Time constant in Inductors:

It is impossible to decide exactly when the maximum point is reached on an exponential curve, or when the curve has fallen to exactly zero.   To enable calculations to be performed a  time constant is used. The time constant gives an indication of the time taken for the current to rise to its maximum value or fall to zero. The time constant is defined as either:

• The time taken for a current to reach its maximum value if the initial rate of increase were maintained.
• The time taken for the current to reach 0.632 of its maximum value (or 63.2%).

The latter definition arises since it is found that after one time constant, the current has always built up to 63.2% of its maximum value.  The time constant for a series LR circuit is given by:

          Time Constant  = L/R seconds

Therefore, although it is not possible to say exactly when the current reaches its maximum value, for all practical purpose it can be considered a maximum after 5 time constants:

          Maximum Current flows after 5L/R