$(20$ Points: $4$ Points each$)$ For the circuit in Fig. $2$:

a$.$ Find the total impedance $Z_T$ in polar form.

b$.$ Find the value of C in microfarads and L in Henries:

c$.$ Find the current I and the voltages $V_R,V_L,$ and $V_C$ in phasor form and d $.$ Draw the phasor diagram of the voltages $E,V_R,V_L,$ and $V_C,$ and the current I.

d$.$ Find the power factor of the circuit and indicate whether it is leading or lagging.

e$.$ Find the sinusoidal expressions for the voltages and current.