What is the value of the power factor in a purely inductive circuit?
(A) 0
(B) 0.1
(C) 1
(D) Infinite

Hint
The power factor is the cosine of the phase angle between voltage and current in an AC circuit. We will use the formula for the power factor in which phase angle is first determined.
Power factor, ${\rm{P}}.{\rm{f}} = \cos \phi $

Complete step by step answer
A purely inductive circuit consists of only an inductor and does not consist of a resistor or a capacitor. The inductor in the purely inductive circuit has negligible resistance. The phase angle denoted by $\phi $ between voltage and current is such that the current lags behind voltage by $90^\circ $ i.e.
$\phi = 90^\circ $
the power factor is determined using,
${\rm{P}}.{\rm{f}} = \cos \phi $
On putting the value of the phase angle in the formula, we get
${\rm{P}}.{\rm{f}} = \cos 90^\circ $
∴ ${\rm{P}}.{\rm{f}} = 0$
This implies that the power factor for a purely inductive circuit is zero.
Therefore, (A) $0$ is the required solution.

Additional Information
The result implies that the power factor is minimum for a purely inductive circuit and the average power dissipated in a purely inductive circuit over a complete cycle is zero and depends on the amount of voltage and the current applied to the circuit. The amount of current that is flowing through the purely inductive circuit does not contribute to the power dissipation resulting in zero power dissipation.

Note
The value of the power factor depends on the phase angle $\phi $ but it is determined by computing the cosine of the phase angle.