Problem $2[30$ points$]$:

Consider the time$-$domain RLC$-$circuit shown below:

Assume:

$R={200}^{},L=2^H,C={0\mathrm{.}1}^{mF}={10}^{-4}F$&$v_S(t)={10}^3$Cos$(100t+10).$

$($a$)-$ Draw the circuit in phasor$-$domain $($OR$,$ complex$-$domain$).$

$($b$)-$ Find the total impedance $(Z_t)$ as seen by the source.

$($c$)-$ Find the time$-$functions for $i(t)$ and $v_L(t).$

Recall: When taking a circuit to complex$-$domain, we use the following:

$v(t)=V_m$Cos$(t+)>V=\frac{V_m}{{?}_{}}$

$R$ remains as $R,L$ becomes $jL$&$C$ becomes $\frac{1}{jC}$