In a one-time constant, current through a series R-L circuit rises nearly

The time in which the current in the circuit increases from zero to 63% of the maximum value of Imax is called the one time constant or the decay constant of the circuit.

Concept:

We know that

\(I = {I_{max}}\left( {1 - {e^{ - \frac{R}{L}t}}} \right)\)

This equation shows the exponential increase of current in the circuit with the passage of time

The figure below shows the plot of current versus time

The growth of current in a circuit containing inductance and resistance

If we put t = TL = L/R in equation 1 then,

\(I = {I_{max}}\left( {1 - \frac{1}{e}} \right) = 0.63{I_{max}}\)