$($I found part a$.$ and b$.$ but i need help with c$.$ part i$.,$ ii$,$ iii., & iv$.)$

An RLC series circuit has a $R=1\mathrm{.}00k$ Ohm resistor, a L $=150$ Micro H inductor, and a C $=25\mathrm{.}0$ nF capacitor. the voltage source has a $Vrms=408V$ at $f=7\mathrm{.}5kHz.$

$($a$)$ Find the circuit's impedance. I found the impedance to $=1307\mathrm{.}42$ohms

$($b$)$ What is the root$-$mean$-$square current Irms that flows in the circuit? I found the $lrmsto=0\mathrm{.}312A$

$($c$)$ Assuming the convention that the current has no phase $,$ determine the following:

i$)$ The phase $$ of the voltage source relative to the current. Indicate its sign as well. Make sure your calculator is in radians!

ii$)$ Based on your answer to i$),$ the voltage source

Leads the current $$ Lags the current

$$ Leads the current

iii$)$ Based on your answer to I$)$ and ii$)$ we say that at this frequency the circuit is

$$ Inductive $($dominated by inductor$)$ Capacitive $($dominated by the capacitor$)$

Briefly justify your selection.

$($FRQ #$4$ Continued$)$

iv$)$ Write down the function that describes the voltage $V(t)$ and the current $I(t)$ as a function of time for this circuit. Make sure you plug in the numerical values in the