After closing the key in the given circuit:
$(a)$ Bulb $(2)$ will glow and maintain its brightness.
$(b)$ Brightness of bulb $(1)$ will gradually decrease and at steady state it goes completely dark.

In the circuit shown in the figure,the switch $S$ is initially open and the capacitor is initially uncharged. $I_1, I_2$ and $I_3$ represent the current in the resistance $2\,\Omega, 8\,\Omega$ and $4\,\Omega$ respectively.

$A$ capacitor $C = 100 \, \mu F$ is connected to three resistors,each of resistance $1 \, k\Omega$,and a battery of $emf$ $9 \, V$. The switch $S$ has been closed for a long time to charge the capacitor. When switch $S$ is opened,the capacitor discharges with a time constant of ...... $ms$.

The charge on the capacitor of capacitance $C$ shown in the figure below will be

$A$ capacitor is discharging through a resistor $R$. Consider in time $t_{1}$,the energy stored in the capacitor reduces to half of its initial value and in time $t_{2}$,the charge stored reduces to one-eighth of its initial value. The ratio $t_{1} / t_{2}$ will be ................

$A$ circuit element is placed in a closed box. At time $t=0$,a constant current generator supplying a current of $1\, A$ is connected across the box. The potential difference across the box varies according to the graph shown in the figure. The element in the box is: