$A$ bar magnet falls from rest under gravity through the centre of a horizontal ring of conducting wire as shown in figure. Which of the following graph best represents the speed $(v)$ vs. time $(t)$ graph of the bar magnet?

Which of the following is constructed on the principle of electromagnetic induction?

$A$ conducting wire frame is placed in a magnetic field which is directed into the paper. The magnetic field is increasing at a constant rate. The directions of induced currents in wires $AB$ and $CD$ are

$A$ source of constant voltage $V$ is connected to a resistance $R$ and two ideal inductors $L_1$ and $L_2$ through a switch $S$ as shown. There is no mutual inductance between the two inductors. The switch $S$ is initially open. At $t=0$,the switch is closed and current begins to flow. Which of the following options is/are correct?
$[A]$ After a long time,the current through $L_1$ will be $\frac{V}{R} \frac{L_2}{L_1+L_2}$
$[B]$ After a long time,the current through $L_2$ will be $\frac{V}{R} \frac{L_1}{L_1+L_2}$
$[C]$ The ratio of the currents through $L_1$ and $L_2$ is fixed at all times $(t>0)$
$[D]$ At $t=0$,the current through the resistance $R$ is $\frac{V}{R}$

The network shown in the figure is part of a complete circuit. If at a certain instant the current $i$ is $5 \, A$ and is decreasing at the rate of $10^3 \, A/s$, then $V_B - V_A$ is: (in $ \, V$)

$A$ square coil $ABCD$ lies in the $x-y$ plane with its centre at the origin. $A$ long straight wire passing through the origin carries a current $i = 2t$ in the negative $z$-direction. The induced current in the coil is