Solution
= Solution
For an <inductor>, $V=L\,dI_L/dt$. In the steady AC solution with no added constant <electric current>,
$$
\boxed{Z_L=i\omega L,\qquad I_L(t)=\frac{V_0}{\omega L}\sin\omega t=\frac{V_0}{\omega L}\cos(\omega t-\pi/2).}
$$
The <electric current> \b[lags the voltage by $\pi/2$]. An ideal <inductor> can also sustain an arbitrary DC current, fixed by initial conditions; it is excluded from this steady sinusoidal comparison.