An ideal inductor in an AC circuit consumes no power, though both $\mathrm{V}$ and $\mathrm{I}$ are non-zero. Why?

In the adjoining $\mathrm{AC}$ circuit, $\mathrm{R}$ is a pure resistance and $\mathrm{X}$ is an unknown circuit element. Using only an $\mathrm{AC}$ voltmeter how will you detect whether $\mathrm{X}$ is (i) pure inductance ?

In the adjoining $\mathrm{AC}$ circuit, $\mathrm{R}$ is a pure resistance and $\mathrm{X}$ is an unknown circuit element. Using only an $\mathrm{AC}$ voltmeter how will you detect whether $\mathrm{X}$ is (ii) pure resistance ?

In the adjoining $\mathrm{AC}$ circuit, $\mathrm{R}$ is a pure resistance and $\mathrm{X}$ is an unknown circuit element. Using only an $\mathrm{AC}$ voltmeter how will you detect whether $\mathrm{X}$ is (iii) resistance-less, inductance-less conductor?