A coil of inductance `L = 300 mH` and resitance `R = 140 m Omega` is connected to a constant voltage source. How soon will the coil current reach `eta = 50 %` of the steady-state value ?

Explanation

The current at time `t` is given by,
`I(t) = (V)/(R) (1 - e^(-t R//L))`
The steady state value is, `I_(0) = (V)/(R)`
and `(I(t))/(I_(0)) = eta = 1 - e^(-1 R//L)` or , `e^(-1 R//L) = 1 - eta`
or, `t_(0) (R)/(L) = IN (1)/(1 - eta)` or, `t_(0) = (L)/(R) In (1)/(1 - eta) = 1.49 s`