Given $R_1 = 1\,\Omega$,$C_1 = 2\,\mu F$ and $R_2 = 2\,\Omega$,$C_2 = 4\,\mu F$. The time constants (in $\mu s$) for the circuits $I, II, III$ are respectively:

After the switch shown in Figure $A$ is closed,there is a current $i$ through the resistance $R$. Figure $B$ indicates current variation curves $a, b, c,$ and $d$ for four sets of values of $R$ and capacitance $C$:
$(i)$ $R_0$ and $C_0$
$(ii)$ $2R_0$ and $C_0$
$(iii)$ $R_0$ and $2C_0$
$(iv)$ $2R_0$ and $2C_0$
Which set goes with which curve?

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

Three identical capacitors are given a charge $Q$ each and they are then allowed to discharge through resistances $R_1, R_2,$ and $R_3$. Their charges,as a function of time,are shown in the graph below. The smallest of the three resistances is

Find the time constant for the given circuit.

$A$ 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 ................