An inductor coil carries a steady-state current of $2.0 \ A$ when connected across an ideal battery of $emf$ $4.0 \ V$. If its inductance is $1.0 \ H$,find the time constant of the circuit in $sec$.

$A$ coil of inductance $300\, mH$ and resistance $2\, \Omega$ is connected to a source of voltage $2\, V$. The current reaches half of its steady state value in $t$ seconds. Find the value of $t$. (in $, s$)

An $LR$ circuit with a battery is connected at $t = 0$. Which of the following quantities is not zero just after the circuit is closed?

$A$ coil of self-inductance $10\,mH$ and resistance $0.1\,\Omega$ is connected through a switch to a battery of internal resistance $0.9\,\Omega$. After the switch is closed,the time taken for the current to attain $80\%$ of its saturation value is: [take $ln\,5 = 1.6$] (in $,s$)

The ratio of time constants during growth and decay of current in the circuit is

Find the current in the $4 \Omega$ resistance shown in the figure in the following cases:
$(a)$ Just after the closing of the key.
$(b)$ $A$ long time after the closing of the key.