Q$1)$ AC Circuit analysis $[10$ Marks$]$:

Express final answers for phasors and complex impedances in polar form. The voltage is expressed as peak magnitude, and the operating frequency is $50$ Hz $.$

a$)$ Write a time domain expression for the voltage source.$[1]$

b$)$ Determine if each component $Z_1$ and $Z_2$ are a capacitor or inductor and calculate the $L$ and $C$ component values. $[3]$

c$)$ Calculate the input impedance $Z_{in}.[2]$

d$)$ Calculate the phasor source current $I_s.[3]$

e$)$ Calculate the phasor voltage $V_o.[1]$