In a transformer let us assume a load is connected consuming certain active power; say 5000 W. Now if we put a different load of low power factor consuming same amount of active power, now here the current has to increase right? Here the active power can be written as VIcos(theta) and reactive power as VIsin(theta). Now as power factor decreases current increases, it means reactive power (VIsin(theta)) also increases (as current increases and theta increases), but why it is said that reactive power is constant? In an induction motor,reactive power is taken constant. And on loading of the motor,power factor is taken as increasing.
Here is some data for a 22 kW, 3-ph, 400 V induction motor at no-load, and 0.25, 0.5, 0.75, 1.0 and 1.25 X rated load. The reactive power (kVAR) more than doubles between no-load and 1.25 X rated load. The power factor increases even though the reactive VA increases because the real power increases more than the reactive VA increases.
Someone might expect the reactive power to remain fairly constant because the magnetizing current is assumed to be constant if the voltage and frequency remain constant. However the effect of the increased current in the stator and rotor leakage reactances apparently represents a significant contribution to the reactive VA.
Transformers are also assumed to have a constant magnetizing current as long as the applied voltage and frequency remain constant. The reactive VA of a transformer may also have a significant contribution to to leakage reactance, but the reactive VA of a transformer is relatively insignificant compared to the real and reactive power of the load.