the numerical value of when C has the value found. $($in rad$/$s$)$