In an $L-R$ circuit connected to a battery of constant $e.m.f.$ $E$,switch $S$ is closed at time $t = 0$. If $e$ denotes the magnitude of induced $e.m.f.$ across the inductor and $i$ the current in the circuit at any time $t$,then which of the following graphs shows the variation of $e$ with $i$?

$A$ conducting square loop of side $L$,mass $M$ and resistance $R$ is moving in the $XY$ plane with its edges parallel to the $X$ and $Y$ axes. The region $y \geq 0$ has a uniform magnetic field,$\vec{B}=B_0 \hat{k}$. The magnetic field is zero everywhere else. At time $t=0$,the loop starts to enter the magnetic field with an initial velocity $v_0 \hat{\imath} \text{ m/s}$,as shown in the figure. Considering the quantity $K=\frac{B_0^2 L^2}{RM}$ in appropriate units,ignoring self-inductance of the loop and gravity,which of the following statements is/are correct:
$(A)$ If $v_0=1.5 KL$,the loop will stop before it enters completely inside the region of magnetic field.
$(B)$ When the complete loop is inside the region of magnetic field,the net force acting on the loop is zero.
$(C)$ If $v_0=\frac{KL}{10}$,the loop comes to rest at $t=\left(\frac{1}{K}\right) \ln \left(\frac{5}{2}\right)$.
$(D)$ If $v_0=3 KL$,the complete loop enters inside the region of magnetic field at time $t=\left(\frac{1}{K}\right) \ln \left(\frac{3}{2}\right)$.

Two circular coils $P$ and $Q$ are fixed coaxially and carry currents $I_1$ and $I_2$ respectively.

$A$ 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?

The figure shows a circuit that contains three identical resistors with resistance $R = 9.0 \,\Omega$ each,two identical inductors with inductance $L = 2.0 \,mH$ each,a capacitor $C$,and an ideal battery with $emf \,\varepsilon = 18 \,V$. The current $i$ through the battery just after the switch is closed is:

As shown in the figure,$P$ and $Q$ are two coaxial conducting loops separated by some distance. When the switch $S$ is closed,a clockwise current $I_P$ flows in $P$ (as seen by $E$) and an induced current $I_{Q_1}$ flows in $Q$. The switch remains closed for a long time. When $S$ is opened,a current $I_{Q_2}$ flows in $Q$. Then the directions of $I_{Q_1}$ and $I_{Q_2}$ (as seen by $E$) are: