Time Constant (Tau) = is the time to reach 63.2% of full Current (inductor) or Voltage (capacitor) where 1 - e^-1 = 63.2%
Time Constant (Tau) = RC
Time Constant (Tau) = L/R
At Time = 1mSec, the current through the inductor is 63.2% of 1A or 632mA.
At Time = 1mSec, the voltage across the capacity is 63.2% of 1V or 632mV.
Close the switch when the initial current or voltage is zero.