$A$ coil of self-inductance $50\,H$ is connected to the terminals of a battery of $e.m.f.$ $2\,V$ through a resistance of $10\,\Omega$,and a steady current is flowing through the circuit. If the battery is now disconnected,the time in which the current will decay to $1/e$ of its steady value is $...\,s$.

Switch $S$ of the circuit shown in the figure is closed at $t = 0$. If $e$ denotes the induced $emf$ in $L$ and $i$ the current flowing through the circuit at time $t$,which of the following graphs is correct?

$A$ coil of inductance $1\,H$ and resistance $100\,\Omega$ is connected to a battery of $6\,V$. Determine approximately:
$(a)$ The time elapsed before the current acquires half of its steady-state value.
$(b)$ The energy stored in the magnetic field associated with the coil at an instant $15\,ms$ after the circuit is switched on. (Given $\ln 2 = 0.693$,$e^{-3/2} = 0.25$)

For the given circuit,the current $i$ through the battery when the key is closed and the steady state has been reached is .....$A$.

$A$ 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 $, s$)

Three identical resistors with resistance $R = 12\,\Omega$ and two identical inductors with self-inductance $L = 5\,mH$ are connected to an ideal battery with an emf of $12\,V$ as shown in the figure. The current through the battery long after the switch has been closed will be $......A$.