An ideal inductor of inductance L and a resistor of resistance R are connected in series to an ideal battery of emf E, as shown in figure. Three switches are also shown in the figure. For this arrangement, mark out the correct options (S).  (Consider all wires of Zero resistance )

 

After $S_1$ has been closed for a long time, $S_1$ is opened and $S_2$ is closed (keeping S3 opened ) at $t=0$ then the current through inductor for any time $t>0$ is zero

After $S_1$ has been closed for a long time, $S_1$ is opened and $S_2$ , $S_3$ are closed  at $t=0,$ then the current through battery as a function of time is zero

After  $S_1$  has been closed for a long time, $S_1$  is opened and  $S_2$  is closed (keeping  $S_3$  opened) at t=0, then the current through inductor as a function of time is $\frac{E}{R}\left[e^{-\frac{Rt}{L}}\right]$

If $S_1$ is closed at t= 0, keeping $S_2$ and $S_3$ open, then the magnetic energy stored in the inductor at $t=\infty$  is $\frac{L{E}^2}{2R^2}$