The current through a coil varies according to the following graph. Plot the graph for induced $emf$ $(e)$ versus time $(t)$ for the coil.

The figure shown has two coils of wires placed in close proximity. The current in primary coil $P$ is made to vary with time as shown in the graph. Which of the following graphs best represents the variation of the emf induced in the secondary coil $S$?

$A$ flat coil of $500$ turns,each of area $50 \,cm^2$,rotates in a uniform magnetic field of $0.14 \,Wb/m^2$ about an axis normal to the field at an angular speed of $150 \,rad/s$. The coil has a resistance of $5 \,\Omega$. The induced $e.m.f.$ is applied to an external resistance of $10 \,\Omega$. The peak current through the resistance is .......... $A$. (in $.5$)

$A$ rectangular loop of sides $12 \text{ cm}$ and $5 \text{ cm}$,with its sides parallel to the $x$-axis and $y$-axis respectively,moves with a velocity of $5 \text{ cm/s}$ in the positive $x$-axis direction in a space containing a variable magnetic field in the positive $z$-direction. The field has a gradient of $10^{-3} \text{ T/cm}$ along the negative $x$-direction and it is decreasing with time at the rate of $10^{-5} \text{ T/s}$. If the resistance of the loop is $6 \text{ m}\Omega$,the power dissipated by the loop as heat is . . . . . . $\times 10^{-9} \text{ W}$.

The current $i$ in a coil varies with time as shown in the figure. The variation of induced $emf$ with time would be:

$A$ 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?