Two coils $P$ and $Q$ are placed co-axially and carry currents $I$ and $I'$ respectively.

$A$ 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 $\frac{V}{R}$

$A$ 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

An electron moves along the line $AB$,which lies in the same plane as a circular loop of conducting wires as shown in the diagram. What will be the direction of current induced,if any,in the loop?

The network shown in the figure is a 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 $V_A - V_B$ is......$V$.

In the circuit shown below,all the inductors (assumed ideal) and resistors are identical. The current through the resistance on the right is $I$ after the key $K$ has been switched $ON$ for a long time. The currents through the three resistors (in order,from left to right) immediately after the key is switched $OFF$ are