Question $1$

$($a$)$ For the circuit shown in Figure Q$1$a$,$ the rms AC voltage source is $220v,50Hz,R_1$ and $R_2$ are $100$ and $200$ respectively, $C_1$ is $47F,$ and $L_1$ is $100$ mH $.$

$($i$)$ Find the Thev$$nin equivalent circuit for the part of circuit on the left$-$hand side of the terminals M$-$N$.$

$(8$ marks$)$

$($ii$)$ Calculate the magnitude and phase angle of the voltage across $C_1,$ assuming the source voltage has zero phase angle.