Question

3-A balanced wye-connected load of (4 + j3) Ω is connected across a three-phase source of 173 V (line-to-line) Find the transmission line current. Find the power factor, P and Q

Please show all work

Answer 1

Given the line voltage is

The balanced wye-connected load having an impedance on each phase is $Z=(4+j3)Omega$

since the load is balanced,

the line to neutral voltage across the load on each phase is

Let the voltage on phase-A load is having a zero phase.

The transmission line current on phase-A is is

So, the magnitude of transmission line current in each phase is 19.9763A

The power factor is

The apparent power on phase-A is

The total apparent power in the three phases is

The 3-phase active power is the real part of 3-phase apparent power

$P_{3phi}=Re[S_{3phi}]=4788.6W$

The 3-phase reactive power is the imaginary part of 3-phase apparent power

$Q_{3phi}=Im[S_{3phi}]=3591.5VAr$