The $12-$pulse diode rectifier shown in Fig. $3,$ is supplied from a $400$ V $($line to line$),50$ Hz ac power supply and feeds a large smoothing inductor in series with a resistive load. Neglect the forward voltage drops in the diodes. The load draws a constant DC current of $50$ A$.$ Assuming transformer$-1$ has a turns ratio of NT$1\_$Y$1/$NT$1\_$Y$2=1$:$1$ and transformer$-2$ has a turns ratio of N T$2\_1/$N T$2\_$Y$2=3$:$1$ :

$($i$)$ Measure the input power factor of the $12$ pulse converter as well as the input power

factor of Bridge$-1,$ comment on the difference of the measured results.