0
1.2kviews
Derive the relationship between Phase and Line voltages and currents for a star connected balanced load across a three-phase balanced system.
1 Answer
0
32views

$V_{R}=V_B =V_Y=V_{ph}$ $V_{L}=V_{RB}=V_{BY}=V_{RY}$ ![](data:image/png;base64,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) $\begin{align*} \therefore V_L &=\bar{V_R} - \bar{V_B}\ &=V_R+j0-V_B\cos 60 -jV_B \sin 60\ &= V_{ph} -V_{ph}\cos 60 -jV_{ph} \sin 60\ &=V_{ph}(1-\cos 60)-jV_{ph}\sin 60\ &=V_{ph}\sqrt{(1-\cos 60)^2 +(\sin 60)^2} =1.732V_{ph} =\sqrt{3}V_{ph}

\end{align*} $

Please log in to add an answer.