An inductance $L$ and a resistance $R$ are first connected to a battery. After some time,the battery is disconnected,but $L$ and $R$ remain connected in a closed circuit. Then the current reduces to $37\%$ of its initial value in

As shown in the figure,a battery of $emf \; \varepsilon$ is connected to an inductor $L$ and resistance $R$ in series. The switch $S$ is closed at $t=0$. The total charge that flows from the battery between $t=0$ and $t=t_{c}$ ($t_{c}$ is the time constant of the circuit) is

$A$ 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 $A \, s^{-1}$)

Two resistors of $10\, \Omega$ and $20\, \Omega$ and an ideal inductor of $10\, H$ are connected to a $2\, V$ battery as shown. The key $K$ is inserted at time $t = 0$. The initial $(t = 0)$ and final $(t \rightarrow \infty)$ currents through the battery are

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 $\ln 2 = 0.7$.

Find $V_A - V_B$ in steady state. (in $, V$)