$A$ 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?

In a decaying $L-R$ circuit,the time after which energy stored in the inductor reduces to one-fourth of its initial value is

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 $\ln 2 = 0.7$.

The resistance in the following circuit is increased at a particular instant. At this instant,the value of resistance is $10\,\Omega$. The current in the circuit will be

An inductor coil stores $U$ energy when $I$ current is passed through it and dissipates energy at the rate of $P$. The time constant of the circuit,when this coil is connected across a battery of zero internal resistance,is

In the given circuit,the switch is in position $a$. For what value of $R$ will the circuit have a time constant of $10\,\mu s$ in $K\Omega$?