When a battery is connected across a series combination of self inductance $L$ and resistance $R$,the variation in the current $i$ with time $t$ is best represented by

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 circuit shown consists of a switch $S$,a battery $B$ of emf $E$,a resistance $R$,and an inductor $L$. What is the current in the circuit at the instant the switch $S$ is closed?

The time constant of an $LR$ circuit is $10 \, s$. When a resistance of $10 \, \Omega$ is connected in series with the existing circuit,the time constant becomes $2 \, s$. The self-inductance of the circuit is ..... $H$.

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

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