In the circuit diagram shown,$E = 5 \, V, r = 1 \, \Omega, R_2 = 4 \, \Omega, R_1 = R_3 = 1 \, \Omega$ and $C = 3 \, \mu F$. The magnitude of the charge on each capacitor plate is......$\mu C$.

$A$ capacitor of capacity $C$ is charged to a steady potential difference $V$ and connected in series with an open key and a pure resistor $R$. At time $t = 0$,the key is closed. If $I$ is the current at time $t$,a plot of $\log I$ against $t$ is as shown in $(1)$ in the graph. Later,one of the parameters,i.e.,$V, R,$ or $C$,is changed while keeping the other two constant,and the graph $(2)$ is recorded. Then:

In the circuit shown,when the key $K$ is pressed at time $t = 0$,which of the following statements about current $I$ in the resistor $AB$ is true?

The charge stored by the capacitor $C$ in the given circuit in the steady state is . . . . . . $\mu C$.

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.

How much time does it take for the current to decay to half of its initial value in the following charging circuit?