Consider the circuit shown in Figure $1.$

Figure $1$: Circuit for Question $1$

The sources $v_{s1}$ and $v_{s2}$ have an rms value of $120$ V at $50$ Hz $,$ and the two are $180$ out of phase. Assume $L=5mH$ and $I_d=10A$ is a DC current. If the the delay angle is $=45,$

$($a$)$ Use PSPICE to obtain waveform for $v_{s1},i_{s1},$ and $v_d.$

$($b$)$ Calculate the average value $V_d$ and the commutation interval $.$

$($c$)$ Calculate the power factor $($carefully think about your answer here$).$