How long does it take for the current in an circuit with = 150Ω and = 65mH to reach half its final value?
i = (V/L)[ 1 - e^(-R t/L) ]
at t = 0, i = 0
at t-->oo , i --> V/L
so when is
[ 1 - e^(-R t/L) ] equal to 1/2 ?
when e^(-Rt/L) = 1/2
ln e^(-Rt/L) = -Rt/L = - .693
so when
t = .693 (L/R)