The current in the $2\, \Omega$ resistance shown in the figure is:
$(a)$ Just after the closing of the key.
$(b)$ $A$ long time after the closing of the key.

In the circuit shown,the switch $S_1$ is closed at time $t = 0$ and the switch $S_2$ is kept open. At some later time $t_0$,the switch $S_1$ is opened and $S_2$ is closed. The behavior of the current $I$ as a function of time $t$ is given by:

An inductor coil stores $64 \, J$ of magnetic field energy and dissipates energy at the rate of $640 \, W$ when a current of $8 \, A$ is passed through it. If this coil is joined across an ideal battery,find the time constant of the circuit in seconds.

In which of the following circuits is the current maximum just after the switch $S$ is closed?

In the circuit shown,$X$ is joined to $Y$ for a long time,and then $X$ is joined to $Z$. The total heat produced in $R_2$ is

$A$ 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 $\ln 2 = 0.693$,$e^{-3/2} = 0.25$)