$A$ coil of inductance $1\, H$ and resistance $10\, \Omega$ is connected to a battery of $emf$ $50\, V$ and negligible internal resistance at time $t = 0.$ The ratio of the rate at which magnetic energy is stored in the coil to the rate at which energy is supplied by the battery at $t = 0.1\, s$ is:

For the given circuit,the current $i$ through the battery when the key is closed and the steady state has been reached is .....$A$.

The time taken for the magnetic energy to reach $25\%$ of its maximum value,when a solenoid of resistance $R$ and inductance $L$ is connected to a battery,is:

In the circuit shown in the figure, what is the value of $I_1$ just after pressing the key $K$?

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 $\ln 2 = 0.7$.

For an $L-R$ circuit,the time constant is equal to