when does minimum value of power factor occurs
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Power factor = R/X. So it is zero when R is zero. This happens for ideal inductor or ideal capacitor, and never in practice.
All practical inductors are made of coils of wires, so however low the resistance is, it has a finite value and is measurable. Capacitor equivalent series resistance is very miniscule, and its power factor is measured as Tan Delta, or loss angle. This is very small, may go to as low as 0.0002, but still never zero.
In all cases, power factor is minimum when resistance in circuit is minimal, or when real active power is at its lowest in comparison with total VAR of circuit.
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