Prove that an ideal capacitor connected to an $\mathrm{AC}$ source does not dissipate power.

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?