Two identical coaxial circular loops carry a current $i$ each,circulating in the same direction. If the loops approach each other,then:

The figure shows a planar conductor located in a magnetic field directed inward,normal to the plane of the figure. The magnetic field starts diminishing. Then the induced current:

$A$ 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 switch $S$ of the circuit shown in the figure is closed at $t = 0$. If $e$ denotes the induced emf in the inductor $L$ and $i$ denotes the current flowing through the circuit at time $t$,which of the following graphs correctly represents the variation of $e$ with time $t$?

An $AC$ generator converts

Two different coils have inductances $L_1 = 4 \ mH$ and $L_2 = 2 \ mH$. At a certain instant,the current in the two coils is increasing at the same constant rate,and the power supplied to the first coil is four times that of the second coil. If $e$,$I$,and $U$ indicate the potential difference,current,and energy stored in the inductance respectively,then which of the following is correct?