In the figure shown,a circuit contains two identical resistors with resistance $R = 5\,\Omega$ and an inductance with $L = 2\, mH$. An ideal battery of $15\, V$ is connected in the circuit. What will be the current through the battery long after the switch $S$ is closed (in $, A$)?

In the circuit shown in the figure, what is the value of $I_1$ just after pressing the key $K$?

Find the current in the sliding rod $AB$ (resistance $= R$) for the arrangement shown in the figure. The magnetic field $\vec{B}$ is constant and directed out of the paper. The parallel wires have no resistance,and the velocity $v$ is constant. The switch $S$ is closed at time $t = 0$.

In an $LR$ circuit,the current increases to one-fourth of its maximum value in $4 \, sec$. What is the time constant of the circuit?

For the given circuit,the current through the battery of $6\,V$ just after closing the switch $S$ will be $.......A$.

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 ............