$A$ coil and a bulb are connected in series with a $DC$ source. $A$ soft iron core is then inserted into the coil. What happens to the intensity of the bulb?

$A$ 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 $t=\left(\frac{1}{K}\right) \ln \left(\frac{3}{2}\right)$.

The bob of a simple pendulum is replaced by a magnet. The oscillations are set along the length of the magnet. $A$ copper coil is added so that one pole of the magnet passes in and out of the coil. The coil is short-circuited. Then which one of the following happens?

$A$ rectangular loop is being pulled at a constant speed $v$,through a region of certain thickness $d$,in which a uniform magnetic field $B$ is set up. The graph between position $x$ of the right-hand edge of the loop and the induced emf $E$ will be

When a coil is placed in a time-dependent magnetic field, the power dissipated in it is $P$. The number of turns, area of the coil, and radius of the coil wire are $N, A$, and $r$ respectively. For a second coil, the number of turns, area, and radius are $2N, 2A$, and $3r$ respectively. When the first coil is replaced with the second coil, the power dissipated in it is $\alpha P$. The value of $\alpha$ is . . . . . . .

The current $i$ in an inductance coil varies with time $t$ according to the following graph. Which one of the following plots shows the variations of voltage $V$ in the coil?