Question

The semiconverter as shown in figure is connected to a 120 V, 60 Hz supply. The load current $I_0$ can be assumed to be continuous and its ripple content is negligible. The turns ratio of transformer is unity. If the delay angle is $\alpha =\pi /2$, then the input power factor is

• A. 0.54 lag
• B. 0.72 lag
• C. 0.64 lag
• D. 0.825 lag

Answer 1

The correct option is C 0.64 lag

$I_{s1}=\frac{2\sqrt{2}}{\pi }{I}_{0}cos\frac{\alpha }{2}$
$I_{s1}=\frac{2\sqrt{2}}{\pi }cos\frac{\pi }{4}{I}_0=0.6366I_0$
$I_{sr}=I_0{(1-\frac{\alpha }{\pi })}^{1/2}=I_0{(1-\frac{\pi }{2\pi })}^{1/2}=\frac{I_0}{\sqrt{2}}$

$Powerfactor=\frac{I_{s1}}{I_{s}r}cos\frac{\alpha }{2}$
$=\left(\frac{\frac{2\sqrt{2}}{\pi }cos\frac{\pi }{4}{I}_0\times cos\frac{\pi }{4}}{\frac{I_0}{\sqrt{2}}}\right)=0.6366$