When a $DC$ voltage is applied at the two ends of a circuit kept in a closed box, it is observed that the current gradually increases from zero to a certain value and then remains constant. What do you think the circuit contains?

If $R$ and $L$ denote resistance and inductance respectively,which of the following has the dimension of time?

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 $\ln 2 = 0.7$.

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

In an $LR$ circuit,the time constant is the time in which the current grows from zero to the value (where ${I_0}$ is the steady-state current):

$A$ constant voltage of $25 \, V$ is applied to a series $L-R$ circuit at $t=0$ by closing a switch. What is the potential difference across the resistor and the inductor at time $t=0$?