pe exam Q 62

[yaoyaodes]

Not sure where is 90 degree come from.

 

[DLD PE]

The key term here is "synchronous reactance". Since the problem states resistance is negligible, you are left with modeling a purely inductive load, so you have a power factor of zero (opposite of a purely resistive load, which would have a power factor of 1). So with the synchronous reactance, you need to include the "j" with the "Xs" and 90 degrees. This is a tricky problem.

 

[yaoyaodes]

Thanks, that makes more sense

 

[akyip]

To add on to what DuranDuran said above, attached is an illustration of the typical per-phase circuit analysis diagram for a synchronous motor. The armature resistance Ra is usually much smaller than the synchronous reactance Xs, and here it's stated that resistance Ra is negligible (approximately equal to zero).

The synchronous reactance expressed as a full impedance phasor is jXs = Xs<90 degrees. Since the current Is lags the voltage, it has a negative phase angle (assuming a reference voltage angle of 0 degrees). This explains the 90 - current angle.