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?

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

An inductor coil stores $64 \, J$ of magnetic field energy and dissipates energy at the rate of $640 \, W$ when a current of $8 \, A$ is passed through it. If this coil is joined across an ideal battery,find the time constant of the circuit in seconds.

$A$ 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?

An inductor with an iron core is connected in series with a resistor $R$ across an ideal $DC$ source. The circuit is in a steady state. If the iron core is removed, what happens to the current flowing through the inductor immediately after the removal of the core?

The figure shows $2$ identical bulbs $B_1$ and $B_2$ and a spinning wheel game divided into $6$ equal parts of different colors as shown. At $t = 0$,switch $S$ is closed and simultaneously the wheel is set to rotate about its center $O$ in a clockwise direction with an initial angular velocity of $2.5\pi \text{ rad/s}$. Find the color on which a student should place a bet if the color appearing on the pointer at the instant when both bulbs give the same illumination is selected for winning. Given: angular retardation of the wheel due to friction and other effects is $2\text{ rad/s}^2$ and take $\ln 2 = 0.7$.