An Inductor at T0 is modeled as a current short and a voltage open
An inductor will try to suck as much current as possible initially then meter it out when power is removed. A current pig.
A Capacitor at T0 is modeled as a voltage short and a current open.
A capacitor is an inverse current pig. It will meter current when power is applied hold then hold it's charge when power is removed.
A charged capacitor will disgorge it's current very rapidly when a short is applied across it. An inductor does not hold charge.
Current represents the flow of charge. Folks generally consider it better to try to think in terms of current flow.