The current $i$ in a coil varies with time as shown in the figure. The variation of induced $emf$ with time would be

$A$ very long solenoid of radius $R$ is carrying current $I(t) = kt e^{-\alpha t}$ $(k > 0)$,as a function of time $(t \geq 0)$. Counter-clockwise current is taken to be positive. $A$ circular conducting coil of radius $2R$ is placed in the equatorial plane of the solenoid and is concentric with the solenoid. The induced current in the outer coil as a function of time is correctly depicted by:

$A$ dynamo is a device for converting:

$A$ short-circuited coil is placed in a time-varying magnetic field. Electrical power is dissipated due to the current induced in the coil. If the number of turns were to be quadrupled and the wire radius halved,the electrical power dissipated would be

$A$ small bar magnet of dipole moment $M$ is moving with speed $v$ along the $x$-direction towards a small closed circular conducting loop of radius $a$ with its centre $O$ at $x=0$ (see figure). Assume $x >> a$ and the coil has a resistance $R$. Which of the following statement$(s)$ is/are true?

The switch $S$ shown in the circuit is closed at $t=0$. The ratio of the current drawn from the battery by the circuit at $t=0$ and $t=\infty$ is: