$A$ coil of inductance $5\,H$ is joined to a cell of $emf$ $6\,V$ through a resistance $10\,\Omega$ at time $t = 0$. The $emf$ across the coil at time $t = \ln \sqrt{2}\,s$ is:....$V$

$A$ 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 $t=0$?

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

In the given circuit,the sliding contact is pulled outwards such that the electric current in the circuit changes at the rate of $8 \text{ A/s}$. At an instant when $R = 12 \Omega$,the value of the current in the circuit will be . . . . . . $A$.

$A$ coil of inductance $0.20 \, H$ is connected in series with a switch and a cell of $emf$ $1.6 \, V$. The total resistance of the circuit is $4.0 \, \Omega$. What is the initial rate of growth of the current when the switch is closed? (in $A \, s^{-1}$)

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 $\ln 2 = 0.7$.