How Does Electricity “Know” a Circuit Is Open or Closed?

Ohm’s law only applies to electrical circuits carrying direct current at equilibrium. When current is changing, whether due to an alternating current supply or transients when a circuit is connected, reactance gets into the game and the inductance and capacitance of the circuit must be taken into account, even if the circuit is composed only of wires. This can lead to all of the wild and wooly phenomena such as reflection of signals and oscillation until the circuit reaches a static state.

When a battery is connected to a pair of wires that extend into a “Y” with one arm shorted and the other open, how does the battery “know” how much current to send into each arm, and how long does it take for this “knowledge” about the circuit to get back to the battery? Is it possible to watch this process play out as it happens?