Example
A 240V load is connected in Y. Each phase of the
load is 24 Ohms in series with j12 Ohms. Designate
the voltage in phase a as the zero phase angle
reference.
a. Find each of the line to neutral voltages.
b. Find each of the line to line voltages.
c. Find each of the line currents that supply the load.
d. Find the real and reactive power consumed in this
three phase load.
j  1
VLL  240  V
ZY  ( 24  j  12)  Ω
a. Find each of the line to neutral
voltages.
VLN 
VLL
3
 138.564 V
VAN  VLN e
VBN  VAN e
j  θA
 138.564 V
 j  120  deg
VBN  138.564 V
VCN  VAN  e
θA  0  deg
j  120 deg
VCN  138.564 V
 ( 69.282  120i) V


θB  arg VBN  120  deg
 ( 69.282  120i) V


θC  arg VCN  120  deg
b. Find each of the line to line voltages.
VAB  VAN  VBN  ( 207.846  120i) V
VAB  240 V
VBC  VAB e

 j  120 deg
VBC  240 V
VCA  VAB e
 240i V


θBC  arg VBC  90  deg
j  120 deg
VCA  240 V

θAB  arg VAB  30  deg
 ( 207.846  120i) V


θCA  arg VCA  150  deg
V CN
V AN
VCN
V BN
VCA
VAN
V BC
V AB
V BN
c. Find each of the line currents that supply the
load.
VAN  138.564 V
ZY  ( 24  12i) Ω
VAN
IA 
 ( 4.619  2.309i) A
ZY
IA  5.164 A
 
θIA  arg IA  26.565  deg
VBN
IB 
 ( 4.309  2.845i) A
ZY
IB  IA e
 j  120 deg
IB  5.164 A
 ( 4.309  2.845i) A
 
θIB  arg IB  146.565  deg
VCN
IC 
 ( 0.309  5.155i) A
ZY
IC  IA e
j  120 deg
VCN
IC
VAN
IC  ( 0.309  5.155i) A
IC  5.164 A
 
θIC  arg IC  93.435  deg
IB
VBN
IA
d. Find the real and reactive power consumed in
this three phase load.
kVAr  kV A

S3φ  3  VAN  IA  ( 1.92  0.96i)  kV A
 
Q3φ  Im  S3φ  0.96  kVAr
P3φ  Re S3φ  1.92  kW
Check by other methods.


P3φ  3  VAN  IA  cos θA  θIA  1.92  kW


Q3φ  3  VAN  IA  sin θA  θIA  0.96  kVAr


IB  cos  θB  θIB  640 W
IC  cos  θC  θIC  640 W
PA  VAN  IA  cos θA  θIA  640 W
PB  VBN 
PC  VCN 
P3φ  PA  PB  PC  1.92  kW
P3φ 


3  VLL IA  cos θA  θIA  1.92  kVAr