Question 22.4: For the residential supply appearing in Fig. 22.7, determine...
For the residential supply appearing in Fig. 22.7, determine (assuming a totally resistive load) the following:
a. the value of R to ensure a balanced load.
b. the magnitude of I_{1} \text { and } I_{2}.
c. the line voltage V_{L}.
d. the total power delivered for a balanced three-phase load.
e. the turns ratio a=N_{p} / N_{s}.
\text { a. } \quad P_{T}=(10)(60 W )+200 W +2000 W.
=600 W +200 W +2000 W =2800 W.
P_{\text {in }}=P_{\text {out }}.
V_{p} I_{p}=V_{s} I_{s}=2800 W \text { (purely resistive load) }.
(2400 V ) I_{p}=2800 W \text { and } I_{p}=1.17 A.
R=\frac{V_{\phi}}{I_{p}}=\frac{2400 V }{1.17 A }=2051.28 \Omega.
\text { b. } P_{1}=600 W =V I_{1}=(120 V ) I_{1}.
and I_{1}=5 A.
P_{2}=2000 W =V I_{2}=(240 V ) I_{2}.
and I_{2}=8.33 A.
\text { c. } V_{L}=\sqrt{3} V_{\phi}=1.73(2400 V )=4152 V.
\text { d. } P_{T}=3 P_{\phi}=3(2800 W )= 8 . 4 k W.
\text { e. } a=\frac{N_{p}}{N_{s}}=\frac{V_{p}}{V_{s}}=\frac{2400 V }{240 V }=10.