If $V _ { c n } = 275 \angle 105 ^ { \circ } V \text {, what are } V _ { a n } , V _ { b n } \text { and } V _ { a b } , V _ { b c } , V _ { c a } \text { for the balanced three-phase }$ sources?

Name: If $V _ { c n } = 275 \angle 105 ^ { \circ } V \text {, what are } V _ { a n } , V _ { b n } \text { and } V _ { a b } , V _ { b c } , V _ { c a } \text { for the balanced three-phase }$ sources?
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\begin{array} { l } \mathrm { V } _ { \mathrm { cn } } = 275 \angle 105 ^ { \circ } \mathrm { V } \\mathrm { V } _ { \mathrm { an } } = 275 \angle 105 ^ { \circ } + 240 ^ { \circ } = 275 \angle 345 ^ { \circ } = 275 \angle - 15 ^ { \circ } \mathrm { V } \\mathrm { V } _ { \mathrm { bn } } = 275 \angle 105 ^ { \circ } + 120 ^ { \circ } = 275 \angle 225 ^ { \circ } = 275 \angle - 135 ^ { \circ } \mathrm { V } \\mathrm { V } _ { \mathrm { ab } } = 275 imes \sqrt { 3 } \angle - 15 ^ { \circ } + 30 ^ { \circ } = 476.314 \angle 15 ^ { \circ } \mathrm { V } \\mathrm { V } _ { \mathrm { bc } } = 275 imes \sqrt { 3 } \angle 15 ^ { \circ } - 120 ^ { \circ } = 476.314 \angle - 105 ^ { \circ } \mathrm { V } \\mathrm { V } _ { \mathrm { ca } } = 275 imes \sqrt { 3 } \angle - 105 ^ { \circ } - 120 ^ { \circ } = 476.314 \angle - 225 ^ { \circ } = 476.314 \angle 135 ^ { \circ } \mathrm { V }\end{array}

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