Transient analysis of a step RL circuit
It is true that the voltage across the 4 ohm resistor is zero because ideally no current flows through it if there’s a short across it. However in reality there would be a small but practically negligible current through the 4 ohms but will assume it’s ideally nothing. This doesn’t mean that the 4 ohms has no current flow when the switch is turned to location B. Therefore we must include 4 ohm in the calculation thevenin resistance and thus to determine the of time constant.