I'm writing up a summary about classic impedances (resistors \$Z_R=R\$, capacitors \$Z_C=1/j\omega C\$ and inductors \$Z_L = j\omega L\$) for students starting out with AC networks.
I was about to tabulate the behaviour of \$|Z|\$ (magnitude), \$\angle Z\$ (phase), \$\textrm{Re}\,Z\$ (resistance) and \$\textrm{Im}\,Z\$ (reactance) for when \$R\$ and \$C\$ and \$L\$ and \$\omega\$ approach either \$0\$ or \$\infty\$, where I'd mention that a capacitor acts like an open circuit for DC signals and an inductor acts like an open circuit when approaching infinitely fast oscillations, since this is standard knowledge. However, it occurred to me: why do we claim this?
An open circuit, as far as I know, is an infinitely resistive path. If that is true, however, then a capacitor and an inductor could never be open circuits, since they have no resistance. It stands to reason that an open circuit is a path for which \$|Z|\$ is infinitely large, which is true when either or both of \$\textrm{Re}\,Z\$ and \$\textrm{Im}\,Z\$ is infinite. But why?
Intuitively, resistance measures how much electrons in a current are scattered and hence reduced in potential, so a big resistance means only a small trickle of current enters and exits a device. Reactance, on the other hand, I have no mental model for. Generally, I associate it with phase shifting (although of course, that's not the full story, since \$1/j\omega C\$ and \$j\omega L\$ can reach any reactance whilst having an ever-fixed phase). What's the intuition about a reactance blocking current when it gets big?