The circuit shown consists of a switch $S$,a battery $B$ of emf $E$,a resistance $R$,and an inductor $L$. What is the current in the circuit at the instant the switch $S$ is closed?

Given $L_1 = 1\, mH, R_1 = 1\,\Omega, L_2 = 2\,mH, R_2 = 2\,\Omega$. Neglecting mutual inductance,find the time constant (in $ms$) for the circuit shown.

In the following figure,what is the final value of current in the $10 \, \Omega$ resistor when the plug of key $K$ is inserted?

In the given figure,an inductor of $L = 4 \, H$ and a resistor of $R = 25 \, \Omega$ are connected in series with a battery of emf $E$ volt. $\frac{E^a}{2b} \, J/s$ represents the maximum rate at which energy is stored in the magnetic field of the inductor. The numerical value of $\frac{b}{a}$ is ............

Three identical resistors with resistance $R = 12\,\Omega$ and two identical inductors with self-inductance $L = 5\,mH$ are connected to an ideal battery with an emf of $12\,V$ as shown in the figure. The current through the battery long after the switch has been closed will be $......A$.

When the switch $S$ is closed at time $t = 0$,what will be the nature of the graphs for the induced $emf$ $e$ across the inductor $L$ and the current $i$ in the circuit?