Two $L-R$ circuits are shown in the figure. Based on the given current-time graph,select the correct relation between the inductances $L_1$ and $L_2$.

An inductor $(L = 100 \ mH)$,a resistor $(R = 100 \ \Omega)$ and a battery $(E = 100 \ V)$ are initially connected in series as shown in the figure. After a long time,the battery is disconnected by short-circuiting the points $A$ and $B$. The current in the circuit $1 \ ms$ after the short circuit 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 $......A$.

An inductor of $10\, \text{mH}$ is connected to a $20\, \text{V}$ battery through a resistor of $10\, \text{k}\Omega$ and a switch. After a long time,when maximum current is set up in the circuit,the current is switched off. The current in the circuit after $1\, \mu\text{s}$ is $\frac{x}{100}\, \text{mA}$. Then $x$ is equal to ...... . (Take $e^{-1} = 0.37$)

$A$ solenoid has an inductance of $60 \, H$ and a resistance of $30 \, \Omega$. If it is connected to a $100 \, V$ battery,how long will it take for the current to reach $\frac{e-1}{e} \approx 63.2\%$ of its final value?

As shown in the figure,a battery of $emf \; \varepsilon$ is connected to an inductor $L$ and resistance $R$ in series. The switch $S$ is closed at $t=0$. The total charge that flows from the battery between $t=0$ and $t=t_{c}$ ($t_{c}$ is the time constant of the circuit) is