Question 23.4: For the Δ-Y system shown in Fig. 23.21: a. Find the voltage ...
For the Δ-Y system shown in Fig. 23.21:
a. Find the voltage across each phase of the load.
b. Find the magnitude of the line voltages.
\text { a. } I _{\phi L}= I _{L} \text {. Therefore },
\begin{aligned}& I _{a n}= I _{A a}=2 A \angle 0^{\circ} \\& I _{b n}= I _{B b}=2 A \angle-120^{\circ} \\& I _{c n}= I _{C c}=2 A \angle 120^{\circ}\end{aligned}The phase voltages are
V _{a n}= I _{a n} Z _{a n}=\left(2 A \angle 0^{\circ}\right)\left(10 \Omega \angle-53.13^{\circ}\right)= 2 0 V \angle- 5 3 . 1 3 ^{\circ}.
V _{b n}= I _{b n} Z _{b n}=\left(2 A \angle-120^{\circ}\right)\left(10 \Omega \angle-53.13^{\circ}\right)= 2 0 V \angle- 1 7 3 . 1 3 ^{\circ}.
V _{c n}= I _{c n} Z _{c n}=\left(2 A \angle 120^{\circ}\right)\left(10 \Omega \angle-53.13^{\circ}\right)=20 V \angle 6 6 . 8 7 ^{\circ}.
\text { b. } E_{L}=\sqrt{3} V_{\phi}=(1.73)(20 V )=34.6 V . \text { Therefore, }E_{B A}=E_{C B}=E_{A C}=34.6 V.
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