In a Balanced Y -Δ Circuit Shown Below, the Magnitude

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In a Balanced  Y -Δ Circuit Shown Below, the Magnitude

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\begin{array} { l } \mathrm { Z } _ { \mathrm { Y } } = \mathrm { Z } _ { \Delta } / 3 = 22 + \mathrm { j } 13 = 25.5539 \angle 30.5792 ^ { \circ } \Omega \\mathrm { Z } _ { \mathrm { t } } = \mathrm { Z } _ { \mathrm { W } } + \mathrm { Z } _ { \mathrm { Y } } = 33 + \mathrm { j } 29 \\mathrm {~V} _ { \mathrm { an } } = 635 \angle 0 ^ { \circ } \mathrm { V } , \mathrm { V } _ { \mathrm { bn } } = 635 \angle - 120 ^ { \circ } \mathrm { V } , \mathrm { V } _ { \mathrm { cn } } = 635 \angle 120 ^ { \circ } \mathrm { V } \\mathrm { I } _ { \mathrm { A } } = \mathrm { V } _ { \mathrm { an } } / \mathrm { Z } _ { \mathrm { t } } = 14.4542 \angle - 41.3086 ^ { \circ } \mathrm { A } \\mathrm { I } _ { \mathrm { B } } = \mathrm { V } _ { \mathrm { bn } } / \mathrm { Z } _ { \mathrm { t } } = 14.4542 \angle - 161.3086 ^ { \circ } \mathrm { A } \\mathrm { I } _ { \mathrm { C } } = \mathrm { V } _ { \mathrm { cn } } / \mathrm { Z } _ { \mathrm { t } } = 14.4542 \angle 78.6914 ^ { \circ } \mathrm { A }\end{array}

\begin{array} { l } V _ { A } = V _ { ext {an } } - Z _ { W } imes I _ { A } = 369.3615 \angle - 10.7294 ^ { \circ } \mathrm { V } \V _ { B } = V _ { b n } - Z _ { W } imes I _ { B } = 369.3615 \angle - 130.7294 ^ { \circ } \mathrm { V } \V _ { C } = V _ { c n } - Z _ { W } imes I _ { C } = 369.3615 \angle 109.2706 ^ { \circ } \mathrm { V } \V _ { A B } = V _ { A } - V _ { B } = 639.7529 \angle 19.2706 ^ { \circ } \mathrm { V } \V _ { B C } = V _ { B } - V _ { C } = 639.7529 \angle - 100.7294 ^ { \circ } \mathrm { V } \V _ { C A } = V _ { C } - V _ { A } = 639.7529 \angle 139.2706 ^ { \circ } \mathrm { V } \I _ { A B } = V _ { A B } / Z _ { \Delta } = 8.3452 \angle - 11.3086 ^ { \circ } \mathrm { A } \I _ { B C } = V _ { B C } / Z _ { \Delta } = 8.3452 \angle - 131.3086 ^ { \circ } \mathrm { A } \I _ { C A } = V _ { C A } / Z _ { \Delta } = 8.3452 \angle 108.6914 ^ { \circ } \mathrm { A }\end{array}

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1+16j; clear ali; format long

\mathrm { Vp } = 635 ; \mathrm { ZD } = 66 + 39 \mathrm { j } ; \mathrm { Zw } = 1

Z D p = R 2 P ( Z D )

theta-2Dp (3)
thetad=ZDp (2)

\mathrm { ZY } = \mathrm { ZD } / 3

\mathrm { ZYp } = \mathrm { R } 2 \mathrm { P } ( \mathrm { ZY } )

\mathrm { Zt } = \mathrm { ZW } + \mathrm { ZY }

V a n = \mathrm { P } 2 \mathrm { Rd } ( \mathrm { Vp } , \mathrm { O } )

V a n p = R 2 P \{ V a n angle

V b n = P 2 R d ( V p , - 120 )

Vbnp=R2P (Vbn\}

V c n = P 2 R d \{ V P , - 240 \}

VCnp-R2P \{Vcn

angle

I A = V a n / Z t

IAP

= R 2 P

(IA)

\mathrm { I } B = V \mathrm { bn } / \mathrm { Zt }

I B p = R 2 P

(IB)

\mathrm { IC } = \mathrm { Vcn } / \mathrm { Zt }

I C P = R 2 P ( I C )

VA=Van

- Z W ^ { * } I A

V A P = R 2 P ( V A )

V B = V b n - Z W ^ { * } I B

\mathrm { VBP } = \mathrm { R } 2 \mathrm { P } ( \mathrm { VB } )

V C = V C n - 2 W ^ { \star } I C

\mathrm { VCP } = \mathrm { R } 2 \mathrm { P } ( \mathrm { VC } )

V A B = V A - V B

V A B P = R 2 P ( V A B )

\mathrm { VBC } = \mathrm { VB } - \mathrm { VC }

\vee B C P = R 2 P \{ V B C \}

\mathrm { VCA } = \mathrm { VC } - \mathrm { VA }

V C A P = R 2 \mathrm { P }

(VCA)

I A B = V A B / Z D

I A B P = R 2 P

(IAB)

I B C = V B C / Z D

\mathrm { IBCP } = \mathrm { R } 2 \mathrm { P }

(IBC)

I C A = V C A / Z D

I C A P = R 2 P \{ I C A \}

Essay