If in a circuit current lags behind EMF by π / 2 . Then it is a/an

Figure shows a purely inductive circuit, in which a sinusoidal emf is applied. The induced emf across the inductor is - $L \frac{d i}{d t}$ so that from Kirchhoff's law, $$\begin{aligned}& \varepsilon_0 \sin \omegat-L \frac{d i}{d t}=0 \\ & \Rightarrow \frac{d i}{d t}=\frac{\varepsilon_0}{L} \sin \omegat \\ & \text{ or }i=-\frac{\varepsilon_0}{\cos } \cos \omegat+C \end{aligned}$$ The constantCcan be shown to $be zero from the fact that, the emf being sinusoidal, the current should also be so, and the average current over one time period has to be zero. \therefore i=-$\frac{\varepsilon_0}{\omega L} \cos \omega \mathrm{t} \quad \text{or }i=\frac{\varepsilon_0}{\omega L} \sin (\omega \mathrm{t}-\pi$/ 2) which shows that the current lags behind the emf by a phase of$\pi / 2