The ratio of time constants during growth and decay of current in the circuit is

The figure shows a circuit that contains three resistors with resistance $R = 2.0 \, \Omega$, two inductors with inductance $L = 2.0 \, mH$, and an ideal battery with $emf$ $E = 9 \, V$. The current $i$ just after the switch $S$ is closed will be .... $A$.

An inductor of $2 \, H$ and a resistance of $10 \, \Omega$ are connected in series with a battery of $5 \, V$. The initial rate of change of current is ...... $A/s$.

In the figure below,the switches $S_1$ and $S_2$ are closed simultaneously at $t=0$ and a current starts to flow in the circuit. Both the batteries have the same magnitude of the electromotive force (emf) $V$ and the polarities are as indicated in the figure. Ignore mutual inductance between the inductors. The current $I$ in the middle wire reaches its maximum magnitude $I_{\max}$ at time $t=T$. Which of the following statements is (are) true?
$(A)$ $I_{\max}=\frac{V}{2R}$
$(B)$ $I_{\max}=\frac{V}{4R}$
$(C)$ $T=\frac{L}{R} \ln 2$
$(D)$ $T=\frac{2L}{R} \ln 2$

In the figure,a lamp $P$ is in series with an iron-core inductor $L$. When the switch $S$ is closed,the brightness of the lamp rises relatively slowly to its full brightness compared to the case without the inductor. This is due to:

Consider the $LR$ circuit shown in the figure. If the switch $S$ is closed at $t = 0$, then the amount of charge that passes through the battery between $t = 0$ and $t = \frac{L}{R}$ is