gate 2017 EE(Set-B) q45-solution

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$$V_L=208V,P=432W$$
$$cos \phi =0.6$$leading
$$P=3V_{ph}-I_{ph}-cos \phi $$
$$P=3.\frac{V^2_{ph}}{Z_{ph}}.cos \phi z_{ph}=\frac{3\times(\frac{208}{\sqrt{3}})^2\times 0.6}{432}=60.08\Omega $$
$$cos^{-1}0.6=53.1^0$$
$$Z_{ph}=60\angle -53.1^0$$
$$Z_{ph}=\frac{V_{ph}}{I{ph}\angle 53.1^0}=\frac{V_{ph}}{I_{ph}}\angle -53.1^0$$