The current $i$ in an induction coil varies with time $t$ according to the graph shown. Which of the following graphs shows the induced $emf$ $(e)$ in the coil with time?

$A$ magnet $NS$ is suspended from a spring and while it oscillates,the magnet moves in and out of the coil $C$. The coil is connected to a galvanometer $G$. Then as the magnet oscillates,

The current $I$ in an $A.C.$ circuit inductance coil varies with time according to the graph given below. Which one of the following graphs gives the variation of voltage with time?

$A$ conducting loop in the shape of a right-angled isosceles triangle of height $10 \ cm$ is kept such that the $90^{\circ}$ vertex is very close to an infinitely long conducting wire (see the figure). The wire is electrically insulated from the loop. The hypotenuse of the triangle is parallel to the wire. The current in the triangular loop is in counterclockwise direction and increases at a constant rate of $10 \ As^{-1}$. Which of the following statement$(s)$ is(are) true?
$(A)$ The magnitude of induced emf in the wire is $\left(\frac{\mu_0}{\pi}\right) \ V$
$(B)$ If the loop is rotated at a constant angular speed about the wire,an additional emf of $\left(\frac{\mu_0}{\pi}\right) \ V$ is induced in the wire
$(C)$ The induced current in the wire is in the opposite direction to the current along the hypotenuse
$(D)$ There is a repulsive force between the wire and the loop

$A$ metallic ring of mass $m$ and radius $l$ (ring being horizontal) is falling under gravity in a region having a magnetic field. If $z$ is the vertical direction,the $z$-component of the magnetic field is $B_z = B_0(1 + \lambda z)$. If $R$ is the resistance of the ring and the ring falls with a velocity $v$,find the energy lost in the resistance per unit time. If the ring has reached a constant velocity,use the conservation of energy to determine $v$ in terms of $m, B_0, l, \lambda, R$ and acceleration due to gravity $g$.

Two inductor coils of self-inductance $3\,H$ and $6\,H$ respectively are connected with a resistance $10\,\Omega$ and a battery $10\,V$ as shown in the figure. The ratio of the total energy stored at steady state in the inductors to that of the heat developed in the resistance in $10\,s$ at the steady state is (neglect mutual inductance between $L_1$ and $L_2$):-