The ratio of power factor of purely resistive circuit to purely...

The power factor of an AC circuit is given by $\cos \phi$, where $\phi$ is the phase difference between the voltage and the current.

For a purely resistive circuit, the voltage and current are in the same phase, so \phi = 0^{}^{\circ}.
Power factor = \cos 0^{}^{\circ} = 1

For a purely reactive circuit (purely inductive or purely capacitive), the phase difference between voltage and current is \phi = 90^{}^{\circ}.
Power factor = \cos 90^{}^{\circ} = 0

The ratio of the power factor of a purely resistive circuit to a purely reactive circuit is:
Ratio $= \dfrac{1}{0} = \infty$

Thus, the ratio is infinite.

Answer: infinite